NORTHWESTERN UNIVERSITY

An Atom is Known by the Company it Keeps: Content, Representation and Pedagogy Within the Epistemic Revolution of the Complexity Sciences

A DISSERTATION

SUBMITTED TO THE GRADUATE SCHOOL IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

for the degree

DOCTOR OF PHILOSOPHY

Field of the Learning Sciences

By

Paulo Blikstein

Evanston, Illinois

June 2009

UMI Number: 3355751

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2

ABSTRACT

An atom is known by the company it keeps: Content, representation and

pedagogy within the epistemic revolution of the complexity sciences

Paulo Blikstein

The goal of this dissertation is to explore relations between content, representation, and peda-

gogy, so as to understand the impact of the nascent field of complexity sciences on science, tech-

nology, engineering and mathematics (STEM) learning. Wilensky & Papert coined the term

“structurations” to express the relationship between knowledge and its representational infra-

structure. A change from one representational infrastructure to another they call a “restructura-

tion.” The complexity sciences have introduced a novel and powerful structuration: agent-

based modeling. In contradistinction to traditional mathematical modeling, which relies on

equational descriptions of macroscopic properties of systems, agent-based modeling focuses on

a few archetypical micro-behaviors of “agents” to explain emergent macro-behaviors of the agent

collective.

Specifically, this dissertation is about a series of studies of undergraduate students’ learning of

materials science, in which two structurations are compared (equational and agent-based), con-

sisting of both design research and empirical evaluation. I have designed MaterialSim, a con-

structionist suite of computer models, supporting materials and learning activities designed

within the approach of agent-based modeling, and over four years conducted an empirical inves-

3

tigation of an undergraduate materials science course. The dissertation is comprised of three

studies:

Study 1 – Diagnosis. I investigate current representational and pedagogical practices in engi-

neering classrooms.

Study 2 – Laboratory Studies. I investigate the cognition of students engaging in scientific in-

quiry through programming their own scientific models.

Study 3 – Classroom implementation. I investigate the characteristics, advantages, and trajec-

tories of scientific content knowledge that is articulated in epistemic forms and representational

infrastructures unique to complexity sciences, as well as the feasibility of the integration of con-

structionist, agent-based learning environments in engineering classrooms.

Data sources include classroom observations, interviews, videotaped sessions of model-building,

questionnaires, analysis of computer-generated logfiles, and quantitative and qualitative analysis

of artifacts.

Results shows that (1) current representational and pedagogical practices in engineering class-

rooms were not up to the challenge of the complex content being taught, (2) by building their

own scientific models, students developed a deeper understanding of core scientific concepts,

and learned how to better identify unifying principles and behaviors in materials science, and (3)

programming computer models was feasible within a regular engineering classroom.

 

4

ACKNOWLEDGEMENTS For my advisor, Uri Wilensky, for his trust, inspiration, guidance, and

especially his unforgiving love for the power of powerful ideas; and my

committee members, Louis Gomez, Bruce Sherin, and Dor Abraham-

son, for their invaluable ideas and infinite patience.

For Simone, for her endless love, for dreaming the same dreams, and for

making life so incredibly happy for all these years.

For my father Izidoro, for the poems, and the hard-to-follow example;

my mother Ester, who taught me to look deeply into each person’s

mind, my brother Daniel, for taking care of me all along the way, and my

sister Flávia, for her natural talent to illuminate people and places; my

grandfather Saulo, for his silent words of encouragement and care, and

for keep asking me about when I was going to finish, for Julia, for re-

minding us of the tastes of Brazil.

For my friends, Arnan Sipitakiat, for his monumental sense of friend-

ship, Dor Abrahamson, for teaching me what excellence (and cognac,

and waterfalls) are all about, Spiro Maroulis, for enthusiastically saving

my life so many times, and Michelle Wilkerson-Jerde, Forrest Stonedahl,

Josh Unterman, Ben Shapiro, Matthew Berland, Bill Rand, Daniel

Kornhauser, for the fun, the papers, the hallway conversations, and be-

ing patient during my terrible rehearsals; and the amazing NetLogo de-

velopment team, Seth Tisue, Esther Verreau, and Craig Brozefsky, for

implementing so many of my useless ideas.

For Seymour Papert, for the brief but absolutely precise words of guid-

ance, encouragement, and inspiration along these years; Edith Acker-

mann, for her always brilliant and inspiring mentoring, and Jacqueline

5

Karaaslanian, Claudia Urrea, and my Media Lab friends, for so many

years of help and friendship.

For Prof. Dr. André Paulo Tschiptchin, for all his support, ideas, and in-

spiration since my undergraduate years and the “Monte Carlo” project,

my first encounter with the joys of agent-based modeling, and Prof. Dr.

Marcelo Zuffo, for teaching me about how action and research can coex-

ist.

For all the students who patiently participated in the studies and pre-

tended not to hate agent-based modeling, and for Jaíne and all the child-

ren from Brazil who kept reminding me, with their incredible ideas and

unforgiving persistence, what this is all about.

And last but not least, for Moriz Blikstein, who gave me my first copy of

Mindstorms when I was 15 years old, but couldn’t be here to see that I

did read it. But he knows.

6

THE SUITCASE IS FORGIVEN Many years ago, I used to carry everywhere a dirty suitcase full of loose

wires, broken bulbs and leaked batteries, with which I built flashlights.

Most of them never worked very well, most were broken, some were just

aborted ideas that I kept for repurposing. But incomprehensively that

suitcase was my whole world.

One day my parents threw that dirty old suitcase away. In my eleven-

year old uncontrollable rage, I destroyed my father’s bookcase, I swore

revenge, and for years I kept writing essays about the suitcase and its

tragic disappearance.

Today I build suitcases for other children. Had I been allowed to keep

mine, I would certainly have never missed it so desperately as to under-

stand what it was all about. And what it was not about.

Parents know why they do things. Even if they never tell you.

Ester, Izidoro, the suitcase is forgiven.

 

7

For Davit, in memoriam.

For Davi, in hope.

8

TABLE OF CONTENTS Acknowledgements .................................................................................................................................. 4 

The suitcase is forgiven ........................................................................................................................... 6 

List of Figures ......................................................................................................................................... 11 

List of Tables .......................................................................................................................................... 18 

I  Introduction ............................................................................. 20 

II  Literature review ...................................................................... 33 II.1.  Summary .................................................................................................................................... 34 

II.2.  Engineering Education ............................................................................................................ 35 

II.2.1.  A crisis in engineering education ...................................................................................................... 35 II.2.2.  Design: the comeback of a forgotten skill in engineering education ........................................ 39 II.2.3.  Open questions ..................................................................................................................................... 40 II.2.4.  A brief history of the uses of modeling, simulation, and other digital tools in materials science education ..................................................................................................................................................... 44 

II.3.  Complexity sciences, computational science, and agent-based modeling ..................... 58 

II.3.1.  A brief history of agent-based modeling .......................................................................................... 58 II.3.2.  Complex systems in materials science ............................................................................................. 63 

II.4.  Agent-based modeling in education ..................................................................................... 67 

II.4.1.  Introduction ........................................................................................................................................... 67 II.4.2.  A framework and taxonomy to analyze educational agent-based software ............................. 71 II.4.3.  Implications of ABM for materials science education .................................................................. 92 II.4.4.  Restructurations .................................................................................................................................... 94 

II.5.  Summary of the chapter .......................................................................................................... 97 

III  Representation comparison ..................................................... 99 III.1.  Summary .................................................................................................................................. 100 

III.2.  Grain growth ............................................................................................................................ 100 

III.2.1.  The phenomenon .............................................................................................................................. 100 III.2.2.  Equational representation of grain growth: a many-to-one approach ................................... 102 III.2.3.  Agent-based representation of grain growth: a one-to-many approach ................................ 105 

III.3.  Diffusion ................................................................................................................................... 108 

III.3.1.  The phenomenon .............................................................................................................................. 108 III.3.2.  Equational representation of diffusion ......................................................................................... 109 III.3.3.  Agent-based representation of diffusion ...................................................................................... 111 III.3.4.  Discussion ........................................................................................................................................... 113 

IV  Methods .................................................................................. 117 IV.1.  Summary .................................................................................................................................. 118 

IV.2.  Introduction............................................................................................................................. 118 

IV.3.  Study 1: Classroom observations and analysis of class materials .................................. 123 

IV.3.1.  Research questions and data sources ............................................................................................ 123 IV.3.2.  First question: most frequent knowledge representations employed during instruction . 124 

9

IV.3.3.  Second question: learning outcomes of equational-based representations and teaching techniques ............................................................................................................................................................... 128 

IV.4.  Study 2: A three-year lab study with volunteer undergraduate students building models ................................................................................................................................................... 132 

IV.4.1.  Research questions and data sources ............................................................................................ 132 IV.4.2.  Description of the study ................................................................................................................... 133 IV.4.3.  Analysis categories and data examples .......................................................................................... 140 

IV.5.  Study 3: Large study with an entire materials science class (2007) .............................. 147 

IV.5.1.  Research questions and data sources ............................................................................................ 147 IV.5.2.  Description of the study ................................................................................................................... 149 IV.5.3.  Summary of analysis procedures .................................................................................................... 155 IV.5.4.  Data analysis for the entire class ..................................................................................................... 156 

V  Software design ...................................................................... 178 V.1.  Summary .................................................................................................................................. 179 

V.2.  NetLogo ................................................................................................................................... 179 

V.3.  MaterialSim ............................................................................................................................. 181 

V.3.1.  A very simple model (solidification) ............................................................................................. 184 V.3.2.  A feature complete model (grain growth) ................................................................................... 186 

V.4.  Summary of the chapter ........................................................................................................ 190 

VI  Study One ............................................................................... 192 VI.1.  Summary of the chapter ........................................................................................................ 193 

VI.2.  Representational practices in a materials science classroom ......................................... 193 

VI.2.1.  A day in an engineering classroom ................................................................................................. 193 VI.2.2.  What kind of work are students supposed to do? ....................................................................... 194 VI.2.3.  Teaching artifacts............................................................................................................................... 197 VI.2.4.  A qualitative dive into the modeling and representation in the classroom ........................... 202 

VI.3.  interview explanations ........................................................................................................... 211 

VI.4.  Final remarks ........................................................................................................................... 218 

VII Study Two ............................................................................... 221 VII.1.  Summary .................................................................................................................................. 222 

VII.2.  Interaction with pre-built models ........................................................................................ 222 

VII.2.1.  Overview and explanation of the phenomenon .......................................................................... 222 VII.2.2.  Description of the activities ............................................................................................................. 224 

VII.3.  building their own models .................................................................................................... 234 

VII.3.1.  Betty’s model ...................................................................................................................................... 235 VII.3.2.  Bob’s model: grain growth with heterogeneous precipitates ................................................... 238 VII.3.3.  Anand’s model: interfacial energy .................................................................................................. 240 VII.3.4.  Jim’s model: polymer chains ........................................................................................................... 242 VII.3.5.  Peter’s model: diffusion vs. interface controlled processes & solidification ......................... 244 

VII.4.  Final remarks ........................................................................................................................... 248 

VIII  Study Three ........................................................................ 252 VIII.1. Summary .................................................................................................................................. 253 

VIII.2. Brief description of the study................................................................................................ 253 

VIII.3. Is modeling viable? Assessing the activity .......................................................................... 255 

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VIII.3.1.  Familiarity with computers.............................................................................................................. 255 VIII.3.2.  Time on task ....................................................................................................................................... 257 VIII.3.3.  Students’ feedback ............................................................................................................................. 261 

VIII.4. Grading the models ................................................................................................................ 266 

VIII.5. Logfile analysis ........................................................................................................................ 275 

VIII.5.1.  Initial data processing and validation ............................................................................................ 276 VIII.5.2.  Coding strategies ............................................................................................................................... 279 

VIII.6. Motivation plots ...................................................................................................................... 292 

VIII.7. Diving into student’s cognition: case studies .................................................................... 295 

VIII.7.1.  Scene one: Benedict’s pre-interview ............................................................................................. 295 VIII.7.2.  Scene two: Benedict’s model building .......................................................................................... 304 VIII.7.3.  Scene three: one year later ............................................................................................................... 314 VIII.7.4.  Fisher .................................................................................................................................................... 323 VIII.7.5.  Chaps .................................................................................................................................................... 327 

VIII.8. Summary .................................................................................................................................. 330 

IX  Discussion .............................................................................. 333 IX.1.  Summary .................................................................................................................................. 334 

IX.2.  Summary and findings ........................................................................................................... 335 

IX.2.1.  Study 1.................................................................................................................................................. 335 IX.2.2.  Study 2.................................................................................................................................................. 338 IX.2.3.  Study 3.................................................................................................................................................. 342 

IX.3.  Conclusion ............................................................................................................................... 358 

X  References .............................................................................. 364 

 

11

LIST OF FIGURES Figure II-1 Some of the many types of veins or ore channels in Agricola’s taxonomy................... 27 

Figure II-2 The content, representation, pedagogy triangle ............................................................... 30 

Figure III-1 A model-based activity for investigating Electron-atom interaction in MATTER

(left), and diffusion simulation, in DoITPoMS (right) ....................................................................... 47 

Figure III-2 Movie from a solidification experiment (left), and an animation of phase

transformation (right), from Visualizations in Materials Science ..................................................... 47 

Figure III-3 McManon’s “Multimedia Tutorials for an Introductory Course on the Science of

Engineering Materials” .............................................................................................................................. 48 

Figure III-4 A screenshot from Ohio State University’s “Gas Laws” online tutorial ..................... 49 

Figure III-5 A screenshot from University of Kiel’s tutorial on defects in crystals ......................... 50 

Figure III-6 Screenshots from the accompanying online materials for the “Chemistry - The

Science in Context” textbook ................................................................................................................... 51 

Figure III-7 Screenshot of the “Manufacturing Advisory Service” applet ........................................ 54 

Figure III-8 Crystal Viewer screen, show an atomic unit cell and a diagonal plane ....................... 55 

Figure III-9 The “Animated phase diagram tutor” ............................................................................... 56 

Figure III-10 The Diffusion Java Applets (top) and a of one of the etomica models (bottom) .. 57 

Figure III-11 A Reaction Kinetics model enabling students to change several variables .............. 77 

Figure III-12 A scripted model-based activity for investigating Brownian Motion ....................... 79 

Figure III-13 Screenshot of a model-based activity ............................................................................. 80 

Figure III-14 Dice Stalagmite model: students observe the emergence of a normal distribution 82 

Figure III-15 The Ohm’s law model, in which students can change sliders and observe the

resulting current in the conductor ........................................................................................................... 83 

Figure III-16 One of Beagle’s model enabling users to interact and change some parameters ... 85 

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Figure III-17 Screenshots of the original EACH models .................................................................... 86 

Figure III-18 In VBot, students create their own circuits and see their friend’s circuits .............. 88 

Figure IV-1 Metallic sample before and after grain growth, during 20 hours at 900ºC (Blikstein

& Tschiptschin, 1999) ............................................................................................................................. 102 

Figure IV-2 Initial and final energy calculations. Black and white arrows denote different or equal

neighbors .................................................................................................................................................... 107 

Figure IV-3 The agent-based diffusion algorithm .............................................................................. 111 

Figure IV-4 Atoms surround a vacancy, constantly vibrating, until one manages to have enough

energy to make its way to the vacancy .................................................................................................. 112 

Figure IV-5 NetLogo’s diffusion model and a plot of 5,000 time steps showing its fit to Fick’s

laws .............................................................................................................................................................. 113 

Figure IV-6 A comparison of the four phenomena: grain growth, diffusion, solidification, and

recrystallization ......................................................................................................................................... 114 

Figure V-1 Representation analysis ....................................................................................................... 128 

Figure V-2 Students had to indicate which grains would grow or shrink in the picture .............. 130 

Figure V-3 Experimental setup (2004) ................................................................................................. 134 

Figure V-4 Paper printouts used in the grain growth model explanation ...................................... 134 

Figure V-5 The interface of MaterialSim’s grain growth model ...................................................... 135 

Figure V-6 The initial setup of the model with two grains ................................................................ 135 

Figure V-7 The initial setup with five grains ........................................................................................ 136 

Figure V-8 Plot generated by a student, showing his model data and theoretical data ............... 136 

Figure V-9 The interface (left) and procedures (right) of NetLogo’s Solid Diffusion model ... 139 

Figure V-10 The evolution of a curved grain boundary .................................................................... 141 

Figure V-11 Liz’ structure with five grains, zoomed out (left) and zoomed in (right) ................ 142 

13

Figure V-12 Betty’s sketches about angles, sine and arcsine. ............................................................ 144 

Figure V-13 Agent-based (left) and aggregate (right) sample models of the same phenomena,

used in the NetLogo tuturial ................................................................................................................... 148 

Figure V-14 Screenshot of the wiki page for scheduling help, with names obscured for

anonymity. .................................................................................................................................................. 151 

Figure V-15 Examples of students’ work during the post interview ................................................ 152 

Figure V-16 Experimental setup for the tutorial and the model-building sessions. One camera

was mounted exactly on top of the drawing area, and the other is pointing to the student. ....... 155 

Figure V-17 An example of the data visualization tools to examine the model coding ............... 160 

Figure V-18 The histogram for model length based on all of NetLogo’s models library ............ 161 

Figure V-19 Word tree (left) and tagcloud (right) visualizations of MaterialSim’s grain growth

model ........................................................................................................................................................... 162 

Figure V-20 Barton’s model, with 132 terms (53 unique) ................................................................ 163 

Figure V-21 Lin’s model, with 1032 terms (210 unique) ................................................................. 163 

Figure V-22 A screenshot of the XML tool used for the trancriptions ........................................... 164 

Figure V-23 One of the forms generated from the data for easy coding, alongside with one of its

filters dialog box. ....................................................................................................................................... 165 

Figure V-24 Examples of coding of students’ verbal utterances (yellow and blue boxes refer to

two different students) ............................................................................................................................ 167 

Figure V-25 A screenshot of the image manipulation software showing some of the thousands of

frames captured ......................................................................................................................................... 168 

Figure V-26 Two example of size of the code versus time plot, for two students over about a

week. ............................................................................................................................................................ 172 

Figure V-27 A summary table with consolidades logfile data. Note that the query box allows the

user to filter and sort events for analysis. .............................................................................................. 173 

Figure V-28 Tables and data relationship in the database ................................................................ 174 

14

Figure V-29 Screenshot of the survey data table ................................................................................. 175 

Figure V-30 Two examples of students’ motivation plots ................................................................. 176 

Figure VI-1 The interface (left) and procedures (right) of a NetLogo model (solid diffusion)180 

Figure VI-2 A screenshot of the Solidification model ........................................................................ 186 

Figure VI-3 The interface of MaterialSim’s grain growth model ..................................................... 187 

Figure VI-4 The interface of MaterialSim’s grain growth model – the normal setup (left), and a

structure created by a student, using the mouse to draw microstructures ..................................... 188 

Figure VI-5 Sequence of screenshots from a student’s experiment ................................................ 188 

Figure VI-6 Plot generated by a student, showing his model data and theoretical data .............. 189 

Figure VII-1 Teaching artifacts per type, with the grey bars indicating the average .................... 198 

Figure VII-2 Teaching artifacts per date ............................................................................................... 199 

Figure VII-3 Plot showing the time spent per equation .................................................................... 200 

Figure VII-4 Histogram of the number of minutes spent per equation .......................................... 201 

Figure VII-5 An illustration of the process of solidification from the textbook. ........................... 203 

Figure VII-6 The picture supporting Porter & Easterling’s derivation of the diffusion equations

...................................................................................................................................................................... 205 

Figure VII-7 Three examples of graphics representations leading to differential equations ...... 210 

Figure VIII-1 The evolution of a curve boundary in the simulation ............................................... 224 

Figure VIII-2 Two grains divided by a curved surface ....................................................................... 225 

Figure VIII-3 The evolution of a curved grain boundary .................................................................. 225 

Figure VIII-4 Four large grains (yellow, green, light and dark blue) surround a small red grain

(left), and a zoomed-in view showing a triple point (right) ............................................................. 226 

Figure VIII-5 The textbook picture explaining how dispersed particles affect boundary migration

...................................................................................................................................................................... 233 

15

Figure VIII-6 Sequence of screenshots from Bob’s experiment ...................................................... 234 

Figure VIII-7 Betty’s model: grain growth with variable misalignments ....................................... 236 

Figure VIII-8 Betty’s sketches about angles, sine and arcsine .......................................................... 236 

Figure VIII-9 Bob's attemps to understand how to calculate the particles' areas, first “hard-

coded” in NetLogo (top), and then figuring out a formula to accomplish it (bottom) .............. 239 

Figure VIII-10 Bob's model for particles with varying size ............................................................... 240 

Figure VIII-11 Anand’s model for detailed study of interfacial energies ........................................ 241 

Figure VIII-12 Jim’s “Polymer Chains” model .................................................................................... 243 

Figure VIII-13 The evolution of a polymer chain in Jim’s model .................................................... 244 

Figure VIII-14 Comparison of the two algorithms............................................................................. 245 

Figure VIII-15 Results of Peter’s model with diffusion control (top), interface control (bottom),

and the chart from the textbook, where we can identify a similar shape (rotated for clarity) .... 246 

Figure IX-1 Various measures of students’ familiarity with computers .......................................... 255 

Figure IX-2 Hours spend on out of class coursework. The bars indicate the percentage of

students in each range, per their responses in the official course evaluations. .............................. 258 

Figure IX-3 Percentage of time spent on each task ............................................................................ 261 

Figure IX-4 Hours for each task ............................................................................................................. 261 

Figure IX-5 Students’ view of the usefulness of the assignment ...................................................... 262 

Figure IX-6 Average scores in the official course evaluation for 2007 (n=18, with

implementation) and 2008 (n=23, without implementation) ........................................................ 265 

Figure IX-7 Students’ grades as calculated by the rubric (top), and the contribution of each

dimension in the overall grade (bottom). ............................................................................................ 271 

Figure IX-8 Smoothed distributions of total time spent on the project, time spent with TA, final

grade, and grades in the course and in the exams ............................................................................... 272 

16

Figure IX-9 Matrix of scatter plots of various measures (time spent on the project, time spent

with TA, final grade, and grades in the course and in the exams) .................................................... 273 

Figure IX-10 Types of logged events, and correct code compilations ............................................ 278 

Figure IX-11 Code size, time between compilations, and erros, for Luca’s logfiles ..................... 280 

Figure IX-12 Phase 1: Luca departs from the exemplar model, and deletes unrelated code ...... 281 

Figure IX-13 Phase 2: Luca copies-and-pastes the code from her first procedure to create the

second procedure ...................................................................................................................................... 282 

Figure IX-14 Phase 3: Luca copies-and-pastes the code from the grain growth model .............. 283 

Figure IX-15 Phase 4: Luca beautifies the code, fixes indenting, names of variables., etc. ......... 285 

Figure IX-16 Code size versus time for Luca, Shana, Che, Liam, and Leen .................................. 286 

Figure IX-17 Error rate versus compilation attempts (time) ........................................................... 290 

Figure IX-18 Samples from the motivation plots................................................................................ 293 

Figure IX-19 Average of all motivation plots ....................................................................................... 294 

Figure IX-20 Benedict in the interview setting.................................................................................... 296 

Figure IX-21 Several screenshots of the grain growth model ........................................................... 301 

Figure IX-22 Solidification model showing surface energy, the volume energy, and the

combination of both ................................................................................................................................. 305 

Figure IX-23 Benedict’s recrystallization model showing the overlaps of crystals ....................... 307 

Figure IX-24 Benedict’s new patch-based recrystallization model.................................................. 311 

Figure IX-25 Benedict’s first attempt at an emergent algorithm ..................................................... 311 

Figure IX-26 Benedict’s first attempt at explaining the liquid to solid transformation ............... 317 

Figure IX-27 Textbook picture showing the energy plots for solidification .................................. 325 

Figure IX-28 Fisher’s attempt at explaining the liquid-to-solid transformation ........................... 326 

17

Figure IX-29 Chaps’ drawings ................................................................................................................ 329 

Figure X-1 Bob's one-level explanation ................................................................................................ 340 

Figure X-2 Liz's two-level structure ....................................................................................................... 341 

Figure X-3 A two-level structure with multiple phenomena ............................................................ 341 

Figure X-4 A student incorrectly “jumps” from grain growth to recrystalization, sewing growth as

a similarity trigger. .................................................................................................................................... 354 

Figure X-5 The content/representation/pedagogy triangle ............................................................ 360 

18

LIST OF TABLES Table III-1 Summary data ......................................................................................................................... 90 

Table IV-1 A comparison of the four phenomena, in terms of algorithms and pseudo code .... 115 

Table V-1 Example of the logging and time stamping of ‘artifacts’ ................................................. 125 

Table V-2 Side-by-side representation of the professor’s speech and the class notes he handed

out ................................................................................................................................................................ 127 

Table V-3 Affordances of agent-based modeling ................................................................................ 147 

Table V-4 Rubric for qualitative rating of the models ........................................................................ 157 

Table V-5 Rubric for quantitative rating of the models ..................................................................... 160 

Table V-6 Pseudo-rules for describing models ................................................................................... 166 

Table V-7 Number of files and events per participant ....................................................................... 171 

Table VII-1 Occurrence of different types of exercises ..................................................................... 197 

Table VII-2 Example of the logging and time stamping of ‘artifacts’ .............................................. 198 

Table VII-3 Average number of variables and equations per minute for the focus classes ......... 200 

Table VII-4. Side-by-side comparison between the professor’s transcription and class notes he

handed out ................................................................................................................................................. 209 

Table VIII-1 Affordances of the agent-based representation ........................................................... 250 

Table IX-1 First programming language and students’ familiarity .................................................. 256 

Table IX-2 Hours spent on out of class coursework, reported in the course evaluations (2007,

n=18, 2008, n=23) .................................................................................................................................... 258 

Table IX-3 Mean hours for each task .................................................................................................... 260 

Table IX-4 Students’ suggestion for improvement ............................................................................ 262 

Table IX-5 Feedback from students about the assignment .............................................................. 264 

19

Table IX-6 Average scores in the official course evaluation for 2007 (n=18) and 2008 (n=23)

...................................................................................................................................................................... 264 

Table IX-7 Rubric for qualitative rating of the models ...................................................................... 268 

Table IX-8 Average and standard deviation of the four dimension across all models ................. 271 

Table IX-9 Correlations between various metrics of the modeling assignment ........................... 273 

Table IX-10 Number of events collected per student ........................................................................ 277 

Table IX-11 Logged events per participant ......................................................................................... 278 

Table IX-12 Leen’s attempts to write the “InsertVacancies” procedure ........................................ 287 

Table IX-13 A summary of Benedict’s two explanations .................................................................. 322 

Table IX-14 A summary of Fisher’s explanation ................................................................................. 327 

Table IX-15 A summary of Chaps’ explanation .................................................................................. 330 

Table X-1 Comparison between discursive micro-behaviors and differential formulations ...... 337 

Table X-2 Studies, activities, data, and goals ....................................................................................... 356 

Table X-3 Methodological contributions, in bold, the original instruments developed for the

dissertation. ................................................................................................................................................ 357 

 

20

I INTRODUCTION 

21

The larger-scale goal of this dissertation is to explore relations between con-

tent, representation, and pedagogy, so as to understand the impact of the

nascent field of complexity sciences on the teaching and learning of STEM

content.

Specifically, this dissertation is about a series of studies of undergraduate

students’ learning of materials science. These studies consist of both de-

sign research and empirical evaluation. I have iteratively designed a

model-based curriculum for materials science – MaterialSim (Blikstein

& Wilensky, 2004) – a suite of computer models, supporting materials

and learning activities designed within the approach of the complexity

sciences and agent-based modeling. Over four years, I conducted an

empirical investigation of an undergraduate materials science course us-

ing MaterialSim at a top-ranked materials science department in a Mid-

west research university.

In this study, I investigate:

a. The learning outcomes of students engaging in scientific inquiry through interacting with MaterialSim.

b. The effects of students programming their own models as opposed to only interacting with pre-programmed ones.

c. The characteristics, advantages, and trajectories of scientific content knowledge that is articulated in epistemic forms and representational infrastructures unique to complexity sciences.

d. The design principles for MaterialSim: what principles govern the de-sign of agent-based learning environments in general and for mate-rials science in particular?

Below, I present this project and then hone on the study’s technical as-

pects and research questions.

Since Rousseau invented childhood (Émile, 1961), progressive educa-

tion theorists have been questioning prevalent assumptions of their time

regarding the project of education (Dewey, 1902; Freire, 1970; Freu-

22

denthal, 1973; Fröbel & Hailmann, 1901; Illich, 1970; Montessori,

1964, 1965; Papert, 1980; von Glasersfeld, 1984). In so doing, for the

most part, these intellectuals have implicitly assumed that their envi-

sioned pedagogical model should sweep across ages, domains, and me-

dia of interaction. Nevertheless, whereas education theory has pro-

gressed considerably since the behaviorists (Pavlov, 1957; Skinner,

1978; Thorndike & Gates, 1929; Tolman, 1951), knowledge-as-

production is still the dominant paradigm in education practice. The

various difficulties progressive pedagogies face in penetrating the main-

stream educational system are the topic of heated debate within the re-

search community. Some reformists advance their progressive agendas

by creating technological tools or curricula, others focus on making stu-

dent-centered, constructivist, project-based learning more accountable

to universal research standards, while others are concerned with build-

ing up firmer cognitive-science argumentation. More recently, however,

there has been growing attention to a new element: content itself as a

determinant of educational design (Kaput, 2001; Wilensky & Papert,

2006). An evaluation of content-driven design is the focus of this disser-

tation.

Granted, reform education has been evaluated for its intellectual, ethi-

cal, and socio-political merits and implications, and implementations of

reform curricula have been tested. Yet, I submit, these evaluations have

typically taken the pedagogy-to-content route, i.e., choosing a ‘blanket’

pedagogical model and then applying it across various content. I pro-

pose to examine the complementary content-to-pedagogy route, i.e., a

more fine-textured analysis of the cognitive, instrumental, and repre-

sentational constraints that specific content puts on pedagogy.

Rather than a mere conjecture, this conceptualization of a bidirectional

relationship between content and pedagogy – mediated by a representa-

23

tional infrastructure (Wilensky, 2006; Wilensky & Papert, 2006; Wi-

lensky, Papert et al., 2005) – stems from the burgeoning epistemic revo-

lution of the complexity sciences themselves, an interdisciplinary scien-

tific field which is redefining the content, methodologies, and episte-

mology of traditional science. Four key characteristics of complexity

sciences set it apart from traditional scientific fields and methodologies:

a. The content of the complexity sciences do not follow the conven-tional disciplinary boundaries, conversely, it reconceptualizes those very boundaries, pulling together apparently disparate fields of knowledge – its content, consequently, is intrinsically transdicipli-nary (Goldstone & Wilensky, 2006; Holland, 1995; Jacobson & Wi-lensky, 2006; Kauffman, 1995; Waldrop, 1992).

b. Innovative principles and modes of inquiry.

c. Intensive use of computational methods.

d. Focus on emergent properties and stochastic behaviors of natural and social phenomena, complementing or replacing the traditional emphasis on differential equations and deterministic modeling (Ioannidou, Repenning, Lewis, Cherry, & Rader, 2003; Wilensky & Resnick, 1995; Wolfram, 2002).

Consequently, in their work, complexity scientists are not only generat-

ing new knowledge, but also new forms of encoding knowledge so as to

complement or replace existing forms. Wilensky & Papert (2006) point

out that we do not have a name for the relationship between knowledge

and its encoding or “representational infrastructure”. They coined the

term “structurations” to express this relationship. A change from one en-

coding to another they call a “restructuration” (Wilensky, 2006; Wi-

lensky & Papert, 2006). One particularly widespread mode of inquiry

(and structuration ‘language’) within the complexity sciences is agent-

based modeling (ABM). In contradistinction to traditional mathematical

modeling, agent-based modeling focuses on the programming of a few

archetypical micro-behaviors of “agents” to explain a large number of

emergent macro-behaviors of the agent collective. The new forms of en-

24

coding brought about by ABM are not merely representational transla-

tions (“0.5” to “1/2”, discursive to pictorial, or equational to graphical),

but entire new taxonomies and formal symbolic languages (Wilensky &

Papert, 2006). For example, the behavior of ideal gases, normally en-

coded in the form of the classical law ‘PV=nRT’, can be restructurated as

set of algorithmic rules to manipulate individual gas molecules (agents),

yielding comparable results without making use of the previous equa-

tional knowledge (Wilensky, 2003). For many scientific phenomena

that traditionally enjoyed only a single mathematical encoding, com-

plexity sciences and ABM are now offering viable non-equational ma-

thematical alternatives1. For example, it has been shown repeatedly that

one of the hallmarks of gas behavior – the Maxwell- Boltzmann distribu-

tion of molecules’ speeds (Wilensky, 1999a) – can be obtained both

through analytical and agent-based methods. Particularly within the ma-

terials science scientific community, these new computational represen-

tations have achieved a similar level of acceptance and reliability as their

corresponding analytical representations (Raabe, Roters, Barlat, &

Chen, 2004).

Wilensky & Papert (2006) put forth that this multiplicity of representa-

tional infrastructures or structurations challenges some taken-for-granted

tenets of models of learning and research on learning, opening up an ex-

citing opportunity for educational researchers. They state that, conven-

tionally, we would regard content (gas laws, acid-base reactions, genetic

evolution, etc.) as a monolithic element in which the object of study and

its representation are coupled as one indivisible unit. Then, we would

evaluate the effectiveness of different pedagogical approaches for that

particular content unit. With the availability of multiple encodings for

the same scientific phenomenon, decoupling the object of study and its 1 For example, computer algorithms.

25

formal representation, it becomes possible to evaluate two different en-

coding forms within one, or more, pedagogical approaches. This new

dimension could advance the field by enabling researchers to evaluate

more comprehensively the bidirectional transactions between pedagogy,

representation and content, toward not only optimizing pedagogy-to-

content matching, but also challenging widely accepted ideas about the

learnability, difficulty, and age-appropriateness of particular content for

learners, as discussed by Wilensky and Papert (2006). It becomes, then,

the researcher’s task to comprehend, evaluate and/or design those repre-

sentations to better achieve the proposed learning goals.

In other fields of knowledge (particularly in linguistics), the influence of

language (or representation) on thought has been a topic of heated de-

bate (see, for example, I. Blikstein, 1995; Boroditsky, 2001; Choi & Bo-

werman, 1991; Gelman & Tardif, 1998; Schaff, 1973). A controversial

claim is that Eskimos have 20 (or 200, depending on the version) words

for “snow”, whereas most languages would have one or two words

(Whorf, 2000). Despite the controversy (for example, the rebuttal of

Pullum, 1991), novel experimental techniques are gathering growing

empirical evidence that language does influence thought. For example,

Daniel Casasanto and collaborators (2004) compared speakers of Eng-

lish, Indonesian, Greek and Spanish, and the results showed that the

dominant metaphors in participants’ first languages predicted their per-

formance on several non-linguistic time-estimation cognitive tasks, to

which the authors concluded that

“The particular languages that we speak can influence not only the representations we build for the purpose of speaking, but also the non-linguistic representations we build for remembering, acting on, and perhaps even perceiving the world around us.” (Casasanto et al., 2004).

26

I do not imply a direct analogy between language and representational

systems in science, but that could be an interesting starting point to ask

the question: Could the “languages” we use to represent scientific phe-

nomena have a similar effect? Could there be differences in students’

understanding explained by intrinsic differences in how we choose to

represent knowledge? Just like in the controversial Eskimo anecdote,

could particular professional and social practices of engineers favor cer-

tain representational practices – which, ultimately, will shape their

teaching? How many words would a materials scientist have for ‘atom’?

Previous research seems to suggest so. The work of Papert, Abelson,

diSessa and collaborators on making differential geometry accessible to

young children by restructuring it with the Logo turtle (Abelson & diSes-

sa, 1981; Papert, 1980), diSessa’s research on physics microworlds with

the dynaturtle (diSessa, 1982) and later with the Boxer programming

language (diSessa, 2000; diSessa, Abelson, & Ploger, 1991), as well as

Wilensky & Resnick’s (1999) work on agent-based modeling in several

scientific domains present strong evidence that changes in encoding

have significant impact on learnability.

The history of materials science itself offers numerous examples of how

available tools and technologies shape representational practices. The

first treatise on metallurgy, Georgius Agricola’s “De Re Metalica”

(1563/1950), contains an entire chapter on the taxonomy of veins and

ore channels. Herbert Hoover, who translated the book from the Latin

(before becoming president of the United States), remarks in a footnote

that Agricola’s nomenclature was “entirely based upon form,” and com-

prised tenths of types of ore channels: fissure (vena profunda), bedded

deposits (vena dilatata), impregnation (vena cumulata), stringers (fibra),

steams(commissurae saxorum), etc. The reproductions in Figure I-1

27

show clearly that Agricola’s taxonomy was based on thickness, shape,

and other salient perceptual characteristics.

Figure I-1 Some of the many types of veins

or ore channels in Agricola’s taxonomy

 

In Agricola’s times, when ore channels were dug by hand, learning his

taxonomy of channels was crucial for every metallurgist – thus an entire

chapter had to be dedicated to the topic. In our days, when such ores are

described by a handful of mathematical equations, learning such no-

menclature is useless. However, while it might be clear in Agricola’s case

that technologies, tools and practices shape the way we see, represent,

and teach scientific content, it is more difficult to see the same process

taking place in our current engineering classrooms. I will attempt to

show how representational practices in current engineering classrooms

are leading to a new “Agricola effect:” a particular approach to encoding

knowledge resulting in fragmented, overly specific classification

28

schemes and taxonomies. Then, I investigate possible alternatives de-

rived from the representations utilized by complexity scientists.

The objective of this dissertation, therefore, is to scientifically evaluate

the characteristics and effectiveness of the knowledge representation

schemes (Wilensky & Papert, 2006) derived from the complexity

sciences, compared to the traditional schemes. That is, I will attempt to

articulate a content-driven argument for the utility of non-traditional re-

presentational schemes and educational practices as means for achieving

widely accepted goals of schooling. Specifically, I will examine the rela-

tions between materials science (the content) and the agent-based

modeling (the representational infrastructure), so as to appraise wheth-

er and how the content is better learned through participating in learn-

ing activities engineered specifically for this representational infrastruc-

ture. The investigation will be an empirical study through which I will

attempt to support an argument for an “organic” fit between content

and representation. Therefore, the rationale of the study will be to assess

students’ learning gains, epistemology, and agency effected by partici-

pating in activities for the target content—activities that differ in their

pedagogical commitments. Based on this study, I will attempt to build

the case that the content-to-representation fit is not arbitrary or general

but, rather, reflects the nature of the content. Specifically, the nature of ma-

terials science—essentially an interdisciplinary study of the structure,

dynamics, and behaviors of atoms and molecules themselves—is intrin-

sically conducive to a complexity studies approach.

Despite the focus of this dissertation on the content-representation

connection, there is a third, inescapable element permeating this re-

search agenda: different representational infrastructures must have an

impact on the pedagogical approaches utilized to engage students. As a

subpiece of this work, I will describe and evaluate the educational design

29

framework used to engineer the tools and activities presented to stu-

dents during the studies. This design, based on the tenets of construc-

tionist (Papert, 1980, 1991) theory, had students program computer

models to simulate a phenomenon of their choice, within the scope of

the courses in materials science they were then attending. I will attempt

to show that the triad content-representation-pedagogy is also not arbi-

trary but could as well reflect the nature of the content. For example, the

epistemological infrastructure of agent-based modeling strikes a chord

with the constructionist principle of syntonicity. When programming the

behavior of a single atom within a material, students oftentimes have to

imagine themselves as an atom to fathom how they would react to in-

creased thermal vibration. Also, agent-based modeling presupposes a

deep knowledge of the system’s micro-rules, which, I hypothesize, can

only be properly learned through the construction of those rules – and

student-centered construction of artifacts is another of the pillars of

constructionism.

It is thus not surprising that some of the most powerful research tools

for the study of complexity spring from the academic bastions of con-

structionism. In addition, as an additional theoretical reference, I draw

on critical pedagogy’s emphasis on literacy, latu sensu, as a tool with

which learners can not only read the word but the world (Freire & Ma-

cedo, 1987) – in other words, learning in an environment in which

knowledge is not stripped away from its context, and learners have free-

dom to choose topics of their own interest to explore, accentuating the

connections between fluency and agency.

Three constructs, therefore, are present here: content (materials

science), approach/representation (the perspectives and methodolo-

30

gies of complexity studies and agent-based modeling2), and pedagogy

(constructionism).

Figure I-2 The content, representation,

pedagogy triangle

 

Emerging from the dissertation is the following conjecture:

The epistemic forms of agent-based modeling can transform tradi-tionally intricate, overly-specific materials science content, encoded as engineering laws and differential equations, into more learnable, malleable, and generative principles and micro-rules, so as to enable students to deal with variant phenomena (adaptive expertise).

Just as Agricola’s taxonomy had more than 30 types of ore channels, to-

day’s content in materials science contains a myriad of phenomena stu-

dents need to learn. Many of those phenomena share similar micro-

mechanisms but have very different equational representations. Thus,

the application of the principles of complexity sciences to materials 2 Even though those perspectives and methodologies could be seen as content themselves, in thi s particular case I am considering only their ways to represent phenomena, i.e., their “lenses” onto phenomena, such as examining the world departing from agents, taking into account simple behaviors and interactions, etc.

Contentmaterials science

Pedagogyconstructionism

RepresentationABM

31

science learning may result in design rationales, interactive media tools,

and evaluation programs with applicability across domains of content

and learning-environment contexts.

I conducted several studies of sophomore engineering students, who in-

teracted with and constructed computer models of materials science

phenomena. Data sources for the evaluation of these studies include

classroom observations, interviews with students, videotaped sessions of

model-building, questionnaires, analysis of artifacts generated by stu-

dents, and the logfiles of students’ interaction with the computer model-

ing environment. To follow and inspect students’ cognitive trajectories,

I employ verbal analysis, ethnographic methods, microgenetic methods,

and data-mining/analysis of computer-generated logfiles.

In the Literature Review, I will discuss the state of undergraduate

STEM education, overview the tenets and domains of complexity stu-

dies and agent-based modeling, and review previous work on ABM and

education. Based on the review of the literature and of existing model-

and computer-based curricula, I also propose a taxonomy for those

types of curricula, which will be useful in design of the software and ac-

tivities for students, and better locate it within current research. . In

Chapter 3, Representational Comparison, I will explore in detail two

phenomena in materials science and show how they are represented

within both the agent-based and equational-based approaches, conclud-

ing with remarks on the affordances of each representation. In the Me-

thods chapter, I introduce the experimental designs, the tools, and de-

tail the methodological constructs to be used in the data analysis. The

next chapter, Study 1, is an examination of representational practices in

a materials science classroom, in which I analyze transcribed classes,

class materials, and textbooks. I also conduct a qualitative study, based

on semi-clinical interviews, of students’ knowledge of some content top-

32

ics in materials science. In Chapter 7, Study 2, I conduct and analyze a

laboratory study in which students interact with and create agent-based

models. Study 3 is a classroom study with 21 sophomore students, in

which they build agent-based models as a regular class assignment. In

each of the three studies, I explain then how the proposed design ex-

presses complexity-studies and constructionist principles, such that the

selected pedagogy supports deep conceptual understanding of the se-

lected content. In Chapter 9, Discussion, I conclude with lessons

learned from the studies, and recommendations for future work.

         

33

II LITERATURE REVIEW 

34

II.1. SUMMARY In this chapter, I review and comment on existing research in the two re-levant areas for the dissertation, as described in the introduction:

Engineering education.

Complexity sciences, and their use in education.

The first part of the review will examine past and current research on engineering education, focusing on two topics: the role of design, and the past and present uses of digital media. I will show how engineers, perhaps the ultimate design professionals, are rediscovering and revolu-tionizing design education, and the related research accomplishments and opportunities. Then, I will review several different education projects that make use of digital media (CD-ROMs, web pages, anima-tions, simulations) in one particular branch of engineering – materials science. This first part of the review will also try to foreground impor-tant points which will impact my design and implementation:

Research on digital media in engineering education have not focused on issues of representation apart from HCI considerations.

Tools for doing, tools for building, tools for visualizing: not all uses of computers in engineering education are made equal – a taxonomy of different modeling and implementation approaches is necessary to evaluate their ultimate goal, effectiveness and affordances.

The “design-versus-analysis” dilemma: How to apply the wealth of research on design-based or project-based pedagogies to analysis-based courses, in which there is not tangible final project, such as a robot or a car, etc.

The second part of the review, comprising complexity sciences, compu-tational science, and agent-based modeling, is a historical account in which I discuss those fields of knowledge and methodologies, their role in modern science, and their relevance to current scientific research, showing how the complexity sciences were conceived as a unique trans-disciplinary field as many scientists found themselves stalled in their dis-ciplines (which is particularly true in materials science, as I will show.) Next, I address the uses of complexity sciences and agent-based model-

35

ing in education, including a review of several educational software, and conclude with remarks on restructuration of knowledge domains.

Despite the two parts being relatively independent, they have a funda-mental connection: whereas the research in engineering design educa-tion has advanced considerably, it has for the most part ignored deeper issues of knowledge representational infrastructures, which the com-plexity sciences could help advance (as put forward, more generally, by Wilensky & Papert, 2006). On the other hand, research on educational uses of complex systems has been lacking on implementation pedago-gies, and the research on design education is contributing to a more sol-id body of work on student-led project-based learning – which could be an appropriate base to tackle pedagogical issues regarding the use of complex systems methodologies for learning. Also, the research on agent-based modeling and its representational infrastructures could help illuminate the issue of preferred representational encodings for dif-ferent classes of phenomena (for example, phenomena involving a few bodies, compared to phenomena with thousands of units). What are the characteristics, advantages, and trajectories of scientific content know-ledge articulated in epistemic forms unique to complexity sciences? How different are those epistemic forms, and how educational designers can make use of them to create learning environments for deep under-standing?

II.2. ENGINEERING EDUCATION II.2.1. A CRISIS IN ENGINEERING EDUCATION In 2007, approximately 400,000 students took college-level engineering

courses in the United States alone (American Society for Engineering

Education, 2007). As early as the nineteen-sixties, education researchers

and national committees (Brown, 1961; Committee on the Education

and Utilization of the Engineering, 1985; Jerath, 1983; MIT Center for

Policy Alternatives, 1975; Panel on Undergraduate Engineering Educa-

tion, 1986) have pointed out that engineering education lags behind in

its adoption of newer approaches to teaching and learning. In recent

36

years, there have been numerous calls for reform from the engineering

education community and several schools have initiated reform initia-

tives (H. H. Einstein, 2002; Haghighi, 2005; Russell & Stouffer, 2005).

Some universities have even taken the step of creating graduate pro-

grams exclusively dedicated to research in engineering education (Pur-

due University being one of the foremost examples.) The push for curri-

cular reform in engineering is motivated by several issues which have

been raised by those researchers and committees , but also, more recent-

ly, by politicians, CEOs, and students themselves: high dropout rates

(Dym, Agogino, Eris, Frey, & Leifer, 2005), declining interest of high-

school students for an engineering career (Panel on Undergraduate En-

gineering Education, 1986), changing workforce demographics, new in-

dustrial dynamics brought about by mass customization, and fast prod-

uct development cycles (Committee on the Education and Utilization

of the Engineering, 1985; Katehi et al., 2004; Tryggvason & Apelian,

2006).

Apart from the broader societal changes, technical advances have also

been an important driving force for engineering education reform pro-

grams. As basic science and engineering become increasingly intert-

wined in fields such as nanotechnology, molecular electronics, and mi-

crobiological synthesis (Roco, 2002), students and professionals have to

deal with time scales from the nanosecond to hundreds of years, and

easily transition from understanding phenomena at the nanoscale to a

scale of thousands of kilometers (Kulov & Slin'ko, 2004). This wide

range of subjects, scales, and problems makes it prudent not to try to

cover all the relevant knowledge in each domain, but instead to help

students become what became popularly known as “lifelong learners,” or

develop what some scholars have termed adaptive expertise (Bransford

37

& Schwartz, 1999; Hatano & Oura, 2003), which they could apply to

new problems and situations.

Many researchers and industrial leaders in the field have noted that

reform initiatives are falling short of their initial grand ambitions to ad-

dress those new challenges (Dym et al., 2005). Ottino (2004) has ar-

gued that the engineering curriculum is still frozen in time and hasn’t

adapted to crucial technical and methodological innovations such as the

complex system approach. Bazzo (1998) and Blikstein (2001) have ar-

gued that engineering curricular reform suffers from a classical “bank-

ing” (Freire, 1974) approach to curricular reform – simply adding new

courses to the curriculum but not promoting deep structural changes.

Hurst (1995) pointed out that syllabi and curricula were so overloaded

with transient or excessively detailed knowledge that there was no time

for fostering students’ fundamental understanding of content matter.

In fact, most of those reform initiatives were based on grand views about

blocks of content or general skills needed for future engineers, or even

socio-economic needs of whole countries (Munjal, 2004), rather than

detailed studies on how engineering students learn – or what they

should be learning. Adding new courses or blocks of courses, consider-

ing the highly departmentalized structure of engineering schools, is

much more practical than changing the overall structure of existing cur-

ricula – however, the situation becomes more problematic as we envi-

sion engineering schools two or three decades from now. At some point,

the limit is reached and if we need to add courses we need to remove

others. A major challenge is in how to go about deciding what courses

can be dispensed with (and what knowledge) – a struggle that was iden-

tified as early as the mid-nineties, when researchers such as Darcy Clark

started suggesting that the dramatic transformation and expansion of

38

the content in materials science was about to bring new issues and prob-

lems for education:

“[…] these problems stem from courses, especially those of the in-troductory or service variety, becoming overcrowded with content and extremely broad in scope. A modern materials science textbook is around 800 pages and presents the lecturer of introductory courses with difficult decisions to make regarding which content to cover and which to omit.” (D. J. M. Clark, 1998)

More generally, the approach of addressing a larger societal need or a

deficit in the training of a particular profession by adding courses is not

new. Tyack and Cuban (1995), more than a decade ago, identified the

“course adding” phenomenon in the majority of 20th century education-

al reform initiatives in the US:

“[…] Once they [Americans] had discovered a problem, they la-beled it and taught a course on the subject: alcohol or drug instruc-tion to fight addictions; sex education to combat syphilis or AIDS […] It is easier to provide vocational education than to remedy in-equities in employment and gross disparities in wealth and income” (Tyack & Cuban, 1995)

Similarly, if the societal diagnosis was that engineering graduates were

not skilled for engineering practice, transporting engineering practice back

into school seemed like a viable alternative – as a new set of courses. A

common approach in many universities, therefore, has been to add de-

sign-based courses, including hands-on engineering design, to the curri-

culum. Being multidisciplinary, engineering design courses represented

a partial solution to the overcrowding of courses as they enable multiple

content domains to be taught in a more integrated fashion, with mul-

tiple skills being tackled in a single course. This push towards engineer-

ing design will be discussed in detail in the next section.

39

II.2.2. DESIGN: THE COMEBACK OF A FORGOTTEN SKILL IN ENGINEERING EDUCATION 

II .2.2.1. The scientif ic engineer is born After the Second World War, in the early nineteen-fifties , there was a

significant push towards analysis, mathematics, and engineering

sciences, and away from traditional “shop work,” (Grinter, 1955) that

was much more present in curricula during the first half of the century

(Dym, 1999). The professional engineer of the first half of the 20th cen-

tury became the scientific engineer of the second half (Tryggvason &

Apelian, 2006). The move away from practical and lab work was not ex-

clusively conceptual – after WWII and during the apex of the American

space program (late nineteen-sixties), engineering schools were flooded

with money from research projects, and enrollment was high. After the

peak of the Apollo program, when funding decreased, the “cheaper”

theoretical classes prevailed over engineering labs or design work (Feisel

& Rosa, 2005). Research in laboratory instruction dwindled too: a sur-

vey of the Journal of Engineering Education revealed a meager 6.5% of

papers on the topic from 1993 to 1997, and 5.2 % from 1998 to 2002

(Feisel & Rosa, 2005).

II .2.2.2. The entrepreneurial/enterprising engineer is born

However, this move toward the scientific engineer exceedingly removed

from the curriculum the engineering design experience – a gap which

started to be missed by faculty and engineering employers in the late six-

ties and seventies (Sheppard & Jenison, 1997b). When the trend started

to be reversed, during the nineties, “capstone” design courses were in-

troduced almost ubiquitously. Later, many schools also introduced

“cornerstone” design courses for freshmen.

They have been relatively successful, and research suggests that students

not only engage in engineering with greater motivation, but learn better

40

many important engineering principles (Colgate, McKenna, & Anken-

man, 2004; Dym, 1999; Dym et al., 2005; Lamley, 1996; Martin, 1996;

Newstetter & McCracken, 2000; Wood, Jensen, Bezdek, & Otto, 2001).

Engineering design became the topic of choice for engineering educa-

tion researchers and, in the best fashion of engineering culture, sophisti-

cated taxonomies and classifications for capstone and cornerstone

courses were devised, such as Sheppard’s individual/team; con-

tent/process based classification dimensions (Sheppard & Jenison,

1997a). Researchers also started to employ sophisticated data collection

and analysis methodologies to better capture students’ cognitive evolu-

tion during design projects, such as latent semantic analysis, analysis of

sketching behavior, and peer evaluations (Agogino, Song, & Hey, 2007;

Dong, Hill, & Agogino, 2004).

One important point in Sheppard’s work was the recognition that the

multiple skills and competencies required for engineers did not fit under

a single type of course, conversely, content (i.e., traditional analytical

courses in the engineering disciplines) and process (the focus of the de-

sign courses) courses were both necessary. Therefore, many of the defi-

ciencies in content-based courses cannot be simply addressed by the

creation of design courses.

II.2.3. OPEN QUESTIONS There are three crucial open questions presented by design-based

courses and the push for reform in engineering education, which have

not been entirely addressed so far: (i) the design-versus-analysis dilemma,

(ii) the focus on tools for doing vs. tools for learning, (iii) the need for a

‘language’ of design. We will discuss them in further detail in the re-

mainder of this section.

41

II .2.3.1. Open question: the design-versus-analysis di-lemma

Since the push toward the scientific engineer during the second half of the

20th century, scientific disciplines were solidified as integral part of the

engineering curriculum. Indeed, a significant part of engineering educa-

tion constitutes of basic science (physics, chemistry), engineering

science (fluid mechanics, thermodynamics), and mathematics (calculus,

linear algebra), and they cannot be easily displaced. The design-versus-

analysis dilemma is one of the common issues regarding the implementa-

tion of progressive engineering curricula: ‘equational’ mathematics is

still seen as the language of engineering, and reformers stress that they

are not calling for a “wholesale replacement of analysis courses with de-

sign courses” (Dym, 1999, p. 146). However, due to the scale and type

of typical design projects (a solar car, or a robot), it is challenging for de-

sign-based courses to directly focus on core theoretical and scientific

topics of the aforementioned knowledge domains. For example, stu-

dents might build models and generate rich theories about moving

gears, but rarely they would go as far as creating scientific models of the

behavior of the metal from which the gears are made. Thus, in design

classes, some fields such as mechanical or electrical engineering are fa-

vored over chemical engineering or materials science. This could be an

obstacle for learning invisible or microscopic phenomena such as chem-

ical reactions or atomic interactions in a more progressive fashion, using

the insights from design pedagogies. In other words, the more progressive,

design-oriented courses end up covering just some particular fields of engi-

neering. The remaining fields get relegated to more traditional pedagogical

approaches (see, for example, Sheppard & Jenison, 1997a; Sheppard &

Jenison, 1997b). Design and analysis courses risk never getting organi-

cally integrated in the engineering curriculum; conversely, they become

two incommunicable containers of disciplines.

42

II .2.3.2. Open question: tools for doing vs . tools for learning

The technological tools used in engineering reform initiatives (such as

modeling and design software) are, for the most part, the same em-

ployed by professional engineers in their everyday practice and not es-

pecially designed for learning. Using professional-based tools might be

tempting as they enable students to more rapidly achieve the desired

engineering design. In some particular domains of engineering this

might not be the best choice. Several of these software tools used do not

afford insight into the computation underlying their design and func-

tioning. For engineering practice, indeed, a tool has to yield reliable and

fast results – understanding what’s “under the hood” is not necessarily

useful. Particularly in domains which involve microscopic entities such

as materials science (as opposed to mechanical or civil engineering, for

example), this could be disadvantageous for learners. The computation-

al procedures might embody an essential, perhaps crucial, aspect of the

subject matter—how the conventional formulas and representations

capture the phenomena they purport to model. Manifestly, no computer

modeling environment can uncover all of its computational procedures

– it would be impractical, for example, to have students wire hundreds of

transistors so as to understand the underlying logic of the modeling en-

vironment. Moreover, in theory-heavy fields such materials science,

many of the traditional formulas themselves are opaque—they embody

so many layers of accumulated scientific discovery into such a complex

and concise set of symbols that they do not afford common-sense in-

sight and grounding of the causal mechanisms underlying the pheno-

mena they purport to capture. Thus, although using formulas and con-

ventional engineering representations is perhaps conducive to successful

doing (designing a new alloy, for example) it does not necessarily lead

to principled understanding (knowing how each of the chemical ele-

43

ments interact and alter the properties of the alloy3), or learning prin-

ciples from one phenomenon that could be transferable to other related

phenomena.

II .2.3.3. Open question: the ‘ language’ of design As early as 1997, Dym pointed out the crucial issue of the ‘language’ of

engineering (Dym, 1999; Dym et al., 2005) having shifted excessively to

traditional mathematical representations:

“For the last fifty years, mathematics has been the language of engi-neering. In addition, mathematical content was seen as the guaran-tor of suitable rigor both for research and for teaching. However, en-gineering faculty know that much of what they really know cannot be expressed in mathematics alone. There’s no question that we use graphics and pictures. […] But this awareness has not yet been fully realized in the engineering curriculum” (Dym, 1999, p. 146).

Behind the apparently naïve statement about engineers’ use of written

text, graphics, and pictures lies a fundamental problem which I will dis-

cuss along this dissertation: the content-representation mismatch. Diffe-

rently from the basic sciences, in which one could possibly discover new

natural laws by simply combining and deriving pre-existing laws, engi-

neers normally cannot afford to do so, either due to (1) the interdiscip-

linary nature of the problems they need to tackle, (2) the focus on

‘getting things done’ without necessarily a fundamental understanding

of every single scientific detail (or the need of that understanding), or

(3) the multiple implications of engineers’ need to design for the real

world. All of this additional knowledge – (1) about how to put together

different content areas, (2) problem-solving heuristics and rules-of-

thumb, and (3) practical knowledge in the ‘real world’, are hardly ex-

pressed with conventional mathematical notation and, thus, hard to

learn in the conventional mathematical analysis-driven engineering

3 For more on design for learning vs. design for use see, for example, Soloway, Guzdial, & Hay, 1994.

44

classroom. With the introduction of computer modeling in engineering

practice, and its eventual use in some undergraduate courses, Dym af-

firms that while engineering still depends heavily on mathematics as a

“language for modeling and (initially) formulating problems”, students

and practitioners are increasingly utilizing “computing as a language for

solving problems” (Dym, 1999), and hints at a fundamental representa-

tional issue:

“Does one acquire a “feel” for a subject through algebraic manipula-tion? Through many computer cycles? Through intelligent use of symbolic computing? Through some magical balance among these three means? While we used to train students in the arts of “feel” and intuition by having them perform a lot of routine algebra, now they are jumping early to the computer. So how and when do we teach them what to look for in computing results? How will they learn to distinguish computing errors from modeling mistakes?” (Dym, 1999, p. 147)

However, these representational issues have not been fully addressed – still, as well-documented in the literature, conventional mathematics is the language of choice for engineering, and relatively little research ex-ists on how to make the “forgotten” languages of engineering share its status and sophistication.

II.2.4. A BRIEF HISTORY OF THE USES OF MODELING, SIMULATION, AND OTHER DIGITAL TOOLS IN MATERIALS SCIENCE EDUCATION 

II .2.4.1. Introduction Another concurrent trend in engineering education for the past two

decades was the use of digital media – pictures, movies, animations, web

pages, applets, and computer models. Particularly in materials science

classrooms, digital media has had a long history. Two characteristics of

the discipline contributed to this state of affairs: first, the intensive use of

computational methods in materials science research itself and, second-

ly, the well-documented need for visual aids to illustrate some crucial

45

content topics – particularly tridimensional, atomistic, and dynamic

phenomena (Clyne, Tanovic, Jones, Green, & Berry, 2000; McMahon

Jr., Weaver, & Woods, 1998; Russ, 1997b; University of Liverpool,

1996; Voller, Hoover, & Watson, 1998).

The early history of modeling, simulation, and digital media in engineer-

ing education can be divided into two chronological phases: the elec-

tronic book age, and the applet age. These two phases overlap in time,

and are not the result of a centrally planned curriculum development in-

itiative, but rather a progression motivated by the availability of new

media and programming environments, as I will show throughout this

review.

A common denominator in most initiatives is that the motivation was,

for the most part, very typical of engineers’ ethos: there was a known

problem (problematic student understanding of tridimensional, atomis-

tic, and dynamic phenomena), and the availability of new tools prompt-

ed many professors to simply try to address the problem.

The implications of this bottom-up approach were that, initially, many

of the projects were not backed by any consistent cognitive or pedagogi-

cal theory, but rather by loose empirical validation of the new curricula

(simple pre- and post-tests, for example). In addition, exactly due to the

lack of theory, many designers were much more innovative than they

might have been had they followed all the canons of the learning

sciences. One example is “Visualizations in Materials Science” (Russ,

1996), one of the first large-scale curricula to be developed, produced at

North Carolina State University. The author, John Russ, described the

development of the project as a natural progression in response to a per-

ceived need:

46

“We began by creating improved graphics for several topics which were projected in class, found that they were helpful to the students. […] This still did not solve the problem of how students could take notes from these graphics, so we turned to multimedia capabilities and created a web site and CD-ROMs.” (Russ, 1997b)

As we will see throughout this review, differently from traditional tech-

nology-in-education implementations, in which external researchers are

the main initiators, many of these implementations were initiated by en-

gineering professors unsatisfied with their own teaching materials and

resources.

II .2.4.2. The electronic book age The first wave of projects in materials science education consisted in di-

gitizing existing instructional materials. One of the largest and pioneering

efforts to date is the MATTER project (University of Liverpool, 1996),

started by the University of Liverpool in 1993 (see Figure II-1, left).

MATTER was set up as a consortium of UK materials science depart-

ments to develop computer-based learning materials and integrate them

into mainstream teaching. The first CD-ROM was published in 1996

and is still in use in several universities. MATTER’s pedagogy is based

on the idea of improving students’ experience using rich multimedia

content, carefully intertwined with text, and presented as interactive

CD-ROMs or web pages. Subsequent variations of MATTER appeared

in the following years, such as MATTER for Universities (University of

Liverpool, 2000), AluMatter (University of Liverpool, 2001a), SteelMat-

ter (University of Liverpool, 1999), and Steel University (University of

Liverpool, 2001b). In the late nineties, the University of Cambridge

launched a similar project: Dissemination of IT for the Promotion of Mate-

rials Science (DoITPoMS) (Clyne, 2000; University of Cambridge,

2000). Differently from MATTER, DoITPoMS (see Figure II-1, right)

was web-based and less structured, also inviting users to contribute with

47

materials (videos and animations), and included more simulation as

well. The DoITPoMS team also had an innovative content-generation

scheme: they organized a yearly summer school in which undergraduate

students, with the guidance of researchers or professors, would create

content for the project.

Figure II-1 A model-based activity for

investigating Electron-atom interaction in MATTER (left),

and diffusion simulation, in DoITPoMS (right)

       

“Visualizations in Materials Science” (Russ, 1997a, 1997b), was another

pioneering development in the field. It comprised about 1000 movies

and animations, as well as about 300 worked examples and quizzes, in-

itially published on a CD-ROM, and later deployed to a website (see

Figure II-2).

Figure II-2 Movie from a solidification

experiment (left), and an animation of phase transforma-

tion (right), from Visualizations in Materials Science 

 

48

At the University of Pennsylvania, McManon et al. (1998) developed

their “Multimedia Tutorials for an Introductory Course on the Science

of Engineering Materials,” (see Figure II-3) covering multiple topics,

from crystallography to electronic materials. In agreement with most

other projects at the time, one of the factors motivating the study was

that:

“A standard science/engineering approach emphasizing formulae and numerical calculations can leave introductory-level students without a grasp of the basic principles […] at the core of the subject. […] An understanding of many of the topics requires the visualiza-tion of three-dimensional moving images or evolving processes that cannot be presented effectively using static illustrations.” (McMahon Jr. et al., 1998)

Figure II-3 McManon’s “Multimedia

Tutorials for an Introductory Course on the Science of

Engineering Materials”

 

Approximately at the same time, professors at the chemistry department

at Ohio State University developed a series of online tutorials (see Fig-

49

ure II-4) and interactive quizzes on topics such as “The Solid and Liquid

States,” “Rates of Reactions,” “Gas Laws,” and “Work and Entropy”

(Grandinetti et al., 1998).

Figure II-4 A screenshot from Ohio State

University’s “Gas Laws” online tutorial

 

Various other similar projects followed, such as the University of Sou-

thampton’s tutorial on phase diagrams (Interactive Learning Centre -

University of Southampton, 1997), the University of Kiel’s comprehen-

sive tutorials on defects in crystals, shown in Figure II-5 (Föll, 2001), a

series of online ‘teaching pamphlets’ edited by the International Union

of Crystallography, for helping materials science teachers worldwide

(based on classic introductory texts, e.g.,Glasser, 1984; Hartmann,

1984; Jones, 1981).

50

Figure II-5 A screenshot from University of

Kiel’s tutorial on defects in crystals

 

As the use of multimedia started to become rapidly popular in engineer-

ing schools (despite unconvincing evidence of their effectiveness), text-

books publishers began to bundle their books with CD-ROMs and on-

line content. Much more polished and carefully crafted, they required

more sophisticated and enticing animations and graphics, and moti-

vated the emergence of a new profession: the online/multimedia in-

structional designer. A good example of the level of sophistication is the

textbook “Chemistry - The Science in Context” (Lange, 2003) (see Fig-

ure II-6).

51

Figure II-6 Screenshots from the accompa-

nying online materials for the “Chemistry - The Science in

Context” textbook

 

In these early ages of the use of digital media in engineering education,

the ‘digital textbook’ era, there was great belief in the power of visualiza-

tion for learning (for a more detailed account on visualization in under-

graduate engineering, see Stieff, 2004). The assumption was that visua-

lization of scientific phenomena was a crucial element to improve un-

derstanding, supposedly an evolution from the overly abstract and ma-

thematical descriptions (C. J. McMahon, Weaver, & Woods, 1998; D. J.

M. Clark, 1998; Jacobs, 1997; Kulov & Slin'ko, 2004; Russ, 1997a). In

the same vein of Russ’ motivation to develop his “Visualizations in Ma-

terials Science” (see quote in Section II.2.4.1), several of these authors

reported a similar reason:

“By offering the student new tools to understand concepts in action, we might provide opportunities for deeper understanding […]. These tools include animation, interactive simulations, virtual reali-ty, and web serving to permit time- and location-independent review of course content.”(D. J. M. Clark, 1998)

“An understanding of many of the topics requires the visualization of three-dimensional moving images or evolving processes that can-not be presented effectively using static illustrations.” (McMahon, Weaver, & Woods, 1998)

52

Despite the great excitement about the new media and the possibility of

visualization otherwise ‘invisible’ processes in materials science, there

was little evidence that such approach significantly improved students’

understanding. Since most of these projects were initiated in engineer-

ing schools by engineering professors, there was no strong interest in

large-scale studies on the effectiveness of such curricula and the metrics

were oftentimes too simplistic. For example, McManon at al. (1998) ran

a study with eight students (two groups of four) in which the only in-

strument was a content-driven post-test. In addition, the only impact he

found, even with a very small sample, was not on scores but on a de-

creased number of hours of study for the ‘multimedia’ group (3.1

hours), as opposed to the control group (4.1 hours). Even larger studies

could not find the much-promised quantum improvement in software-

only groups, as opposed to lecture-only groups (Hashemi, Chandrashe-

kar, & Anderson, 2006).

One of the reasons was that, in general, research in the nineteen-nineties

focused on Human-Computer Interaction (HCI) aspects of the design,

such as “provide opportunities for interaction at least every three or four

screens or, alternatively, about one per minute” (Orr, Golas, & Yao, 1994)

and not on cognition or pedagogy (for a literature review of the HCI-

related work, see Stemler, 1997), which resulted in a myriad of very sim-

ilar projects based on the naïve idea that “to visualize is to learn.” In oth-

er words, the assumption was that the students’ difficulties were due to

the lack of visual insights into the phenomenon, but not to fundamental

representational issues generated by the disconnect between the equa-

tional and the pictorial representations. Much later, chemistry educators

would suggest that not only was that not always the case, but that par-

ticular kinds of visual representation were more effective than others –

often for counter-intuitive reasons (see, for example, Copolo & Houn-

53

shell, 1995; Stieff, 2004; Wu, Krajcik, & Soloway, 2001; Wu & Shah,

2004). In general, these CD-ROM or online-based materials offered a

very basic level of user experience and a simple navigation scheme. Stu-

dents could change parameters and run simple simulations within a

semi-structured sequence. There was no insight into the algorithms or

the code, and the models were, for the most part, deterministic dynamic

visualizations of the phenomena under examination, i.e., not real simula-

tions derived from first principles or actual scientific models.

These materials are still used in several universities worldwide as add-

ons to the conventional teaching, for classroom demonstrations or as ex-

tra study materials for students. Despite being designed more than a

decade ago, the basic theoretical underpinnings of such systems are very

much present in several contemporary computer-based materials.

II .2.4.3. The applet age One key technology prompted an evolution in many of the online mate-

rials science curricula: the possibility of publication of computer pro-

grams embedded in web pages, mainly using the Java™ programming

language. Enriched by improved levels of interactivity, rich programma-

ble media, and the possibility of making available ‘real’ computer mod-

els, there was a surge in novel or updated online curricula. This was fur-

ther favored because researchers could just publish simplified versions

of models that were being developed for research, without necessarily

having to develop educational materials from scratch.

The “Manufacturing Advisory Service” software (Wright, 1996, 1999),

developed at UC Berkeley, is an example of a research application dep-

loyed for educational purposes (see Figure II-7). Users could input a set

of properties for a conceptual part, and get real-time feedback regarding

possible manufacturing methods, process chains and cost estimates – a

procedure that can save a designer hundreds of hours of trial-and-error

54

work. Along the same lines, the “Sugar Engineers’ Library” (Sugartech,

2005) provided a front-end to a comprehensive database of properties

of several sugar-based materials.

Figure II-7 Screenshot of the “Manufactur-

ing Advisory Service” applet

 

Tridimensional visualization of crystal structures was one of the most

explored fields in the ‘applet age,’ due to the historic difficulties that stu-

dents reported understanding the subject matter. Again, the idea that

simply visualizing a 3D structure would be a helpful learning aid was

dominating. CrystalViewer (D. Kofke, 2002), part of the etomica project

at the University of Buffalo, was one of the most complete packages

(Figure II-8). Students could construct atomic unit cells of different

kinds of crystals and define ‘cutting planes’ to clearly visualize its geome-

trical properties – one of the most challenging tasks in crystallography

education. Many similar packages were produced in later years, such as

Vale’s “Software for Crystallography” (Vale, 2004).

55

Figure II-8 Crystal Viewer screen, show an atomic unit cell and a diagonal

plane

 

XRayView and XRayPlot, developed at the Department of Biochemistry

at the University of Wisconsin-Madison were ambitious attempts of a

virtual X-ray lab to introduce concepts of X-ray diffraction by crystals

(Phillips Jr., 2007); Lu & Jin “Animated phase diagram tutor” (Figure

II-9) enabled students to enter parameters to generate and visualize 2D

and 3D diagrams (Lu & Jin, 1997). The “Copolymer equation” applet

enabled students to generate and visualize plots illustrating the copoly-

mer theory (Nairn, 2001).

56

Figure II-9 The “Animated phase diagram

tutor”

 

But the new Java technology soon sparked the idea of not only 2D or 3D

visualization, or equation-based models, but atomistic simulations –

showing the behavior of individual atoms as described by computer

code. Examples of this approach are Diffusion Java Applets (Figure II-10,

top) developed by Gliksman and Lupulesco at the Rensselaer Polytech-

nic Institute (2004), the etomica project (D. A. Kofke, 2007), at the

University at Buffalo (Figure II-10, bottom).

57

Figure II-10 The Diffusion Java Applets

(top) and a of one of the etomica models (bottom)

 

 

The idea was to use the computer media to show individual atoms of

molecules within a ‘virtual’ material, a significant evolution from show-

ing equation-based plots, or pre-programmed animations. Since re-

searchers had then started to use atomistic methods in their own re-

search, it was expected that those methods would end up in educational

projects generated by engineering professors. Interestingly, just half of

that prediction was fulfilled: the number of atomistic simulations online

grew quickly, and even projects from the ‘electronic book’ era were up-

dated to include such simulations. Still, students’ were still passive “visu-

58

alizers” of models. The transition to model-building never took place in

a convincing manner, and this is one of the open questions which I hope

to address in this dissertation.

But atomistic methods were just one manifestation of a bigger trend: the

push to integrate computational methods into engineering, not only as a

tool to calculate equational models, as an entirely new way of formulat-

ing and testing hypotheses – and this is the topic of the next section.

II.3. COMPLEXITY SCIENCES, COMPUTATIONAL SCIENCE, AND AGENT-BASED MODELING

II.3.1. A BRIEF HISTORY OF AGENT‐BASED MODEL‐ING 

The past two decades have witnessed a true scientific revolution:

Science is becoming computational. The power and importance of

computational representations are not merely a thought exercise. A re-

cent report from the National Science Foundation on Simulation-Based

Engineering Science stated,

“For over a decade, the nation’s engineering and science communi-ties have become increasingly aware that computer simulation is an indispensable tool for resolving a multitude of scientific and technol-ogical problems facing our country” (Oden et al., 2006).

This is even truer in fields such as materials science. Computer simula-

tion is not just a verification or visualization tool anymore, but also a

scientific instrument that generates and confirms first level hypotheses,

as Vicsek states:

"Traditionally, improved microscopes or bigger telescopes are built to gain a better understanding of particular problems. But comput-ers have allowed new ways of learning. By directly modeling a system made of many units, one can observe, manipulate and understand the behavior of the whole system much better than before. […] In

59

this sense, a computer is a tool that improves not our sight (as does the microscope or telescope), but rather our insight into mechanisms within complex systems." (Vicsek, 2002)

Not serendipitously, in less than a decade, science is experiencing

groundbreaking advances in genomics, biomedical engineering, new

materials, and nanoscale chemistry – disciplines in which computational

methods are intensively utilized. Granted, the abundance of computa-

tional power is a crucial driving force behind this sea change in scientific

research, but it is only part of the story. A fundamental philosophical dis-

tinction is behind the transformation: scientists are focusing on the

modeling of individual atoms, molecules or cells (microsimulation), in-

stead of the traditional focus on macroscopic attributes of systems (ma-

crosimulation). A principal methodology for conducting microsimula-

tion, Agent-Based Modeling (ABM), has grown considerably over the

last two decades, mainly due to its explanatory power to address some

analytically-intractable phenomena previously beyond the reach of re-

searchers due to their innate complexity. In their introduction to agent-

based modeling, Wilensky and Rand (2009) trace the history of the

agent-based modeling field. One important source they identify is cellu-

lar automata theory as developed by von Neumann and Conway (Gard-

ner, 1970; Neumann, 1966). Cellular automata are systems consisting of

a regular discrete grid, in which each element in the grid (or cell) has a

finite number of states. At every time step, the state of the cell is updated

based on a pre-defined rule based on the neighborhood of the cell. They

used local interactions to generate global behaviors, which served as a

proof-of-concept that simple rules could give rise to complex, emergent

phenomena.

Wilensky and Rand identify many distinct sources for the origins of

ABM. They point to an important but often neglected source for the

idea of an agent – the Logo turtle (Papert, 1980) which was an early

60

precursor of an embodied behaving agent. Other important sources in-

clude Monte Carlo methods and stochastic modeling which provided

some of the tools and knowledge necessary to understand probabilistic

models (Metropolis and Ulam, 1949). Monte Carlo methods (named

after the capital of Monaco and of games of chance), randomly sample

from a Probability Distribution Function describing the physical system,

and perform a trial on that sample according to a predefined set of rules.

Depending on the results of the trials, successful trials are kept, unsuc-

cessful trials are discarded (based on the predefined rules), the system is

updated, and the process is repeated. Two characteristics of Monte Car-

lo methods granted them exceptional power over differential methods.

A carefully defined sample size enables the modeler to achieve impress-

ing precision by testing a relatively small number of elements within a

system. In chemistry or physics, this opened up a myriad of research

possibilities, since the actual systems under scrutiny were comprised of

millions of elements, and thus were almost impossible to simulate com-

putationally without sampling. In addition, Monte Carlo methods ena-

ble the study of systems in which equilibrium occurs only locally (Rol-

lett & Manohar, 2004)

CA and Monte Carlo methods are important ancestors of modern ABM.

There were several other modeling approaches that were also in its

roots. System dynamics modeling provided insight into how to model at

the aggregate level, as opposed to the individual level (Forrester, 1968),

but even aggregate modeling provided clues as to how to build complex

models. Additionally, one crucial advantage of ABM is the ability to

create adaptive agents that can change not only their actions over time

but also their strategies; this work has been heavily influenced by evolu-

tionary computation (Holland, 1995).

61

As the technology and knowledge for ABM was being created, scientists

in other fields were already applying this approach to their research.

Schelling (1971) did not have a modern-day computer, and so he used

nickels and dimes to symbolize his agents and a checkerboard to de-

scribe his environment in his research on residential patterns in urban

settings. Cohen (1972) used the concepts of March and Simon (1958)

to create a model of organizations using agents. Axelrod (1984) ex-

plored the evolution of cooperation by giving many agents different

strategies in a shared game. Anderson, Srolovitz and collaborators

(1984b; 1984) succeeded at simulating grain growth in metals using a

Monte Carlo approach, eventually matching with great precision the

analytical solutions. Reynolds (1987) used some of the techniques de-

veloped in work on parallel computation and Logo to create his models

of birds flocking. DeAngelis and others (1992) were using individual-

based models to explore ecological systems. In biology, researchers tried

to model the development of cell cultures, ant colonies or whole ecolo-

gies in terms of exclusively local interaction rules (Judson, 1994). In ar-

tificial intelligence, Minsky (1986) hypothesized that the intelligent

mind could be deconstructed into non-intelligent micro-agents, each

performing uncomplicated, non-intelligent, cognitive operations.

Rapidly, researchers began to realize that agent-based modeling was not

only as potentially accurate as macrosimulation, but could also enable

the exploration of previously uncharted territory in chemistry (Troisi,

Wong, & Ratner, 2005), physics (Wolfram, 2002), biology (Grimm &

Railsback, 2005), economics (Arthur, 1994), social science (Axtell, Axe-

lrod, Epstein, & Cohen, 1996; Maroulis & Wilensky, 2005, 2006), anth-

ropology (Kohler & Gummerman, 2001), business (North & Macal,

2006), political science (Axelrod, 1984) and evolution (Holland, 1995).

62

These multiple research tracks eventually coalesced in the field of ABM.

In the mid-eighties, Cliff Lasser and Steve Omohundr at the Thinking

Machines Corporation (1985) created StarLisp to program the nascent

Connection Machine, one of the first computers for massive parallel

computation. In the early nineties, at the MIT Media Laboratory, Res-

nick and Wilensky (1990) developed StarLogo as the first general-

purpose ABM language (at the time called object-based parallel modeling

language). StarLogo’s designers had a particular interest in its educa-

tional applications and worked to incorporate it into learning environ-

ments. Researchers at the Santa Fe Institute (SFI) (Arthur, 1991; Wal-

drop, 1992), MIT and at the University of Michigan (Holland & Miller,

1991), among other places, began to realize that ABM was a separate

computational method, deserving its own research and study. At Tufts

University, StarLogoT (Wilensky, 1997) was developed, which would

ultimately lead to Wilensky’s authoring of NetLogo modeling environ-

ment (Wilensky, 1999b)4.

In contrast to most other ABM languages, Wilensky designed NetLogo

with great attention to both “low threshold” and “high ceiling” criteria

(Tisue & Wilensky, 2004). NetLogo became the only ABM environ-

ment in wide use both by researchers and educators and across different

age groups. At SFI, Langton and others (1997) developed the Swarm

simulation system, developed for the purpose of building agent-based

models. John Holland at the University of Michigan formalized his

thoughts on the basic tenets of agent-based models in Hidden Order

(Holland, 1995). Since these early days there has been an explosion of

interest in ABM, which has led to the development of new computa-

tional toolkits and languages like, Repast (Collier, Howe, & North,

4Later in this text we will more extensively discuss NetLogo’s design and evolution over the last decade.

63

2003), and MASON (Luke, Cioffi-Revilla, Panait, Sullivan, & Balan,

1995).

The use of ABM in computational science is, thus, dramatically chang-

ing the theory, practice, and professional motivation of scientists and

engineers. Computational agent-based science is less about purely nu-

merical outputs and more about emergent behaviors and qualitative

larger-scale patterns, less about static and deterministic equilibria and

more about dynamic and stochastic processes; therefore its very nature

encourages the modeling of complex systems instead of simple systems

(Wilensky, Blikstein, & Rand, 2008; Wilensky & Rand, 2009). Also,

ABM is converting scientists into true polymaths of the 21st century, un-

earthing similarities between apparently disparate phenomena in biolo-

gy, sociology, chemistry, economics, and physics. The same local micro-

scopic rules that describe the movement of atoms in a crystal could be

used to describe population flow, the development of local dialects, and

the ascension and demise of whole economies, as Wilensky and Jacob-

son state:

“Complex systems approaches, in conjunction with rapid advances in computational technologies, enable researchers to study aspects of the real world for which events and actions have multiple causes and consequences, and where order and structure coexist at many differ-ent scales of time, space, and organization. Within this complex sys-tems framework, critical behaviors of systems that were systematical-ly ignored or oversimplified by classical science can now be included as basic elements that account for many observed aspects of our world” (Jacobson & Wilensky, 2006).

II.3.2. COMPLEX SYSTEMS IN MATERIALS SCIENCE In materials science, complex systems and its derived approaches (i.e.,

molecular dynamics, ABM, cellular automata, Monte Carlo methods)

have truly revolutionized the field. Since the fifties, ab initio models (de-

signing materials “on paper” based solely on first principles, such as ba-

64

sic atomic properties) have fascinated materials scientists (Ceder, 1998)

– but the absence of powerful computers and software was a significant

stumbling block. However, after the seminal papers by Anderson, Srolo-

vitz et al. in the early eighties (1984a), an unstoppable sequence of pub-

lications followed, in fields such as crystal growth, adhesion, crystalliza-

tion, and diffusion (M. P. Anderson, Grest, & Srolovitz, 1985; M. P.

Anderson et al., 1984a, 1984b; Hassold & Srolovitz, 1995; Rollett, Sro-

lovitz, Anderson, & Doherty, 1992; Srolovitz, Grest, & Anderson,

1986). Srolovitz’ inspiration came from Ising and Potts models, well-

know to physicists (for an excellent review of the history of ABM in ma-

terials science, see Rollett & Manohar, 2004). Working for a corporate

research lab, Srolovitz happened to have a physicist as his cubicle neigh-

bor who was working on Ising models5 – one day, he got interested in

trying out such models to a classical problem in materials science, which

was also heavily dependent on ‘local’ behaviors and rules: crystal

growth. Srolovitz’ motivation for creating the first ABM crystal growth

algorithm is revealing: for decades, materials scientists had tried to

model how multiple metallic crystals (or “grains”) evolve under high

temperature, but the complexity of the problem was daunting: analyti-

cally, it was close to impossible to model hundreds of asymmetrically-

shaped and placed crystal boundaries moving in all directions at differ-

ent rates and subject to local and global fluctuations in temperature and

concentration (Srolovitz, 2007). His idea of using local rules proved so

effective that in the interval of three years, his team published an un-

precedented five full papers at the top metallurgy journal (Acta Metal-

lurgica) by simply generating variations of the local rules of the model.

All five were unique and original, but the relatively ease which with Sro-

5 I interviewed David Srolovitz about his work on ABM in materials science.

65

lovitz was able to generate new data altering simple local behaviors is

one of the key affordances of ABM – and made him famous.

Another important affordance of ABM is ridding materials scientists of

the long-standing curse of having to abuse numerical methods to solve

multi-body problems in real-world materials, as Ohno et al. states:

“Since materials are complex in nature, it has never been possible to treat them directly by theory: experimental studies have always been the main method in materials research. In the past, physical con-cepts could only be applied to pure crystals, and real materials with defects and grain boundaries could not be treated theoretically. Re-cent progress in computer technology is now opening a new era in which one can treat real, complex materials as they are.” (Ohno, Es-farjani, & Kawazoe, 1999, p. 1)

The exact same issue has plagued for decades engineering education, and particularly materials science education. The theoretical models re-quire several adaptations to be meaningful in ‘real’ materials, and these numerous adaptations are difficult to learn due to their sheer number and specificity. At the same time, the results coming from the engineer-ing lab oftentimes generate purely empirical results, or ‘engineering laws,’ that frequently do not connect well to theory – especially in the heads of overwhelmed learners.

Computational methods and ABM could realize the ultimate dream of the field: design materials based on first principles (ab ignitio calcula-tion), as Gerbrand Ceder wrote in Science:

“It has always been a dream of materials researchers to design a new material completely on paper, optimizing the composition and processing steps in order to achieve the properties required for a giv-en application. In principle, this should be possible, because all the properties of a material are determined by the constituent atoms and the basic laws of physics. […] Although still in its infancy, the field of computational materials science, or "computational alchemy" […] has become one of the most promising developments in mate-rials research”. (Ceder, 1998)

66

The ‘ultimate dream’ of researchers could also be the dream of engineer-ing educators, since computational methods could better connect theory and real materials. The excitement about computational me-thods in materials science motivated a myriad of new research directions and graduate programs, which coalesced into the new field of computa-tional materials science. In recent years there have been numerous na-tional scientific efforts calling for an even more comprehensive and radi-cal integration of computational methods. For example, the National Research Council has recently published two landmark reports: “In-spired by Biology: From Molecules to Materials to Machines” (Committee on Biomolecular Materials and Processes, 2008) and “Integrated Compu-tational Materials Engineering: A Transformational Discipline for Improved Competitiveness and National Security” (Committee on Integrated Com-putational Materials Engineering, 2008).

Today, a significant part of the research breakthroughs in materials science are driven by advances in computational methods – in particu-lar, agent-based methods and its related methodologies. Whereas the new computational research tools are enabling researchers to accelerate scientific discovery and explore uncharted territory within their fields, computational methods have not yet reached the mainstream engineer-ing classroom. Thornton and Asta (2005) conducted a comprehensive survey about the state of computational Materials Science in undergra-duate and graduate courses at the 20 leading programs in the United States. While many universities are creating or planning to initiate com-putational materials science courses, one striking conclusion is that the prevailing mindset advocates that students should learn modeling after learning the traditional science. Thornton and Asta detected a worrying, but not surprising, phenomenon: computational modeling is currently regarded as “icing on the cake” to take place after the “real” scientific understanding, and not as an integral part of learning science – in other words, it is currently believed that students should learn the science be-fore the modeling, not by modeling. However, as early as the nineties some educators were already aware of the significant cognitive advan-tages of building models – as the next section will show.

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II.4. AGENT-BASED MODELING IN EDUCATION

II.4.1. INTRODUCTION The generativity and conceptual support of agent-based modeling did

not stop at scientists. Indeed, ABM research took an important turn

with the realization, by Wilensky and Resnick (Resnick & Wilensky,

1993, 1998; Wilensky & Resnick, 1995, 1999), that it was not only a

powerful tool for scientists but had particular ‘learnability’ properties –

and thus learning by modeling would be even more beneficial. Inspired

by the Logo programming environment, and constructionist pedagogies

(Papert, 1980, 1991), they created a computer programming environ-

ment for learners to “think with” computational agents: StarLogo (Res-

nick & Wilensky, 1992). Wilensky and Resnick hypothesized about the

learning implications of modeling phenomena using local rules and be-

haviors, instead of the traditional aggregate representation convention-

ally taught in science classrooms. As Wilensky states,

“An understanding of patterns as emergent phenomena, rather than as results of equations, is both a more accurate picture of nature AND easier for most people to understand. Science becomes more accessible, not less, as a result of this change in viewpoint.” (Wi-lensky, 2001b)

For instance, to study the behavior of a chemical reaction, a student us-

ing agent-based modeling would observe and articulate only the beha-

vior of individual molecules — the chemical reaction is construed as

emerging from the myriad interactions of these molecular “agents.”

Once the student–modeler assigns agents their local, micro rules, she or

he can set them into motion and watch the overall patterns that emerge.

Behaviors of individual atoms, molecules, or animals are more intuitive

and easier to understand than the corresponding macro-behaviors of

chemical reactions, flocks of birds, or whole populations. Thus, using

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ABM, the mathematical machinery and sophistication required to un-

derstand the phenomenon under scrutiny decreases significantly. Mi-

cro-behaviors more often than not are simpler than the macro-behaviors

they generate. For example, temperature is a macroscopic, aggregate de-

scription of a microscopic state of individual molecules (their speed or

energy), just as pressure is an aggregation of the number of collisions be-

tween gas molecules and the walls of the container.

This work has been carried on by several researchers over the past dec-

ade, and there is strong evidence, for many age groups, that it is easier

for students to understand simple rules governing one agent than ma-

croscopic, abstract laws. Nonetheless, there are also initial resistances to

some aspects of ABM. One of them is that students tend to see central

control where control is distributed and emergent (a flock of birds, for

example, has no leader), what Wilensky and Resnick called the deter-

ministic/centralized mindset (Resnick & Wilensky, 1993; Wilensky &

Resnick, 1999). But after a brief interaction with agent-based modeling

tools, students would abandon the centralized mindset in favor of an

emergent view. ABM-inspired activities flourished in a variety of set-

tings: undergraduate chemistry (Stieff & Wilensky, 2003), high-school

chemistry (Levy, Kim, & Wilensky, 2004; Levy, Novak, & Wilensky,

2006; Wilensky, 1999a, 2000a), probability and statistics (Abrahamson

& Wilensky, 2005; Wilensky, 1995), complex systems and robotics

(Berland & Wilensky, 2005, 2006), biology (Buckley et al., 2004; Hme-

lo-Silver, Marathe, & Liu, 2007; Hmelo-Silver & Pfeffer, 2004a), physics

(Sengupta & Wilensky, 2005), evolution (Centola, Wilensky, &

McKenzie, 2000a; Wilensky, Rand, Novak, & Nichols, 2005), and sev-

eral other fields (Horwitz, Gobert, Wilensky, & Dede, 2003; Klopfer,

2003; Repenning, 2000; Resnick, 1994).

69

As described in the Introduction, the constructionist approach to learn-

ing and educational design (Papert, 1991) was at the core of the very

first complex systems tools used in education (StarLogo and NetLogo):

building models (as opposed to interacting with pre-built models) was

the core activity in these early implementations. This does not come as a

surprise, since the very nature of the ABM approach was to construct

complexity departing from simple elementary parts, which is central to

constructionism and to the Logo programming language (its first soft-

ware implementation). One of the crucial insights of Logo was the pro-

grammable turtle. It put the child-programmer in a radically new, ‘ego-

centric’ perspective: instead of describing the world “from the outside,”

the Logo programmer sees it through the eyes of the turtle he/she con-

trols through code – the idea of the turtle itself was the idea of an agent.

Thus there is a natural fit between the tools (Logo, StarLogo, NetLogo)

and the constructionist approach.

However, the aforementioned ABM-in-education designs, materials,

and curricula were not all made equal. For different reasons, some de-

signs and implementations shifted their focus from building models to

interacting with pre-build models (as extensively discussed in Wi-

lensky, 2003). One reason was scale – some designers wanted to “scale

up” their implementations, and electronically-delivered scripted curricu-

la seemed like an efficient solution (e.g., Buckley et al., 2004). Other re-

searchers were more interested in novice vs. expert studies of complex

sciences instead of full-blown model-building implementations (Hme-

lo-Silver et al., 2007; Jacobson, 2001), while some had a stronger inter-

est in interaction with model-based curricula (Stieff & Wilensky, 2003).

This diversity of projects and goals, together with an oftentimes diffuse

use of the term “constructionism,” as well as multiple interpretations of

what would qualify as a constructionist microworld (or simply an ani-

70

mation-based curricula, or “demonstration modeling,” Wilensky, 2003)

could be problematic for evaluating or implementing these novel learn-

ing tools. In what follows, I will examine existing research and projects in

the field in order to develop a framework and a classification scheme for

different computer- and model-based curricula.

A first important criterion to set apart these designs refers to the exis-

tence of curriculum in building models is at the core of the acticities, ver-

sus the interaction with models. I will refer to building-based construc-

tionist curricula (BBC) designs in which students’ main task is to build

models, as opposed to interaction-based constructionist (IBC).

The important of this distinction is manifold. The consequences of a de-

sign choice between BBC and IBC activities are significant. In IBC activ-

ities the designer has to focus on creating sequences of models with careful

interface design, and well-planned transitions between models. In BBC

activities, the designer’s foci are good code example, model examples,

and efficient materials/tutorials to support students in learning how to

program models. These examples and materials have to focus not only

on content matter but also on students’ modeling and coding skills. Evi-

dently, the human and technological infrastructure to implement a BBC

activity will be very different from an IBC activity. This is one of the

elements of the framework developed in the last part of the review,

which will guide my classroom implementation as well as my analysis of

the epistemic forms of the complexity sciences.

II .4.1.1. Open question: How to embed constructionist modeling activit ies in engineering classrooms?

Most of the work in agent-based modeling in education has focused on

middle- or high- school, after school projects, or large-scale implementa-

tions of scripted curriculum. Fewer researchers have focused on incor-

porating constructionist modeling activities within engineering class-

71

rooms, particularly as part of a regular course. There are several impor-

tant questions and design tradeoffs related to this goal: How open-

ended should the activities be? How to provide adequate support? How

much should students access the code of a model, and how much would

they just observe a pre-programmed model?

II .4.1.2. Open question: What are the characterist ics , ad-vantages, and trajectories of scientif ic content knowledge articulated in epistemic forms unique to complexity sciences?

One of the hallmarks of the complexity sciences is their new ways to

represent knowledge – local versus macroscopic behaviors, algorithmic

rules versus differential equations. I want to further the cognitive re-

search on those novel epistemic forms, particularly when students en-

gage in longer-term modeling tasks.

Addressing these open questions, I believe, is crucial to both provide

more evidence of the learnability claims of complexity scientics, and also

provide better roadmaps for educators interested in implementing ABM

in real classrooms.. Thus, in what follows, I will review many ABM-

inspired curricula, and develop a framework for analyzing the different

affordances, design choices, and outcomes for each.

II.4.2. A FRAMEWORK AND TAXONOMY TO ANALYZE 

EDUCATIONAL AGENT‐BASED SOFTWARE Wilensky’s (2003) pioneering framework addressed one dimension of

this analysis, identifying different modeling styles and approaches to

model-based curricula:

1. Aggregate vs. Agent-Based Modeling: Wilensky compares aggregate modeling tools, such as STELLA (Richmond & Peterson, 1990), and agent-based environments, such as RePast (Collier & Sallach, 2001), Swarm (Langton & Burkhardt, 1997), and NetLogo (Wilensky, 1999b). System dynamics tools replace purely algebraic representation with stocks and flows, but they are ontologically still

72

similar, in which the variables and measurements are aggregate and macroscopic. Object-based modeling goes one step further by shifting the focus to the actual ‘agents’ of the model.

2. Phenomena-Based (“backwards”) modeling (Wilensky, 1997b; Resnick and Wilensky, 1998) vs. Exploratory (“forwards”) modeling) (Wilensky, 1997b): in phenomena-based modeling, modelers first choose a phenomenon (i.e., the behavior of an ideal gas in a container) and try to create a model of it. In ‘forwards’, or exploratory modeling, modelers first explore different sets of rules and then iteratively try to match them to some known phenomenon.

3. Construction vs. observation: Wilensky identifies 5 steps for progressing from observation to model construction (Wilensky, 2001):

Phase 1: The teacher engages students in off-computer activities to provoke thinking about emergent phenomena. Sometimes this phase also takes place as a computer-based participatory simulation (Wilensky & Stroup, 2000, 2002), in which a server runs a classroom-wide simulation while each students controls one on-screen agent through their computers.

Phase 2: A “seed” model is presented and discussed with the whole class

Phase 3: Students run the model and explore its parameter space.

Phase 4: Each student (or group) proposes and implements an extension to the model. The extended models are added to the project’s library of extensible models and made available for others to work with as “seed” models.

Phase 5: Students propose a phenomenon and build a model of it “from scratch.”

I extend Wilensky’s taxonomy and develop a series of dimensions along

which model-based curricula and activities could be evaluated. Since

model-based activities vary greatly in their theoretical underpinnings,

technologies, visualization sophistication, learning goals, and pedagogi-

cal approaches, it is crucial for researchers and practitioners to clearly

map out the space of possible combinations of content, modeling peda-

gogies, and implementation strategies. Based on my review of previous

73

work, I constructed a taxonomy based on a number of dimensions and

rubrics. In subsequent chapters, I justify my design choices based on the

constraints and characteristics of my specific case studies. This taxono-

my, extending Wilensky’s, was conceived having in mind the particular

goals and open questions that I intend to investigate, but also as a gener-

al purpose classification scheme for educational designers. The twelve

dimensions that I utilize are explained below.

Dimension 1: Type of user experience

1.1 Observation Students just observe a running simula-tion or animation.

1.2 Interaction Students observe a simulation and can change some exposed parameters.

1.3 Interaction with minor code changes

Students observe a simulation, change its exposed parameters, and can make minor changes to the code.

1.4 Extending a model Students extend a model in a significant way, adding a new core feature.

1.5 Designing a model Students can design rules in verbal lan-guage or pseudo-code, but not coding it entirely.

1.6 Building a model Students can build entire models from scratch, including the coding.

Dimension 2: Curriculum navigation

2.1 Strictly-structured Students are taken from one micro-activity within a model to the next in a strict fashion.

2.2 Semi-structured Students can choose a particular se-quence of activities within a model, or a particular sequence of models, within some pre-defined paths or structures.

2.3 Open-ended Students can freely choose which mod-els to explore and how to explore them.

Dimension 3: Emergent algorithms

3.1 Low Models do not employ any emergent behaviors. All behaviors are hard-coded.

3.2 Medium Some behaviors are deterministic/hard-coded, some are emergent.

3.3 High The most significant behaviors are emergent.

Dimension 4: Media

4.1 On-screen only All models are exclusively on-screen.

4.2 On-screen with non-computational physical arti-facts

All models are exclusively on-screen, but the activities involve other non-computational media (paper cutting, manipulatives, etc.)

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4.3 On-screen with asynchron-ous computational physical artifacts

Models are on-screen, but students use sensors or robotics to interact with the physical world, asynchronously.

4.4 On-screen with synchron-ous computational physical artifacts

Models are on-screen, but students use sensors or robotics to interact with the physical world, synchronously.

Dimension 5: Data validation

5.1 No validation Validation of the model data is not present in the activity

5.2 Qualitative validation Approximate visual validation, either through the model’s visualization win-dows or plot(s) of aggregate results.

5.3 Quantitative validation with published data

Comparison of large sets of aggregate results from the model with published empirical or theoretical data.

5.4 Quantitative validation with collected data

Comparison of large sets of aggregate results from the model with empirical data collected by the modeler.

Dimension 6: Transparency of the code/rules

6.1 Opaque The code and the rules of the simulation are not accessible for users.

6.2 Semi-transparent: rules vis-ible

The code is not visible, but the overall rules of the system are visible in an al-ternative representation (block dia-grams or pseudo-code).

6.3 Transparent: code visible The code is visible, but not changeable.

6.4 Transparent and changea-ble

The code is visible and changeable.

Dimension 7: Modeling methodology

7.1 Phenomena-based (back-ward modeling)

Modelers choose one phenomena and try to create a model of it.

7.2 Mixed-mode Modelers switch between phenomena-based and exploratory modes.

7.3 Exploratory (forward mod-eling)

Modelers explore different sets of rules until they match some known pheno-menon.

Dimension 8: Data collection automation

8.1 No automation Data collection is not automated; users must run each individual experiment by hand.

8.2 Scripted automation Data collection is automated, but the batches of experiments are pre-scripted in the activity.

8.2 User-defined automation Data collection is automated; modelers design their own batches of experi-ments.

Dimension 9: Communication between users

9.1 No interac- By design, users interact with the system with no contact with other users

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tion/communication

9.2 Analog communication, non-simultaneous

Users communicate with one another through analog channels, after the activ-ity (e.g., for example, after the modeling session, they are encouraged to talk to one another)

9.3 Analog communication, simultaneous

Users communicate with one another through analog channels, during the activity (e.g., during the modeling ses-sion, they are encouraged to talk to one another)

9.4 Computer-based communi-cation, non-simultaneous

Users communicate with one another through computer-based channels, after the activity (e.g., after the modeling session, they are encouraged to email each another)

9.5 Computer-based communi-cation, simultaneous

Users communicate with one another through computer-based channels, during the activity (e.g., during the modeling session, they are encouraged to instant-message)

Dimension 10: Participatory interactions

10.1 No participatory interac-tions

Users do not engage in participatory interactions

10.2 Participatory interaction, asynchronous

Users interact with one another through an asynchronous server-based computer simulation, in which users have an active role (e.g., users send messages to the server, which runs the simulation asyn-chronously)

10.3 Participatory interaction, synchronous

Users interact with one another through a server-based computer simulation, in which students have an active role (e.g., each student plays an agent during the modeling session)

Dimension 11: Graphical realism

11.1 Text-based/no graphics Text-based interface, no graphical visua-lization

11.2 Simple graphics Graphical visualization with simple geometric shapes only, such as squares, circles, triangles.

11.3 Intermediate graphics Graphical visualization with interme-diate graphics: geometric, freeform shapes, simple effects.

11.4 Elaborate graphics Graphical visualization with elaborate graphics: geometric shapes, freeform shapes, photos, transparency, shading, true color.

11.5 Photo-realistic Photo-realistic visualization, with com-plex shapes, pictures, shading and tex-tures.

Dimension 12: Maximum visualization dimensions

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12.1 1D Unidimensional visualization

12.2 2D Bidimensional visualization

12.3 3D 3D visualization

II .4.2.1. Connected Chemistry The Stieff & Wilensky (2004) version of Connected Chemistry, tar-

geted for undergraduate students in chemistry, is an evolution com-

pared to the typical ‘electronic book’ model-based curricula such as

ViMS, MATTER and DoITPoMS (“electronic books” – see section

II.2.4). First, it is not a sequence of scripted web pages and models, but

rather a collection of models that can be employed in more flexible ways

in the classroom. Second, all the behaviors follow simple agent-based

rules and the simulations are not mere recorded animations or movies,

i.e., they happen in real time as students explore them. A third and im-

portant difference (and also a departure from conventional “educational

applets”) is that the code can be inspected by students, and thus beha-

viors and algorithms are not disconnected.

Stieff & Wilensky reported positive results in undergraduate chemistry

classrooms: students’ interactions with the models enabled them to re-

conceptualize chemical equilibrium and correctly identify many of the

factors affecting it (previously regarded as a ‘static’ phenomenon). Stieff

& Wilensky attribute this cognitive gain to the possibility, afforded by

the design, for students to transition between micro-, macro- and sym-

bolic levels.

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Figure II-11 A Reaction Kinetics model

enabling students to change several variables

 

Summary:

Dimension 1: Type of user experience – 1.2 (Interaction)Dimension 2: Curriculum navigation – 2.2 (Semi-structured) Dimension 3: Emergent algorithms – 3.2 (Medium) and 3.3 (High) Dimension 4: Media – 4.1 (On-screen only)Dimension 5: Data Validation – 5.2 (Qualitative validation) and 5.3 Dimension 6: Transparency of the code/rules – 6.4 (Code visible/changeable)Dimension 7: Modeling methodology (N/A) Dimension 8: Data collection automation – 8.2 (Scripted automation) Dimension 9: Communication between users: 9.1 (No communication) Dimension 10: Participatory interactions : 10.1 (No interactions) Dimension 11: Graphical realism : 11.3 (Intermediate graphics) Dimension 12: Maximum visualization dimensions 12.2 (2D)

II .4.2.2. Molecular Workbench Influenced by Wilensky and others’ joint work on the MAC/Connected

Chemistry project (see previous section), the Molecular Workbench

(MW), by the Concord Consortium, is another type of model-based

educational design, addressed in particular to educational designers (not

students) to author model-based curricula. There are advanced options

78

for interface design and interaction (changing sliders and parameters),

but students cannot modify the code or change the activities. Most cur-

ricula built with MW are scripted sequences of models (note the snap-

shot of a scripted activity in Figure II-12, left). Because MW is an au-

thoring system rather than a fixed disciplinary curriculum, both aggre-

gate- and object-based models are plausible within its authoring system.

Indeed, some models of Gas Laws or Brownian motion exhibit emer-

gent behaviors, but since the code hidden from students, the perception

of emergence is limited to the behavior of the on-screen objects. Indeed,

in Figure II-12 (right), we observe a modeling activity in which students

can add atoms to a model to observe their trajectory. However, details of

the simulation’s code which would be key for deeper understanding of

the phenomenon. One example is how the implementation of elastic

collisions are hidden (Stieff & Wilensky, 2003). A plot of the Maxwell-

Boltzmann distribution can be achieved using the data from the simula-

tion, however, a deep understanding of such distribution would be facili-

tated by analyzing the model’s code (Wilensky, 1999a, 2003), which is

not possible in MW.

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Figure II-12 A scripted model-based activity

for investigating Brownian Motion

        

Summary:

Dimension 1: Type of user experience – 1.2 (Interaction)Dimension 2: Curriculum navigation – 2.1 (Strictly-structured) Dimension 3: Emergent algorithms – 3.2 (Medium)Dimension 4: Media – 4.1 (On-screen only)Dimension 5: Data Validation – 5.1 (No validation)Dimension 6: Transparency of the code/rules – 6.1 (Opaque) Dimension 7: Modeling methodology – (N/A) Dimension 8: Data collection automation – 8.1 (No automation) Dimension 9: Communication between users: 9.1 (No communication) Dimension 10: Participatory interactions : 10.1 (No interactions) Dimension 11: Graphical realism : 11.2 (Simple graphics)Dimension 12: Maximum visualization dimensions 12.2 (2D)

II .4.2.3. Modeling Across the Curriculum (Connected Chemistry)

The Connected Chemistry curriculum (CC1, see Figure II-13), within

the Modeling Across the Curriculum (MAC) project (Gobert et al.,

2004; Levy et al., 2006; Levy & Wilensky, 2004) is an example of model-

based curricula with sophisticated options for user interaction, but with-

in a strict sequence of activities. Compared to Molecular Workbench, its

innovation is mainly around its exclusive reliance on emergent beha-

80

viors. Compared to the Stieff & Wilensky’s version of Connected Che-

mistry, it offers some open-ended features, such as ‘zand-box’ modules

and the possibility to type in text commands in the command center to

control the simulation. The code, however, is hidden from students, but

the emergent algorithms are minimally explained in text along the curri-

culum.

In several papers, Levy, Kim, Novak & Wilensky (Levy et al., 2004; Levy

et al., 2006; Levy & Wilensky, in press-a, in press-b; Wilensky, 1999a,

2000a) report, also, positive results in students learning Kinetic Molecu-

lar Theory with the curriculum. Most students transitioned from a pure-

ly macroscopic view of pressure, for example, to a macro/micro perspec-

tive – in fact, the correct understanding of the micro and macro levels of

the concept of pressure went from 6% in the pre-test to 65% in the post-

test.

Figure II-13 Screenshot of a model-based

activity 

 

Summary:

Dimension 1: Type of user experience – 1.2 (Interaction)Dimension 2: Curriculum navigation – 2.1 (Strictly-structured) Dimension 3: Emergent algorithms – 3.3 (High)

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Dimension 4: Media – 4.1 (On-screen only)Dimension 5: Data Validation – 5.2 (Qualitative validation)Dimension 6: Transparency of the code/rules – 6.2 (Rules visible) Dimension 7: Modeling methodology (N/A) Dimension 8: Data collection automation – 8.1 (No automation) Dimension 9: Communication between users: 9.1 (No communication) Dimension 10: Participatory interactions : 10.1 (No interactions) Dimension 11: Graphical realism : 11.3 (Intermediate graphics) Dimension 12: Maximum visualization dimensions 12.2 (2D)

II .4.2.4. ProbLab Probability Laboratory – ProbLab (Abrahamson, Janusz, & Wilensky,

2006; Levy et al., 2004) is a suite of models for exploring probability and

statistics. It does not include a pre-set sequence of models or a step-by-

step curriculum, but rather a set of activities that can be mixed-and-

matched in the classroom (such ProbLab activities also exist and were

implemented in the classroom). Compared to other curricula, such as

Connected Chemistry, it brings two innovations. First, some of its activ-

ities employ off-screen media. In the “Combinations Tower” activity

(Abrahamson & Wilensky, 2002, 2004c) students build a paper-based

histogram while exploring analogous computer models, or use a “marble

scooper” to sample marbles from a box. Second, it uses the HubNet ar-

chitecture (Abrahamson & Wilensky, 2004a; Wilensky & Stroup, 2002)

for engaging whole classrooms in participatory simulations, in which

each student play the role of one agent within the classroom simulation.

ProbLab activities do not emphasize changes to the model’s code (sim-

ple code changes have taken place in some implementations), or creat-

ing new models. Emergence is a key component of the suite of models,

since the aggregate results (the combinations tower, for example) are ef-

fectively constructed from non-deterministic micro-behaviors.

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Figure II-14 Dice Stalagmite model: students

observe the emergence of a normal distribution

 

Summary:

Dimension 1: Type of user experience – 1.2 (Interaction)Dimension 2: Curriculum navigation – 2.2 (Semi-structured) Dimension 3: Emergent algorithms – 3.2 (Medium)Dimension 4: Media – 4.2 (On-screen with non-comp. physical artifacts) Dimension 5: Data Validation – 5.3 (Qualitative validation with data) Dimension 6: Transparency of the code/rules – 6.3 (Code visible) Dimension 7: Modeling methodology (N/A) Dimension 8: Data collection automation – 8.1 (No automation) Dimension 9: Communication between users: 9.3 (Analog, simultaneous) Dimension 10: Participatory interactions : 10.3 (Participatory, synchronous) Dimension 11: Graphical realism : 11.3 (Intermediate graphics) Dimension 12: Maximum visualization dimensions 12.2 (2D)

II .4.2.5. NIELS NetLogo Investigations in Electromagnetism – NIELS (Sengupta & Wi-

lensky, 2005) is a set of models and activities built in the tradition of

curricula such as Connected Chemistry, in which learners interact with

models rather than building or modifying them. In NIELS, students in-

teract with models guided by worksheets in a pre-determined sequence.

NIELS brings innovations in terms of visualization. For example, stu-

dents can easily follow and visualize one electron in the electrical wire.

83

Also, in the Coulomb’s Law model, learners can not only observe the

model and change parameters, but ‘build their own’ atom by manipulat-

ing different electrical charges with the mouse. Different versions of

NIELS exist – in some of them, for the sake of code simplicity and age-

appropriateness, the complexity of some behaviors was greatly reduced.

For example, the actual mechanism giving rise to electrical resistance,

the collisions between electrons and atoms, is replaced by a ‘catch-all’

collision-rate parameter, and the atoms are not represented in the mod-

el. This is a different take than, for example, the Connected Chemistry

curriculum, in which the collisions are at the core of the model and also

the learning goals behind the curriculum. In newer versions of the curri-

culum, atom-eletron collisions were introduced, and thus students’ per-

ception of emergence was emphasized.

Similarly to the aforementioned designs, the authors reported positive

results. Interacting with NIELS and reasoning at the micro, atomic level,

5th graders were able to conceptualize resistance and Ohm’s Law as the

emergent result of a myriad of moving electrons along a conductor

(Sengupta & Wilensky, 2005). NIELS also has a HubNet version.

Figure II-15 The Ohm’s law model, in which students can change sliders and observe the resulting current in

the conductor

 

Summary:

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Dimension 1: Type of user experience – 1.2 (Interaction)Dimension 2: Curriculum navigation – 2.2 (Semi-structured) Dimension 3: Emergent algorithms – 3.2 (Medium)Dimension 4: Media – 4.1 (On-screen only)Dimension 5: Data Validation – 5.2 (Qualitative validation)Dimension 6: Transparency of the code/rules – 6.3 (Code visible) Dimension 7: Modeling methodology (N/A) Dimension 8: Data collection automation – 8.1 (No automation) Dimension 9: Communication between users: 9.3 (Analog, simultaneous) Dimension 10: Participatory interactions : 10.3 (Participatory, synchronous) Dimension 11: Graphical realism : 11.3 (Elaborate graphics) Dimension 12: Maximum visualization dimensions 12.3 (3D)

II .4.2.6. BEAGLE Biological Experiments in Adaptation, Genetics, Learning and Evolution

(BEAGLE) is a suite of models to explore evolution and genetics (No-

vak & Wilensky, 2007). Similarly to Connected Chemistry and NIELS,

it emphasizes the interaction with pre-built models. That design choice

stems from its implementation plan: it is designed to be a stand-alone

curriculum to be deployed in schools with minimal human, on-site sup-

port. BEAGLE is probably the most complete and advanced “non-

model-building” curriculum, since it intensively makes use of emergent

behaviors, has comprehensive documentation, detailed guides for

teachers and students, and carefully designed activities for a variety of

classroom scenarios. BEAGLE also enables users to see its extensively

commented code, and employs the HubNet (Wilensky & Stroup, 2002)

architecture for classroom-wide participatory simulations. It is the only

participatory simulation which has been deployed to a new always-on

HubNet web platform, which enables for dozens of users to connect si-

multaneously to the server and play evolution games online. BEAGLE is

particularly effective because it enable learners to easily grasp challeng-

ing concepts such as catastrophic population imbalances, inheritance,

phenotypes/genotypes, and survival of the fittest, since all of these ideas

can be easily represented in terms of simple agent rules.

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Figure II-16 One of Beagle’s model enabling

users to interact and change some parameters

 

Summary:

Dimension 1: Type of user experience – 1.2 (Interaction)Dimension 2: Curriculum navigation – 2.2 (Semi-structured) Dimension 3: Emergent algorithms – 3.3 (High)Dimension 4: Media – 4.1 (On-screen only)Dimension 5: Data Validation – 5.2 (Qualitative validation)Dimension 6: Transparency of the code/rules – 6.3 (Code visible) Dimension 7: Modeling methodology (N/A) Dimension 8: Data collection automation – 8.1 (No automation) Dimension 9: Communication between users: 9.2 (Analog, simultaneous) Dimension 10: Participatory interactions: 10.3 (Participatory, synchronous) Dimension 11: Graphical realism:11.3 (Intermediate graphics) Dimension 12: Maximum visualization dimensions: 12.2 (2D)

II .4.2.7. EACH Project The goal of the Evolution of Altruistic and Cooperative Habits project

(EACH) was to “develop sets of activities that would enable students to de-

velop intuitions about the complex dynamics of individuals and groups in an

evolutionary system” (Centola, Wilensky, & McKenzie, 2000b). The

project’s design had four major phases: (1) students view a projected

model and engage in classroom discussions, (2) students explore the

pre-built models on their own (3) students change the model’s code,

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and (4) students create their own conceptual models and code them.

Therefore, the EACH project had a special focus on building models,

and had pre-designed “seed” models to both guide students’ explora-

tions of particular phenomena, and inspire them to pick a topic to build

a model from scratch. The authors reported quite impressive learning

gains for the participants. One particularly difficult concept in popula-

tion dynamics is the interaction among individual traits, group characte-

ristics, and environmental factors. While building a model, one student

quickly realized that the competition of “greedy” and “cooperative”

populations was very much dependent on the mobility of these popula-

tions (viscosity). Greedy and mobile populations would always out-

compete cooperative populations, but greedy localized populations

would perish.

Figure II-17 Screenshots of the original

EACH models

Summary:

Dimension 1: Type of user experience – 1.6 (Building)Dimension 2: Curriculum navigation – 2.2 (Semi-structured) Dimension 3: Emergent algorithms – 3.3 (High)Dimension 4: Media – 4.1 (On-screen only)Dimension 5: Data Validation – 5.1 (No validation)Dimension 6: Transparency of the code/rules – 6.4 (Code visible/changeable)Dimension 7: Modeling methodology – 7.2 (Mixed-mode)Dimension 8: Data collection automation – 8.1 (No automation) Dimension 9: Communication between users : 9.2 (Analog, simultaneous) Dimension 10: Participatory interactions : 10.1 (No participatory interactions)

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Dimension 11: Graphical realism:11.3 (Intermediate graphics) Dimension 12: Maximum visualization dimensions: 12.2 (2D)

II .4.2.8. VBOT VBot (Berland & Wilensky, 2004, 2006) is an agent-based curriculum

that includes model building in its very core – VBot is a construction kit

for building and programming robots. The goal in VBot is for students to

collectively build and program virtual (or physical, in PVBot) robots to

achieve a pre-defined task. The task can be as simple as chasing a light

source, or a more elaborate game, such as variants of the Disease Spread

activity, in which students assume various roles (doctor, patients, etc.)

The physical VBot (PVBot) activities are slightly different – typically, a

simplified version of “robot soccer.”

The results reported by the authors suggest that, in both the virtual and

physical versions of VBot, building circuits to control the behavior of

one agent within a larger system resulted in deeper understanding of

some key complex systems concepts, such as decentralized control and

emergence. VBot implemented many innovative features, such as the

ability to share circuits with other players, and an extensive logging ca-

pability, which enable researchers to inspect students’ behavior in

minute detail (for example, investigating patterns of communication

and complexity of circuits built.)

In terms of its strong constructionist inspiration, the authors reported

that “students learned as a result of being able to play relatively freely

with the system,” and that students’ desire to tinker with the system was

the main motivational factor (equally across genders.) Particularly, the

study shows that “sharing, tinkering, and performance were strongly

correlated.” (Berland, 2008)

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Figure II-18 In VBot, students create their

own circuits and see their friend’s circuits

 

Summary:

Dimension 1: Type of user experience – 1.6 (Building)Dimension 2: Curriculum navigation – 2.3 (Open-ended)Dimension 3: Emergent algorithms – 3.2 (Medium)Dimension 4: Media – 4.3 (On-screen with asynch. comp. physical artifacts) Dimension 5: Data Validation – 5.1 (No validation)Dimension 6: Transparency of the code/rules – 6.4 (Code visible/changeable)Dimension 7: Modeling methodology – 7.3 (Exploratory)Dimension 8: Data collection automation – 8.1 (No automation) Dimension 9: Communication between users : 9.4 (Computer-based, simultaneous)Dimension 10: Participatory interactions : 10.3 (Participatory, synchronous) Dimension 11: Graphical realism:11.3 (Intermediate graphics) Dimension 12: Maximum visualization dimensions: 12.2 (2D)

II .4.2.9. Summary A common denominator in most studies is that authors report that even

a simple interaction with agent-based models can effect significant

changes in conceptual understanding. Despite ABM’s constructionist

roots, it branched out considerably over the past decade, and there is a

large variety of model-based curricula and activities, each differing sig-

nificantly from the other with respect to the 12 dimensions analyzed, as

89

well as their theoretical underpinnings and desired learning outcomes.

For example, non-ABM projects such as MATTER rely simply on the

notion that sheer visualization is “good” for learners (MATTER was re-

viewed in the first section of the Literature Review). Molecular Work-

bench, on the other hand, espouses the idea that model-based curricula

should focus on interaction with models (not just looking at them), but

with no insight into the algorithms. Connected Chemistry, NIELS, and

BEAGLE, allow for more advanced interactions since they enable learn-

ers to see the underlying code and minimally interact with it. In contrast,

in VBot students build models from scratch. This simple difference ge-

nerates an important distinction in the implementation strategies, sup-

port materials, and expected outcomes. These trends can be better ob-

served in Table II-1 (note that it is not an attempt to rank or grade the

curricula, but to identify high- and low-density areas.)

90

Table II-1 Summary data

Some clear trends are that can be inferred from the data and the sum-

mary table are:

91

Strictly and semi-scripted curricula are the majority.

More often than not, rules and code are visible for users.

There are relatively less building-based constructionist curricula (BBC) model-building curricula than interaction-based constructionist (IBC).

There are fewer curricula with quantitative data validation with published or collected data, as well as data collection automation.

The importance of identifying these trends is manifold. For example, the

consequences of a design choice between BBC and IBC activities are

significant. In IBC activities, the designer has to focus on creating se-

quences of models with careful interface design, and well-planned transi-

tions between models. In BBC activities, the designer’s foci are good

code examples, “seed” models, model examples, and efficient mate-

rials/tutorials to support students in learning how to program models.

These examples and materials have to focus not only on content matter

but also on students’ modeling and coding skills. The human and tech-

nological infrastructure to implement a BBC activities will be very dif-

ferent, as a result.

Also, there is a feedback cycle between the creation of advanced scientif-

ic models and quantitative data validation, since modelers oftentimes

use real data to validade and refine their models. That is perhaps a rea-

son for the relatively fewer projects with data validation – if the learner is

not building models, quantitative data validation is less useful. If the user

is simply interacting with models, there is an assumption that the given

model is correct (at least in terms of the fundamental rules).

Communication among users is also a desirable feature of model-

building designs – in VBot, one of the important predictors of perfor-

mance was the number of shared circuits per user (Berland, 2008). This

can also be easily confirmed by the “boom” of communication and col-

laboration tools focused on the open-source development community,

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to whom sharing pieces of code is fundamental. From the review, it

seems that VBot is the only project which has implemented a communi-

cation scheme within its core software framework.

Therefore, this analysis suggests that the twelve dimensions are not li-

nearly independent – some design elements go together. Building-

based constructionist curricula (BBC) requires an ecology of activities

and resources to make it effective – automated data validation, commu-

nication, “seed” models, code transparency, materials, and support.

However, the results are also qualitatively different. The two predomi-

nantly BBC projects in this review, EACH and VBot, reported strong

evidence for the usefulness of building. In VBot “sharing, tinkering, and

performance were strongly correlated.” (Berland, 2008). In EACH, it

was not before Goeff (one of the participants) built his own model with

“mobility viscosity” that he had the fundamental insight on how to fa-

thom the interaction between two different factors in cooperation and

competition.

However, the interaction-based constructionist curricula also reported

important conceptual gains amongst students. But they do not report as

often students going beyond the content that was originally built into the cur-

ricular unit. It seems, therefore, that BBC curricula could be more appli-

cable when the given content is a springboard for students, rather than

the “finishing line.” Interaction-based constructionist curricula, on the

other hand, could be more effective when the designer has a very defi-

nite content agenda (note, for example, that most IBC curricula had a

very definite disciplinary goal – gas laws, electromagnetism, etc.)

II.4.3. IMPLICATIONS OF ABM FOR MATERIALS 

SCIENCE EDUCATION At an aggregate level, many engineering phenomena become rapidly

complicated, and thus numerous equations and models have to be em-

93

ployed to predict them, oftentimes “mixing-and-matching” different le-

vels of explanation and mathematical modeling approaches, making

them particularly difficult for students to learn. In a typical undergra-

duate materials science class, students can be exposed to as many as one

new equation every 2.5 minutes (Blikstein & Wilensky, 2006a). On the

other hand, at the microscopic level, the number of events and pheno-

mena influencing a local interaction is dramatically lower than at an ag-

gregate level, due to the fact that the many of the variables observed ma-

croscopically are just emergent properties of the local behaviors. Thus,

aggregate descriptions are much more sensitive to the superposition of

variables, parameters, and phenomena than agent-based descriptions. I

refer to this pedagogical approach as many-to-one: many models and

equations to describe one phenomenon, and suggested that although

the many-to-one modeling approach might describe well properties of

materials in real-world engineering, this multitude of models can be an

obstacle to student understanding, since the mathematical machinery to

weave them together is sophisticated. As Wolfram would say,

“And this, I believe, is the fundamental reason that traditional theo-retical science has never managed to get far in studying most types of systems whose behavior is not ultimately quite simple. […] it is in-evitable that the usual methods of traditional theoretical science will not work. And indeed I suspect the only reason that their failure has not been more obvious in the past is that theoretical science has typi-cally tended to define its domain specifically in order to avoid phe-nomena that do not happen to be simple enough to be computation-ally reducible." (Wolfram, 2002, p. 741)

A crucial feature of the agent-based approach is the capture of the intri-

cacy of the phenomenon in just one model – and a simple one which,

being close to the elementary atomistic behavior, could be used to un-

derstand other phenomena within a field as well – a one-to-many mod-

eling framework (Blikstein & Wilensky, 2005, 2006b).  

94

The one-to-many perspective could be especially useful in a scenario of

increasing technological complexity and specialization. The number of

materials, alloying elements, fabrications techniques, and industrial ap-

plications has grown so quickly and vastly that “covering” all the know-

ledge by simply adding new information to the curriculum would be in-

feasible. Additionally, the high level of abstraction that the new advances

in materials science are bringing makes it increasingly difficult to give

students any real world intuition for the ideas learned in the classroom,

as well as clear connections with their previous knowledge.

II.4.4. RESTRUCTURATIONS Both traditional methods and computer-based methods of investigating

grain growth rely on modeling. The scientific enterprise is the process of

creating models that are the best approximations to reality we can find.

The models of each period reflect the tools available at that time. Tradi-

tional scientific models in materials science employed the best represen-

tational tools available – mathematical equations. This reveals one

common practice in many fields of academic research, in particular en-

gineering. The availability of certain technologies for research shapes

how researchers approach a certain problem, and the subsequent “en-

coding” of the knowledge is heavily influenced by those technologies. As

the initially empirical or exploratory hypothesis gradually transition to

becoming full-blown theories, they transmit much of those influences to

the theories themselves, and consequently to the curricula. Therefore, as

Wilensky and Papert suggest in their seminal papers on restructurations

(Wilensky & Papert, 2006; Wilensky, Papert et al., 2005) the “encoding”

of the knowledge could be a function of the research technology, the

state of the field itself, and not an intrinsically superior way of structur-

ing knowledge.

95

First, in materials science, many of the traditional formulas themselves

are opaque—they embody so many layers of accumulated scientific

knowledge into such a complex and concise set of symbols that they do

not afford common-sense insight and grounding of the causal mechan-

isms underlying the phenomena they purport to capture. Differently

from the basic sciences, engineering knowledge is a complex matrix of

empirical “engineering laws,” theories derived from fundamental ma-

thematical or physical models, approximations, and rules-of-thumb.

Making sense of this complex matrix is challenging.

Secondly, there is an important distinction to be made in how represen-

tations relate to the phenomena they purport to describe. We are not ar-

guing that equational representations are intrinsically ill-suited for learn-

ing engineering or science. Far from it – there are many cases in which

equational representations are fruitful for learning. Sherin (2001), for

example, showed how the symbolic manipulation of formulas can lead

to a gain in conceptual understanding in physics. However, Sherin also

discusses that different symbol systems could have different relation-

ships with content. He characterizes algebra-based physics as “a physics

of balance and equilibrium” and programming-based physics as “a phys-

ics of processes and causation” (Sherin, 1996).

We are arguing that in some cases equations can hide important infor-

mation needed for learning. In some areas of science, equations are di-

rectly postulated at the macro level, i.e., they are not necessarily an ag-

gregation of simpler, local behaviors, or the microscopic behaviors are

not relevant to the phenomenon under scrutiny. For example, in simple

Newtonian motion, we are interested in predicting the motion of bo-

dies, but looking at the individual atoms of the body might not offer ad-

ditional insight into the phenomenon—the macroscopic and micro-

scopic behaviors could be analogous, i.e., the body and its atoms would

96

be moving in the same fashion. In such areas, equations reveal most of

the needed information. In other domains, however, the opposite is

true: equations are an aggregation of microscopic behaviors, and those

offer fundamental insights into the phenomenon, and are not analogous

(for example, statistical mechanics, or diffusion). Therefore, for the lat-

ter categories of phenomena, aggregate equational representations

might generate an epistemological gap—the mathematical machinery

needed to derive macro behaviors from micro behaviors is intricate, and

frameworks to guide such work are still being developed (see, for exam-

ple, Daniel, 2005; Parunak, Savit, & Riolo, 1998; Wilkerson-Jerde & Wi-

lensky, 2009). This epistemological gap makes it difficult to keep track

of how micro- and macro-level parameters are related and influence

each other, or to understand how intuitive, simple micro-behaviors are

represented in aggregate analytical forms. An exclusive use of equational

representations for those types of phenomena can constitute an obstacle

for students in acquiring conceptual understanding in domains of engi-

neering in which the interaction of microscopic entities is at the core of

the content matter. For those phenomena, in which equational repre-

sentations represent an aggregation of micro-behaviors, it seems to be

especially beneficial to unpack and deconstruct the traditional aggre-

gate representations, restructuring domains of knowledge around the

study of local, individual, “non-aggregated” phenomena (Wilensky &

Papert, 2006; Wilensky, Papert et al., 2005).

Restructurations of domains have three crucial aspects: the representa-

tional, the cognitive, and the pedagogical. The representational aspects

of restructurations refer only to a change in representation. That process

can happen independently from any cognitive or pedagogical intentions

or implications. For example, when Anderson et al. (1984a) devised a

new way to represent grain growth, they were not concerned with issues

97

of learnability, but exclusively concerned with building a powerful scien-

tific model. The fact that their model was both scientifically powerful

and cognitively advantageous is not a mere coincidence, since the mod-

el’s algorithm was closer to atomic behaviors, and those behaviors, in the

case of materials science, happen to be more learnable. However, that

might not be always the case—depending on the scientist’s interest and

level of analysis, his/her restructured domain might be harder to learn,

even using agent-based representations. For example, Newtonian phys-

ics might be more learnable from a macroscopic perspective than from

an atomistic perspective with billions of interacting atoms, but for a par-

ticular scientific endeavor, the atomistic perspective might be more po-

werful.

The pedagogical aspect of restructurations is a third important pillar in

this puzzle. A restructured domain might call for different teaching

strategies. In the case of materials science, a structuration based on deep

knowledge of atomic behaviors might call for students to learn to design

such behaviors, therefore, student-centered pedagogies, such as con-

structionism, would be more adequate, as I will discuss in more detail

throughout the dissertation.

II.5. SUMMARY OF THE CHAPTER This chapter had five goals:

a. Show that there is a strong reform effort in engineering schools, and that these efforts are geared at offering students more opportunities for engineering design.

b. Lay out the evolution of the use of digital media in engineering edu-cation, and point out how this evolution was coupled with available technological tools and research trends.

c. Explain how the complexity sciences are changing the practice of scientists, and how radical of a transformation it is generating in the

98

way researchers represent knowledge. Additionally, show how ma-terials science was one of the most transformed fields of knowledge.

d. Review several model-based learning designs in order to develop and refine a particular framework and taxonomy.

e. Finally, suggest some open questions and gaps in related literature, such as:

Research on digital media in engineering education have not focused on issues of representation apart from HCI considerations.

Tools for doing, tools for building, tools for visualizing: not all uses of computers in engineering education are made equal – a taxonomy of different modeling and implementation approaches is necessary to evaluate their ultimate goal, effectiveness and affordances.

The language of design, the language of ABM: are there preferred representational encodings for different classes of phenomena (for example, phenomena involving a few bodies, compared to phenomena with thousands of units)? What are the characteristics, advantages, and trajectories of scientific content knowledge articulated in epistemic forms unique to complexity sciences?

The “design-versus-analysis” dilemma: How to apply the wealth of research on design-based or project-based pedagogies in areas where there is not “tangible” final project (such a robot, or a car)? Can we extend these pedagogies to analysis courses? Could BBC modeling activities fulfill this role in real-world engineering classrooms?

    

99

  

  

III REPRESENTATION COMPARISON 

100

III.1. SUMMARY One of the main research questions of this dissertation is: What are the

specific learning affordances and representational properties of agent-

based modeling compared to equational forms? To illustrate the differ-

ences between those two representational infrastructures, in this chapter

I will examine in detail two canonical phenomena in materials science:

grain growth and diffusion. The analysis will start with a description of

the phenomena, followed by an explanation of the two representations,

and a discussion.

III.2. GRAIN GROWTH III.2.1. THE PHENOMENON There are three main reasons for choosing grain growth as a canonical

example: (1) it is one of the most important phenomena in materials

science; (2) it was the first phenomenon successfully modeled with

agent-based-like approaches (M. P. Anderson et al., 1984a, 1984b), and

(3) the fit of the analytical and the ABM solutions is impressive, and

both representations are widely accepted in the scientific community

(Kinderlehrer, Livshits, & Ta’asan, 2006; Rollett & Manohar, 2004).

Before diving into the representations, a brief explanation of the phe-

nomenon itself is necessary.

Most materials are composed of microscopic crystals. Even though we

commonly associate the term “crystal” with the material used in glass-

ware manufacturing, its scientific use is different. A crystal is just an or-

derly arrangement of atoms, a regular tridimensional grid in which each

node is occupied by an atom. Therefore, a crystalline material has its

atoms orderly arranged in a regular geometrical grid. Conversely,

amorphous materials (such as glass) have a random atomic arrange-

ment. Since the vast majority of the metals used in our industries are

101

crystalline, understanding how these geometrical grids form and evolve

is of crucial technological and scientific importance. In materials

science, scientists use the term “grain” to refer to each crystal within a

material (see Figure III-1.)

Among other properties, grain size determines how much a material will

deform before breaking apart, which is one of the most important issues

in engineering design. For example, a car built with steel with a wrong

grain size could just fall apart during normal use, or could be destroyed

even in a minor accident. But grain size can change, too, when the tem-

perature is high, and enough time is given for the process to unfold –

typically hours. This phenomenon, known as grain growth, is exhaustive-

ly studied in materials science. Due to the increased temperature, there

is increased atomic movement, and atoms tend to move to locations

where they are more stable: the emergent result of atoms relocating to

more stable positions is that the surface area between grains in mini-

mized. If left for a very long time, the entire material would be com-

posed of just one grain – a monocrystal – a scenario in which the sample

would be mostly homogeneous (except for impurities) and any atomic

movement would be merely random.

Macroscopically, during grain growth, what is observed is that, due to

the minimization of grain boundary area, small grains disappear while

bigger ones grow (the overall volume is maintained) – which has intri-

gued materials scientists for decades. Airplanes turbines, for instance,

can reach very high temperatures in flight – an incorrectly designed ma-

terial could undergo grain growth and simply break apart. The following

photographs (magnified 850x) show typical results for steel before (left)

and after (right) 20 hours of heat treatment under 900ºC.

102

Figure III-1 Metallic sample before and after grain growth, during 20 hours at

900ºC (Blikstein & Tschipt-schin, 1999)

   

III.2.2. EQUATIONAL REPRESENTATION OF GRAIN GROWTH: A MANY‐TO‐ONE APPROACH 

Burke (1949) was one of the first to introduce a law to calculate grain

growth and proposed that the growth rate would be inversely propor-

tional to the average curvature radius of the grains:

nR kt= (III.1)

where R is the mean grain size of the grains at a given time, t is time, k is

a constant that varies with temperature, and n depends on the purity and

composition of the material, as well as other initial conditions (its theo-

retical value is 0.5 for pure materials under ideal conditions). Therefore,

generally, it is a logarithm growth:

graindiameter (time )na (III.2)

In other words, Burke’s law states that large grains (lower curvature ra-

dius, or R) grow faster, while small grains (high curvature) have slower

growth, or shrink. The mathematical formulation of Burke’s law also re-

veals that, as grains grow, the growth rate decreases. A simple derivation

of expression(III.2), substituting n for 0.5, shows that:

103

1

growth rate2 time

a (III.3)

A system composed of numerous small grains (see Figure III-1, left)

would have a very fast growth rate, while a system with just a few grains

(see Figure III-1, right) would change very slowly. One of Burke’s ap-

proximations was to consider grains as spheres with just one parameter

to describe their size (their radius). For most practical engineering pur-

poses (and, also, due to the primitive technologies available to measure

grain size in the nineteen-fifties), this approximation yields acceptable

results – however, as we previously discussed, its practical efficacy does

not necessarily mean that this approach is the best way to understand the

phenomenon. One example of potential learning issues with the spheri-

cal approximation is that it is not a space filling geometry, whereas actual

grains do fill entirely the 3D space—which is an important aspect of the

phenomenon. After all, grain growth is not about expansion of the ma-

terial, but rearrangement of its atoms, keeping the volume constant.

Indeed, traditional engineering teaching relies on a large number of ad-

hoc models, approximations, metaphors, and practical shortcuts, which

have been accumulating over decades. They constitute a web of ideas of

very different natures, granularities, levels of analysis, and mathematical

descriptions. Due to the applied and integrative aspect of engineering

research and practice, oftentimes explanations are drawn from a variety

of sources: empirical equations, geometrical proof, thermodynamics, al-

gebraic deductions, or statistical mechanics. My classroom observations

revealed that, for explaining grain growth and deriving Burke’s law, at

least three sources were employed during the classes covering the phe-

nomenon:

The Laplace-Young equation for pressure is commonly used in fluid dynamics to calculate surface tension in liquid-gas interfaces

104

(such as a drop of water). It states that the surface tension grows as the pressure difference is increased, and as the radii of curvature decreases. In other words, any small grain (with a low radius of curvature) will have high surface tension (and thus less stability), as opposed to large grains. The equation is written as follows:

2

p pR

b a g= + (III.4)

c

du V dp= (III.5)

where pa and pb are the outside and inside pressures, R is the spherical particle radius, du the change in chemical potential, and

cV the partial molar volume.

The flux equation (based on statistical mechanics), which states that the probability of an atom to jump to a neighboring grain increases exponentially with temperature, and therefore the mobility of a grain boundary also grows with temperature. The equation is written as follows:

1 2 2 1 1exp

grain grain

GF An

RT

a

n

æ öD ÷ç ÷= ç ÷ç ÷÷çè ø (III.6)

where F is the flux, 2A is the probability of the atom being

accommodated in the other grain, 1n the number of atoms in grain 1

in position to make the jump, 1 the vibrational frequency of an atom in grain 1.

Geometrical approximations are a common technique used to calculate average grain size. Real grains are asymmetrical, which poses a problem for equational models. For example, to model the effect of impurities in grain growth, the impurity is also approximated as a sphere, and the grain boundary as a uniform, well-behaved surface. When they hit each other, a force (P) is applied by the stationary particle to the moving grain boundaries, halting or stopping its movement, and is given by:

sin(2 )P rp q g= (III.7)

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where P is the force, q is the angle with the grain boundary, r is the particle radius.

I refer to this pedagogical approach as many-to-one: many models and

equations to describe one phenomenon. Although the many-to-one model-

ing approach might describe well properties of materials in real-world

engineering, as I will show in this dissertation, this multitude of models

can be an obstacle to student understanding, since the mathematical

machinery to weave them together is sophisticated, and the process

takes a significant toll on classroom time.

III.2.3. AGENT‐BASED REPRESENTATION OF GRAIN GROWTH: A ONE‐TO‐MANY APPROACH 

Massive computing power, in the early eighties, has made a new and

promising approach possible: computer simulation of grain growth. An-

derson, Srolovitz et al. (1984a, 1984b) proposed the widely known

theory for computer modeling of grain growth using the multi-agent

based approach (then referred to as “Monte Carlo method”). This kind

of simulation allowed for a completely new range of applications. Re-

searchers were no longer constrained by approximations or general equ-

ations, but could make use of more precise mechanisms and realistic

geometries. As stated by Anderson, Srolovitz et al. (1984a):

“While it is generally observed that large grains grow and small grains shrink, instances where the opposite is true can be found. [...] The results indicate the validity of a random walk description of grain growth kinetics for large grains, and curvature driven kinet-ics for small grains.” (1984a)

In other words, they state that the classic rule-of-thumb for grain growth

(“large grains grow, small grains shrink”) is not always valid, and that

randomness plays an important role. Curvature driven kinetics is accu-

rate for small grains, but less precise for configurations with larger grain

sizes. Given the microscopic spatial and temporal scale of the phenome-

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non, the only way to conceptualize and visualize this new finding is

through computer simulation. In contrast, the traditional methods for

investigating grain size and growth reflect the tools (and visualization

techniques) that were available in the nineteen-fifties: mathematical ab-

stractions, geometrical modeling, approximations, and empirical data.

These traditional methods and techniques, having become the methods

of choice to explain the phenomena, made their way to textbooks and

classrooms and were solidified as the mainstream path to study grain

growth. Aa rule of thumb which described only partially a behavior

(“large grains grow, small grains shrink”), despite being an artifact of the

existing representational infrastructure, became over time part of the

content itself. This tells an important and typical story of how many top-

ics in engineering curricula were originated as byproducts of representa-

tional practices and got integrated into textbooks and course notes

without further questioning.

The agent-based approach for modeling grain growth offers a different

perspective. Its principle is the thermodynamics of atomic interactions –

a simple micro-behavior. The first step in the model is to represent the

material as a square or triangular bidimensional matrix, in which each

site corresponds to an atom and contains a numerical value representing

its crystallographic orientation (the angle of orientation of the atomic

planes in one particular grain compared to an arbitrary fixed plane).

Contiguous regions (containing the same orientation) represent the

grains. The grain boundaries are fictitious surfaces that separate grains

with different orientations – but they have no physical representation in

the model, i.e., they are not objects in themselves. The grain growth al-

gorithm is described below, and is based on the calculation of the initial

and final energies of each element in the system:

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1. Each element (or agent) of the matrix has its energy6 (Gi) calculated based on its present crystallographic orientation and the count of neighboring atoms of different crystallographic orientation – the more neighbors of differing orientation, the higher the element’s energy.

2. Figure III-2 (left side), shows the central element (with crystallographic orientation 2) with four different neighbors (with crystallographic orientation 1), hence the value of its initial energy (Gi) is 4.

3. One new random crystallographic orientation is chosen for that central element among the orientations of its neighbors. In this case, as observable in Figure III-2, the current value of the central agent is 2 (left side), and the attempted new value will be 1 (right side).

4. The agent’s energy is calculated again (Gf), with the new proposed crystallographic orientation, 1. Figure III-2 (right side) shows that there are only two different neighbors in the new situation (black arrows), thus the final energy (Gf) decreases to 2.

Figure III-2 Initial and final energy calcula-

tions. Black and white arrows denote different or equal

neighbors

                         

5. The two states are compared, and the value that minimizes the energy is chosen. In this case, Gi=4 and Gf=2, so the latter value is lower and constitutes a state of greater stability. Interestingly, it is also easy to notice that the initial boundary had more curvature than the final one, which is straight.

A simple, non-technical summary of this model is: the more different

neighbors one has, the less stable one is, and thus more inclined to switch to a

different orientation.

6 Although the rigorous term would be “free energy,” for simplicity I will use “energy”.

1

1

1 1

2

2

2 2

21

1

1 1

1

108

A crucial feature of the agent-based approach is the capture of the intri-

cacy of the phenomenon in just one micro-behavior – and a simple one

which, additionally, as I will show in the next chapters, could be used to

understand other phenomena as well, such as diffusion or recrystalliza-

tion – in other words, a one-to-many modeling framework.

III.3. DIFFUSION III.3.1. THE PHENOMENON Diffusion, alongside with grain growth, is one of the fundamental phe-

nomena in materials science. Even Albert Einstein wrote extensively

about the topic, and was one of the first to connect diffusion to the

Brownian motion of atoms (A. Einstein, 1956). Diffusion can take place

in gases, liquids, or solids. In solids, particularly, diffusion occurs due to

thermally-activated random motion of atoms - unless the material is at

absolute zero temperature (zero Kelvin), individual atoms keep vibrat-

ing and eventually move within the material. One of the possible net ef-

fects of diffusion is that atoms move from regions of high concentration

of one element to regions with low concentration, until the concentra-

tion is equal throughout the sample. Since most real-world materials are

not perfect crystals, they have a certain percentage of “vacancies” – sites

that should be occupied by an atom but are actually empty. These voids

or vacancies play a central role, since atoms can “jump” into a vacant site

and leave a vacancy behind, which could be occupied by yet another

atom (‘substitutional diffusion’). Essentially, solid substitutional diffu-

sion is the process of atoms jumping into vacancies. The extent to which

the diffusion can happen depends on the temperature (related to the

“jump rate”), and the number of vacancies in the crystal7.

7 This is a simplification; there are various other conditions that are needed for solid diffusion to occur. Some examples of these are similar atomic size, similar crystal structure, and similar electronegativity.

109

III.3.2. EQUATIONAL REPRESENTATION OF DIFFU‐SION 

Traditionally, diffusion is taught as a series of equations related to Fick’s

laws, derived by Adolf Fick in 1855. His first law relates the flux of diffus-

ing atoms to the concentration gradient. In one dimension, it is ex-

pressed as:

J Dx

f¶=-

¶ (III.8)

where J is the diffusion flux (the amount of material that will flow

through a certain area in a given period of time), D is the diffusion

coefficient, which changes for each material, f is the concentration,

andx is the position. Fick’s first law states that the amount of material

diffusing is proportional to the concentration difference and the diffu-

sion coefficient. Fick’s second law relates the concentration gradient and

time, predicting how much time we should leave a particular material

under a given temperature to obtain a particular concentration profile:

2

2D

t x

f f¶ ¶=

¶ ¶ (III.9)

the units are the same, and t is time. Note that Fick’s equation for diffu-

sion is analogous to the heat equation, except that the diffusion coeffi-

cient would be replaced by the “thermal diffusion” coefficient, k . A mi-

riad of mathematical and physical models use some version of a Fick or

heat equation, such as Brownian motion, Schrödinger’s equation for a

free particle, and even stock market models for option pricing (such as

the Black–Scholes model.)

The power of Fick’s second law is considerable: it allows an engineer to

quickly compute, for example, how far would material “A” diffuse into

material “B,” given a fixed temperature and time interval. Departing

110

from Fick’s equations, we quickly obtain that the diffusion length, how

far would one material would diffuse into the other (d

L ) is given by:

4d

L Dt= (III.10)

and it follows that

2

4dL

Dt

= (III.11)

In other words, if we know the diffusion coefficient, it is very practical to

use such mathematical relationships to design a manufacturing process.

However, such mathematical formulation backgrounds important as-

pects of the phenomenon itself, as Ursell states in his (rather traditional)

undergraduate tutorial about diffusion:

“Given a group of non-interacting particles immersed in a fluctuat-ing (Brownian) environment, the movement of each individual par-ticle is not governed by the diffusion equation. However, many iden-tical particles each obeying the same boundary and initial conditions share statistical properties of their spatial and temporal evolution. It is the evolution of the probability distribution underlying these sta-tistical properties that the diffusion equation captures. The function ( , )c x t is a distribution that gives the probability of finding a per-

fectly average particle in the small vicinity of the point x at time t .” (Ursell, 2007, p. 2)

In other words, Ursell says that each particle is not following the diffu-

sion equation – that equation is just the aggregation of a myriad of “per-

fectly average particles” moving. The ‘jump’ from atomic to aggregate

behavior has deep consequences for the learning of diffusion. In a simi-

lar vein of the paper by Anderson & Srolovitz (1984a) on computational

simulation of grain growth, Ursell recognizes that there is a qualitative

and conceptual difference between the local and the global description:

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“The evolution of some systems does follow the diffusion equation outright: for instance, when you put a drop of dye in a beaker of wa-ter, there are millions of dye molecules each exhibiting the random movements of Brownian motion, but as a group they exhibit the smooth, well-behaved statistical features of the diffusion equation.”

Hence, it seems increasingly clear the issue of “levels” (Wilensky & Res-

nick, 1999) is at play in this case as well. However, in both examples,

what is at play are not solely the learning or pedagogical implications,

but the fundamental idea behind the phenomenon – Fick’s description

of diffusion, on its own, backgrounds the very mechanism of diffusion.

III.3.3. AGENT‐BASED REPRESENTATION OF DIFFU‐SION 

Similarly to grain growth, the agent-based representation of diffusion

follows a simple neighborhood-based rule: atoms ‘look around’ and try

to find a vacancy, and have a certain probability of moving into that va-

cancy. Schematically, the model follows these three simple steps (also

see Figure III-4):

Figure III-3 The agent-based diffusion

algorithm

 

Step 3

If I have at least one vacancy around me, I move to its location. If I have two or more vacancies, I randomly pick one.

Step 2

I look around and count the number of vacancies around me.

Step 1

Atoms are randomly activated (or “asked” perform an action.)

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Figure III-4 Atoms surround a vacancy,

constantly vibrating, until one manages to have enough energy

to make its way to the vacancy

The agent-based model does not “know” about Fick’s differential equa-

tions, however, it departs from Fick’s very principles and integrates it

over time – without backgrounding the mechanism of diffusion.

But could these simple rule match, at least numerically, Fick’s well-

established results? Overtime, the two materials in a diffusion pair

would penetrate each other up to a certain distance, max

L . From equa-

tion (III.11), we know that 2d

L t should be constant, and the plot li-

near. Indeed, a run of NetLogo’s diffusion model (Wilensky, 2007) over

5,000 time steps yields a plot remarkably linear, on average, but main-

taining the stochastic characteristic of diffusion itself – note the irregular

shape of the curve in Figure III-5, bottom (the upper part of the picture

is a screenshot of the actual model.)

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Figure III-5 NetLogo’s diffusion model and a plot of 5,000 time steps showing

its fit to Fick’s laws

III.3.4. DISCUSSION Despite being based on similar stochastic, random walk, flux-based

processes, the equational representation of diffusion bears little resem-

blance to the equational formulation of grain growth. The driving force

for diffusion is a concentration gradient, while grain growth’s driving

force is the excess curvature of the boundaries. Therefore, their equa-

tional formulations depart from very different perspectives, and the final

inscriptions describing the processes are quite different.

114

Their micro-behaviors, however, are similar. In both cases, atoms are

looking at their neighbors to decide their next step based on a simple

energy-minimization rule. In the case of grain growth, the central atom

attempts to change its state to lower the number of different neighbors.

In diffusion, instead of counting different neighbors, atoms “count”

neighboring vacancies, and move into their location. But the applicabili-

ty of neighborhood-based rules does not stop at grain growth or diffu-

sion. Other key phenomena in materials science, such as solidification

and recrystallization, can also be explained in terms of neighborhood-

based rules. In solidification, for example, atoms in the liquid are ‘look-

ing around’ for solid clusters. When they hit an atom pertaining to a sol-

id cluster, they too become solid. Recrystallization is the process of crea-

tion of new crystals within a highly deformed material. The new crystals

have much lower energy than the old, deformed crystals, so the process

is energetically favorable. Again, a simple neighborhood-based rule can

describe the phenomenon: atoms can search for less-deformed (thus

lower-energy) regions and decide to recrystallize based on their present

and future energies. In Figure III-6 we can observe a visual summary of

the four phenomena, and in Table III-1 a summary of the algorithms

and pseudo-code representing them:

Figure III-6 A comparison of the four

phenomena: grain growth, diffusion, solidification, and

recrystallization

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Table III-1 A comparison of the four

phenomena, in terms of algorithms and pseudo code

Phenomenon Algorithm Pseudo-code Grain growth count atoms with

different orientation around the central atom, switch orienta-tion, decide

ask neighbors if orientation != my-orientation increase present-energy attempt-new-orientation ask neighbors if orientation != my-orientation increase future-energy if future-energy < present-energy keep-new-orientation

Recrystallization count atoms with different orientation around the central atom

ask neighbors calculate present-energy attempt-recrystallization ask neighbors calculate future-energy if future-energy < present-energy recrystallize

Diffusion count number ofvacancies around the central atom, and jump into it

if any? vacancy around me [move-to-vacancy]

Solidification count number of ‘solids’ around the liquid atom, and become solid

if any? solids around me [become-solid]

From Table III-1, it is clear that the similarities among the phenomena

are foregrounded when the agent-based representation is employed. For

example, diffusion (“if any? vacancy around me [move-to-vacancy]”) and

solidification (“if any? solids around me [become-solid]”) become clearly

two variations of the same mechanism – demonstrating the usefulness of

the one-to-many approach. Not only could students more easily transi-

tion in between different phenomena, but also be more prepared to un-

dertake scientific explorations employing just a few kernel models.

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In general, the examples of the equational representations of grain

growth and diffusion are illustrative of a common practice in many fields

of academic research, in particular engineering. The availability of cer-

tain technologies for research shapes how researchers approach a certain

problem, and the subsequent “encoding” of the knowledge is heavily in-

fluenced by those technologies—as described in the Introduction,

Georgius Agricola’s taxonomy of ore channels (1563/1950) is a canoni-

cal example of this process. As the initially empirical or exploratory hy-

pothesis gradually transition to becoming full-blown theories, they

transmit much of those influences to the theories themselves, and con-

sequently to the curricula. Therefore, as Wilensky, Papert and collabora-

tors (Wilensky & Papert, 2006; Wilensky, Papert et al., 2005) suggest in

their seminal work on restructurations, the “encoding” of the know-

ledge could be a function of the research technology, the state of the

field itself, and not an intrinsically superior way of structuring know-

ledge. Their work will be the theoretical guide for most of the analysis of

the dissertation. In the next chapter, we will dive deeper into that issue

by analyzing classroom transcripts and written materials, as well as in-

terviews with students.

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IV METHODS 

118

IV.1. SUMMARY I herein describe the methods utilized in the three studies of the disser-

tation, conducted during five spring quarters at the materials science

department of a Midwestern research arts university (2004, 2005, 2006,

2007, and 2008).

These studies are:

1. A three-year study consisting of classroom observations, recording and coding of classes, collection and analysis of course materials.

2. A three-year lab study with volunteer undergraduate students (n=6, in 2004, n=11 in 2005, and n=4 in 2006), in which students interacted with and built computer models.

3. A classroom implementation study (2007) with an entire materials science class (n=21), in which students interacted with and built models as part of a regular, graded, 4-week course assignment. This study also included a follow-up in which volunteers from the 2007 study were interviewed (n=4), alongside with sophomore students who did not have the treatment (n=4.)

In the following, I will describe each of those studies in detail. For clari-

ty, some details of the methodologies will be described in the data analy-

sis chapters themselves, as to avoid excessive repetitions, and also to be

able to present data and more detailed methods alongside, when neces-

sary.

IV.2. INTRODUCTION The research described in this dissertation lies in the intersection of en-

gineering education, constructionist learning, and complexity sciences

applied to education. The methods used will reflect this diversity.

One pillar of the research methods comes from the engineering educa-

tion literature, which is characterized by a bimodal distribution of me-

thodological approaches. Engineering education researchers have either

119

employed an almost simplistic stance toward research methods, or at-

temped very innovative methodological experimentation.

The origins of the first approach are understandable. During its first

decades, engineering education research was done by engineering pro-

fessors themselves, as a “side job” to their main research field. When the

dissatisfaction with the state of affairs in engineering education hit engi-

neering schools, cross-disciplinary collaborations with education

schools were uncommon, and learning sciences programs were still in

their infancy. Engineers, then, took matters in their own hands (see the

Literature review for a more detailed account). Despite their expertise in

their engineering fields, typically few had training in social sciences or

learning sciences. The result was a relatively simplistic approach, in-

spired by engineering quality control techniques: test, design, re-test.

For the most part, methods used included simple pre-post designs, HCI-

inspired questionnaires and protocols, or purely anecdotal descriptions

of how they changed a course or created a new activity. A prototypical

example of the first case is McManon at al. (1998) study, with eight stu-

dents divided into 2 groups (implementation group and control group)

in which the only instrument was a content-driven post-test. Anderson

& Hashemi (2006) created a comprehensive virtual laboratory for mate-

rials science learning, but out of five pages, dedicated two paragraphs for

the evaluation of the tools. Voller, Hoover & Watson (1998) created a

sophisticated fluid dynamics multimedia course but used only one-line

sentences from 7 students as evidence of success. Orr, Golas & Yao

(1994) study of multimedia learning systems for engineering attempted

to use classic HCI methods to detect how many interactive screens the

system should present to students per minute (for a review of the HCI-

related methods, see Stemler, 1997).

120

The other group of methodological approaches to engineering educa-

tion comprises innovative, hybrid approaches to attempt to capture the

full complexity of the engineering design experience. These approaches

will be more relevant to the dissertation. One of the first of such ap-

proaches was the “data triangulation” technique used by Agogino et al.

(Agogino et al., 2007; Dong et al., 2004). Well aware of the complexity

of the design process, Agogino devised the triangulation approach so as

to get a closer picture of the work of designers, simultaneously using

questionnaires/team documents, computational linguistics, and sketch

analysis. For example, they realized that designers used sketching not as

a substitute or placeholder for written text, but as a standalone, shared,

evolving document. Also, their sketch analysis protocol, when triangu-

lated with other sources of data, revealed rather non-intuitive findings,

such as (i) the volume of email exchanged within a design team has no

effect on student learning or group performance, (ii) the likelihood of

success is correlated with the thoroughness of the early exploration of

possible solutions to a problem, as revealed by the sketches, and (iii) the

level of detail of the sketches only becomes a good predictor of success

when students are in the late stages of design (Agogino et al., 2007). De-

spite not all of Agogino’s findings or methodological ideas being rele-

vant to this work, some principles and ideas will be employed. Namely, I

also employ the idea of tentatively triangulating apparently disparate da-

tasets (for example, computer code, verbal data, questionnaires, and

motivation plots), in order to dive deeper into the modeling process.

Similarly, the findings of my triangulated data oftentimes tell a counte-

rintuitive story. For example, the motivation plots (an instrument ex-

plained later in this chapter) revealed volatile levels of student motiva-

tion, which could not be detected by any of the other data sources alone.

What is more, student motivation was oftentimes the mirror image of

121

project advancement – the more advanced and complex the project, the

less motivated they were.

In terms of overall experimental design for the classroom implementa-

tions, my approach follows much of the constructionist literature: stu-

dents are assigned a project and work on it for a limited amount of time.

The researchers/facilitator then tracks and documents the entire

process and analyses the final artifact (for example, see Harel, 1990;

Martin, 1996; Papert, 1991; Papert & Harel, 1991). In particular, I draw

from the agent-based modeling tradition, in which the project is an

agent-based computer model of a scientific or social phenomenon. Wi-

lensky, Resnick and collaborators pioneered the methodology for using

such modeling approach in classrooms, and devised several strategies.

Wilensky identifies five steps for progressing from observation to model

construction (Wilensky, 2001b; Wilensky & Reisman, 2006):

a. Off-computer activities to provoke thinking about emergent phe-nomena.

b. “Seed” model is presented and discussed

c. Students explore the “seed” model.

d. Each student proposes and implements an extension to the model. The extended models are made available for others to work with as “seed” models.

e. Students propose a phenomenon and build a model of it “from scratch.”

Data collection in most of these studies is largely based on interviews

and artifact analysis. Their data analysis is mostly qualitative, despite

more recent efforts to use logfiles to detect patterns of interaction with

models (Levy & Wilensky, 2005, 2008). The coding and analysis is co-

herent with the characteristics of agent-based modeling as a representa-

tional infrastructure. Researchers try to identify, for example, pivotal

moments of conceptual change, such as “slippages between levels” (Wi-

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lensky & Resnick, 1999) (misattribution or misidentification of micro-

behaviors as macrobehaviors), failed expectations or surprises when

running/building a model, and moments of epistemic transition be-

tween centralized and decentralized descriptions of phenomena (Wi-

lensky & Resnick, 1999). In this analytical approach, each model-

building process is described both in the third person (the researcher in

storytelling mode, talking about the student’s progress), and with raw

transcriptions to exemplify some important moments. One example

comes from Wilensky & Resnick’s (1999) analysis of a high school stu-

dent (Benjamin) building a predator-prey StarLogo model:

Benjamin assumed that the rule for cloning would somehow “bal-ance” the rule for dying, leading to some sort of “equilibrium.” He explained: “Hopefully, it will balance itself out somehow. I mean it will. It will have to. But I don’t know what number it will balance out at.” After a little more thought, Benjamin suggested that the food supply might fall at first, but then it would rise back and become steady: “The food will go down, a lot of them will die, the food will go up, and it will balance out.” (p. 18)

In the above passage, the authors both tell the ‘modeling story’ and

show transcriptions of pivotal moments throughout the process. The

transcriptions, field notes, rules and pieces of computer code, therefore,

are merged into a unified narrative (Centola et al., 2000b; Wilensky,

2001b). I will also build on the foundational methodological work of

diSessa and Sherin (diSessa, 1993; Sherin, 2001), particularly, their

semi-clinical interviewing techniques.

My own methodological contribution will be focused on the specialized

instruments and frameworks I devised to analyze the artifacts generated

by students and their trajectories during the model-building process:

1. An analytical framework to compare and contrast students’ manipulation of different types of representations of materials

123

science phenomena, as well as a methodology to collect, code, and interpret teaching “artifacts” used in the classroom.

2. Rubrics to code the computer programs (“code the code”) as to assess the complexity of students’ agent-based models

3. An initial methodology to analyze the automated logfiles generated during the model construction process.

4. An instrument to represent self-reported motivation (the “motivation plot”)

In what follows, I will comments on the studies themselves and, intert-

wined with their descriptions, the different methodological contribu-

tions will be presented.

IV.3. STUDY 1: CLASSROOM OBSERVATIONS AND ANALYSIS OF CLASS MATERIALS

IV.3.1. RESEARCH QUESTIONS AND DATA SOURCES The goal of this study was to understand the current teaching approach-

es and knowledge representations used in a typical engineering class-

room, particularly in a course with theoretical engineering content. De-

sign courses, in which students create real engineering projects in a

project-based fashion, seem to be far more researched than strictly theo-

retical courses (Dym et al., 2005). Theoretical engineering courses,

however, account for the majority of an engineering degree. The ‘Micro-

structural Dynamics’ course was chosen since it deals with a variety of

microscopic processes happening in materials, such as diffusion, crystal-

lization, crystal growth, and deformation mechanisms, which are partic-

ularly difficult to tackle in a design-based course. Also, in most engineer-

ing curricula, this course marks the transition between general materials

knowledge and expert knowledge, being regarded as students’ initiation

into materials science.

The research questions of this study are described below, alongside the

data sources for each of them.

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a. What are the most frequent knowledge representations em-ployed during instruction, and what teaching strategies are used to enact them? Data sources: two quarters of classroom observations and field notes, transcriptions of classes, time-stamped notes about each of the teaching artifacts used during a 10-week period (equa-tions, plot, and photos), exams, class notes, textbooks, online class materials, grades.

b. What are the consequences of those representations and teach-ing techniques for students’ conceptual understanding? Data source: semi-clinical content-driven interviews with stu-dents, over three quarters.

IV.3.2. FIRST QUESTION: MOST FREQUENT KNOW‐

LEDGE REPRESENTATIONS EMPLOYED DURING 

INSTRUCTION To answer this first question and collect the classroom data, I attended

the Microstructural Dynamics course in 2004, 2005 and 2006. Classes

ran for 80 minutes, twice a week. In class, I sat behind all students, trying

to be as invisible as I could. I took field notes, and audio recorded about

five hours of class. The selection of recorded classes was driven by topic

– I focused on the content topics more relevant to the subsequent activi-

ties that students were going to engage. I also developed special Pocket

PC software in order to timestamp all equations, variables, plots and

drawings used by the professor during his explanations. As the professor

was lecturing, I would take note of all “teaching inscriptions/artifacts”

and pictorial materials utilized, alongside with their timestamp. For ex-

ample, if the professor wrote nD kt on the board, that would be

coded as category “equation,” with four variables (D, k, t, and n). Other

categories were “plot” and “drawing.” A small excerpt of these data is

shown below, in Table IV-1.

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Table IV-1 Example of the logging and time

stamping of ‘artifacts’ Date Time type: variables minute/variable minute/equation 28-Nov-05 10:12 equation: 5 vars 0.20 1.00 28-Nov-05 10:13 equation: 6 vars 0.33 2.00 28-Nov-05 10:15 equation: 5 vars 1.00 5.00 28-Nov-05 10:20 Plot 28-Nov-05 10:21 Drawing

Also, each quarter, I collected and scanned about 200 pages of class

notes, one midterm and one final exam, five pieces of homework and

commented solutions, students grades, and the course textbook. Across

different years, class notes had an overlap of approximately 90%. Two

professors taught the course over the three-year period.

Pairing these data with the class notes, I was able to track how many eq-

uations and variables were utilized to explain each phenomenon. I con-

ducted such analysis for some key materials science phenomena, identi-

fying, for example, how many equations were utilized to derive the diffu-

sion law and the approximate time spent.

To identify the most common expected learning outcomes in the

course, I also analyzed about 60 homework assignments and quizzes,

and created a simple coding scheme with six prototypical homework

and classroom exercises:

Proof.

Draw.

Plot and infer.

Theoretical constructs.

Derive.

Plug and solve.

Another form of data analysis was to pair transcriptions of the profes-

sor’s speech and the text in the transparencies (see example in Table

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IV-2), examining each derivation step so as to make sense of the repre-

sentations employed and the trajectories of the explanations. I was par-

ticularly interested in inter-textual correspondence, i.e., how the profes-

sor would describe orally a phenomenon and how he would write it on

the board. Within those inter-textual correspondence moments, I tried

to identify formalization transitions, i.e., when the professor starts with a

micro-level explanation and moves to a macro-level formalization. Also,

I identified, for different phenomena, the explanation trajectory and the

representational objects used in the process, in four instances:

1. Initial conceptual explanation.

2. Graphical representation.

3. Graphical formalization.

4. Transition to mathematical formalization.

Table IV-2 shows the transcription data on the left, and the transparen-

cies on the right, a representation inspired on Abrahamson’s “transclip-

tions” (Fuson & Abrahamson, 2005), in which he pairs representative

movie frames of research subjects and transcriptions.

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Table IV-2 Side-by-side representation of the professor’s speech and the

class notes he handed out

[…] Delta-G*A here, we are going to take that to be, uhh, the energy involved, the free energy change involved for an atom to detach itself from this grain  here,  grain-1,  and  move  into grain-2. And then once it finds a home in grain-2, it has a lower energy than this atom in grain-1, a lower free energy, so we can write  this down as,  it  involves, of course, a Boltzmann expres‐sion, this is the flux of atoms from grain-1 to grain-2,  involves this  Boltzmann  factor  involving  this  free  energy  change  here, delta-GA over RT, and then you have a free factor which you know from your physics,  this  is  just  the probability,  this  is  the probability that this atoms surmount this barrier. NU-1 is the frequency with which this atoms attacks the barrier, ok, so  you’d have,  and  that  you’re  familiar with  from your  course on diffusion, and NU-1 here, as  I  said,  is  the vibrational fre-

quency, N-1 now, this is the number of atoms per unit area in grain-1  that are in a favorable position to make the jump, and  I  showed  you what we meant  by  favorable  position,  that they have to be at the end of an atomic type ledge in this simple model,  and  then A-2, you see, note  the difference here,  this  is A-sub-2 because this is the probability of it being accommo-

dated in grain-2, everything else refers to grain-1 whereas here A-2 is referring, I’m sorry, everything here refers here to grain-

1with the exception of a-2, which is a probability, not an area, of it being accommodated in grain-2. We surely, we are going to, we  don’t  know  what  this  number  is,  we  are  going  to  shortly take it equal to 1, let’s wait a minute before doing that.

Another variant of this data analysis is to examine the textbook’s text

and pictorial materials looking for those same four moments in the ex-

planation trajectory - (1) initial explanation, (2) graphical representa-

tion, (3) graphical formalization, (4) mathematical formalization. Fig-

ure IV-1 shows one example of such analysis. The first block has initial

textual explanation of diffusion, based on atomic, local behaviors. Then,

a graphical representation tries to capture the text with circles and ar-

rows. In step three, the ‘balls and arrows’ representation is connected to

a plot, and then to the equations, which are also in step 4.

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Figure IV-1 Representation analysis

By collecting, assembling, and interpreting such explanation trajectories,

I detect the most common procedures for transitions between represen-

tations within the teaching materials (textbooks, and transparencies) of

the ‘Microstructural Dynamics’ course. Study 1 will describe this ap-

proach in more detail.

IV.3.3. SECOND QUESTION: LEARNING OUTCOMES OF EQUATIONAL‐BASED REPRESENTATIONS AND TEACHING TECHNIQUES 

The second research question of this study was to evaluate student un-

derstanding of relevant phenomena in materials science as a result of the

representational approaches analyzed in the previous section. To answer

this question, I conducted 21 clinical interviews with students, over

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three years. My protocol was inspired by Stieff & Wilensky’s (2002,

2003) study on chemical equilibrium. Their pre-interview protocol was

comprised of three main parts. In the first part, students were asked to

explain, in their own words, chemical equilibrium (recall and explain).

The second part attempted to investigate participants’ ability to apply

chemical equilibrium concepts to textbook questions (traditional prob-

lem solving.) Finally, the third part required students to predict chemi-

cal equilibrium for particular cases. Their data analysis was qualitative,

and identified elements in the students’ discourse related to (1) defining

equilibrium for a chemical system; (2) characterizing factors affecting

equilibrium; and (3) transitioning between micro-, macro-levels during

problem solving. For this study, I only utilized a ‘recall and explain’ and a

‘traditional problem solving’ protocols, looking for similar dimensions

within the materials science content, for example, defining and identify-

ing factors affecting grain growth (Study 2 will address the micro-macro

transitions.)

The interviews took place in a lab environment, in a semi-structured fa-

shion (Ginsburg). The subjects were volunteers, and were compensated

for their time with gift cards. The recruitment process began with a 15-

minute presentation during regular class hours, and a simple sign-up

sheet. In later studies, I setup up a wiki-based sign-up sheet to expedite

the process and prevent scheduling overlaps. The interview took be-

tween 20 and 30 minutes, and students had access to all their class mate-

rials. The interview was comprised of the following items:

1. ‘Recall and explain’ a. What is a grain? b. What is a grain boundary? c. What is grain growth?

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d. Could you indicate in this picture which grain will grow and which will shrink? (Students were presented with a sche-matic drawing showing grains of different size in a material)

e. What is the driving force for grain growth? f. What is the driving force for recrystallization?

2. Traditional problem solving a. What is the effect on grain growth of dispersed precipitates?

Why? b. In grain growth, grain boundaries always migrate toward

their center of curvature. How does this decrease the free energy?

c. In recrystallization, the new grains migrate away from their center of curvature. How does this lead to a decrease in the free energy?

d. Indicate in the following picture (see Figure IV-2) which grains would grow or shrink.

Figure IV-2 Students had to indicate which grains would grow or shrink in

the picture

All sessions were videotaped and students’ drawings were scanned and

stored. I watched all the interviews and randomly selected 50% of the

students from each of the first 2 years (2004 and 2005) for full transcrip-

tion and analysis, totaling seven. Their interviews were transcribed and

the analysis focused on the adherence to the standard textbook explana-

tions, and how much and in which aspects their explanations varied

across students. My analysis established qualitative accounts of the dif-

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ferences between explanation, narratives of meaningful moments

throughout the clinical interviews, evaluation of students explanations,

and comparison with standard textbook accounts. For example, let us

examine these three explanations of grain growth:

a. “A grain is a solid substance in which the atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions.” (textbook)

b. If you have a metal and you are looking at it under a microscope, at the surface of the metal, where different what I call grains grow, and these grains are just areas where the atoms collect and the bounda-ries in between the grains are sinks and sources for dislocations and vacancies and so.

c. It is so hard to explain... When I think of grain, those kinds of pic-tures that we see, what comes to my mind […] I feel that it is a word that we use in the English language and you always associate with something small, that is individual, you can see its limits and stuff like that. So when you use it in class, you just associate it with... like... I mean, a grain of rice... it is just one, out of many, that you can see right now.

The difference between (a) and (b, c) is apparent – conventional ele-

ments such as regularity and tri-dimensionality are not present in stu-

dents’ explanations. On the other hand, (b) and (c) differ considerably

as well. In (c), the visual aspect of a grain is preponderant (“those kinds

of pictures,” “a grain of rice”), whereas in (b) the explanation (despite

being incorrect) is more related to the actual elements within the ma-

terial (vacancies, etc.) Many of such differences were identified and de-

scribed in the study, for three of the protocol’s questions.

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IV.4. STUDY 2: A THREE-YEAR LAB STUDY WITH VOLUNTEER UNDERGRADUATE STUDENTS BUILDING MODELS

IV.4.1. RESEARCH QUESTIONS AND DATA SOURCES The results of Study 1, as we will see in subsequent chapters, suggested a

mismatch between the materials science content and the representa-

tions employed to teach it, with sizeable impact on students’ conceptual

understanding. The design of MaterialSim, a model-based set of activi-

ties for materials science, (see Design chapter) attempted to address this

mismatch by offering students a tool to ‘mobilize’ simple rules about

atomic behavior in a computer simulation. To further examine the po-

tential impact of the agent-based perspective, I designed a series of lab

studies over three years, with the following research questions:

a. Did the interaction with models effect significant cognitive change?

Data sources: field notes, videotaped interviews, post interview, post-

survey.

b. Did the building of models effect significant cognitive change?

Data sources: field notes, video recording of model-building process,

post interview, post-survey.

c. Was the design of the grain growth model effective as an exemplar (see Design section)? Would students be able to build, in a short pe-riod of time (approximately 2 hours), a computer model of a phe-nomenon in materials science, based on MaterialSim’s framework? What are the kinds of additional human/material supports needed to facilitate model building?

Data sources: field notes, models built by students, external rating of

models, surveys about student interest, motivation, and difficulty of

the task.

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In the following subsections, I first describe in detail the whole study,

and subsequently hone the three research questions and their data

sources.

IV.4.2. DESCRIPTION OF THE STUDY The study was structured as two individual sessions, to start approx-

imately one week after students’ exposure to the relevant topics in their

regular classes.

As previously described in Study 1, over three years, 21 students volun-

teered to participated in both studies (1 and 2) – 6 in 2004, 11 in 2005

and 4 in 2006. In order to recruit volunteers, I made one presentation at

the beginning of each quarter to the class explaining the idea of the

study. Gift cards were offered to the participants as compensation for

their time. All sessions were videotaped, with one or two fixed cameras,

and students’ computer interactions were recorded using real-time con-

tinuous screen-capture software. Approximately 2-3 hours of video were

captured per student, with a total of 50-65 hours of footage. Since a con-

siderable amount of time was spent building computer models, part of

the video footage has no verbal utterances, so just approximately half of

it contained speech. Experiments done by students, as well as the mod-

els they built, were incrementally saved and analyzed in various stages of

their development. Due to the considerable size of each student’s data

set (models, videos, screen capture), and having in mind the goals of the

study, just like in Study 1, I randomly selected one third of the students

for transcription and analysis.

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Figure IV-3 Experimental setup (2004)

The first individual session, 45 minutes long, was comprised of:

1. General presentation of the NetLogo programming environment.

2. Demonstration of five canonical agent-based models from the NetLogo models library (fire spread, virus contamination, racial segregation, gas molecules in a container, and a chemical reaction.)

3. Explanation of the grain growth model and its algorithm. I used the following paper (Figure IV-4) printouts in the explanation, in which two scenarios are pictured: one with several competing grains with similar stabilities (left), and another one with two grains, one (red) clearly less stable than the other (blue).

Figure IV-4 Paper printouts used in the

grain growth model explanation

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4. Hands-on interaction with the grain growth model (agent-based problem solving, see Stieff & Wilensky, 2003), with simultaneous think-aloud interview, and three activities (see Figure IV-5):

Figure IV-5 The interface of MaterialSim’s

grain growth model

a. First, students were asked to draw two grains (see Figure IV-6) and hypothesize about what would happen once the model started to run. Then they would actually run the model and compare their predictions and the actual result.

Figure IV-6 The initial setup of the model

with two grains

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b. Subsequently, they were asked to draw a structure with 5 grains (one small in the middle and four large ones surrounding it, see Fig-ure IV-7), hypothesize about what would happen, run the model, and comment.

Figure IV-7 The initial setup with five grains

c. The third activity was open-ended, and included running the model with different values for matrix size, temperature, composition, as well as recording and plotting experiments sweeping the whole pa-rameter space of one variable, and comparing the data with pub-lished data. The work done by students (spreadsheets, graphs) was saved. Below we have one example of a plot created by students in this activity, showing his model data (solid line) and the data pre-dicted by the equation (dotted line). In this particular example, the students is comparing grain growth in pure materials versus grain growth in materials with a dispersion of particles (from 1 to 10%).

Figure IV-8 Plot generated by a student, showing his model data and

theoretical data

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5. Finally, as homework, learners were asked to choose a challenging and/or interesting topic from the course and think of a model to build, which would be implemented during the next session. Students also had the option of just extending the functionality of the existing grain growth model, in a significant way.

The second session (150 minutes) was dedicated to:

6. Introduction to the basic commands of the NetLogo modeling language. This was accomplished by building a simple model together with students, such as diffusion-limited aggregation (DLA) or crystallization, emphasizing the use of NetLogo’s help file, its models library and the code samples as sources of further information. The algorithms present in the grain growth model were also explained in detail.

7. Implementation (i.e., coding) of the new model. Participants were always in front of the computer and in control of the task – I would help students as needed with language commands and general programming issues, but not take control of the keyboard or the computer. At times, I would also help them conceptualize the problem in agent-based terms. After the model-building session, in addition to video and model files, drawings on paper were also scanned and stored. The creation of a NetLogo model consists of the following phases (see Figure IV-9):

- Thinking about the phenomenon, its components (agents, or “turtles” (Papert, 1980)) and rules. For example, an atomic diffusion model would have as agents atoms, and vacancies, perhaps with different properties (atoms of material 1, atoms of materials 2, etc.) Those agents would have some particular behaviors, such as check for vacancies, move to vacancy, or move randomly.

- Writing computer code in the NetLogo language, i.e., ‘translate’ the behaviors into computer code. The prototypical NetLogo model has at least two components: a setup procedure, which creates the models’ initial world, and a go procedure, which causes the agents to perform their respective actions until a stop condition occurs. Other typical features of a NetLogo model include plotting and different visualization techniques (manipulating color and shape). For example, NetLogo’s diffusion model has the following setup and go procedures (the model has four

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more procedures, not shown here for simplicity). The setup procedure performs the following actions:

Clears the screen.

Creates green atoms on the left side of the screen (x coordinate < 0).

Creates blue atoms on the right side of the screen (x coordinate > 0).

Initializes the plots.

to setup clear-all set-default-shape turtles "square" ;; make green atoms on left ask patches with [pxcor < 0] [ sprout 1 [ set color green ] ] ;; make blue atoms on right ask patches with [pxcor > 0] [ sprout 1 [ set color blue ] ] ;; plot the initial state of the system setup-plots update-plots end

The go procedure contains the following actions:

Asks vacancies to ask a neighboring atom to move into the vacancy.

Updates the system’s clock (“tick”).

Updates the plots. to go ;; asks vacancies to ask a neighboring atom to ;; move into the vacancy ask patches with [not any? turtles-here] [ move-atom-to-here ] tick update-plots end

- In tandem with writing the code, creating an interface (buttons, the graphical view, sliders, plots, monitors).

- Debugging the model.

- Running experiments, sweeping the model’s parameters space.

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Figure IV-9 The interface (left) and

procedures (right) of NetLogo’s Solid Diffusion model

8. Short Likert-scale/open-ended post-survey to evaluate differences in motivation from the first (interacting with models) to the second session (model building). The items of the survey were:

- How motivating was the work in the first session? (5-point scale)

- How interesting was the second session? (5-point scale)

- How motivating was the work in the second session? (5-point scale)

- What was the most important reason for you to participate in the study?

- Did the two sessions help you better understand some topic(s) in the course? If so, which topic(s)?

- During the first session, you were able to visualize grain growth and other phenomena using the computer. How would you rate the usefulness of computer visualization tools for materials science learning? (5-point scale)

- During the second session, you programmed your own model using NetLogo. How would you rate the usefulness of that activity for learning? (5-point scale)

- Between the first and the second sessions, you were asked to come up with your own idea for a project. How important

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was that for you motivation in the second session? (5-point scale)

- During the second session, you programmed your own model using NetLogo. How difficult was it? (5-point scale)

IV.4.3. ANALYSIS CATEGORIES AND DATA EXAMPLES MODEL COMPLETION

To answer the first research question of this study (would students be

able to build models?), I employ a simplified set of metrics which were

fully developed in Study 3. These simplified metrics include a qualitative

analysis of the code, examining its complexity given the problem chosen,

and a comparison with introductory, published NetLogo models. This

analysis indicates if students were able to at least learn the basics of the

language and complete a working model in the given timeframe, in or-

der to evaluate NetLogo’s “low-threshold” affordance – how difficult

was it for the students to learn the language. This is an important con-

sideration for evaluating its fit for engineering class projects, many of

which are time-constrained, and populated by students with a range of

programming skill levels.

COGNITIVE CHANGE IN INTERACTING WITH MODELS

To answer the second question (‘Does interacting and building models

effect significant cognitive change?’), I employ verbal analysis and mi-

cro-genetic (Siegler & Crowley, 1991) methods for detecting cognitive

change during the interaction with and construction of models. The

verbal analysis also employs adaptations of the procedures used by Stieff

& Wilensky (2003), Wilensky & Resnick (1999), Levy, Wilensky and

collaborators (Levy et al., 2004; Levy & Wilensky, 2008), in which I

analyze the cognitive shift pre- and post-interaction identifying evidence

in students’ speech for centralized vs. descentralized control, bottom-up

vs. top-bottom mechanisms, and levels thinking, as the following exam-

ples show.

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First, let us consider the data from students interacting with the grain

growth model, when they were asked to draw two grains and predict the

behavior of the boundary. Figure IV-10 shows snapshots of the first dy-

namic simulation that students observed. I documented students’ reac-

tions and tried to interpret the cognitive shift as the simulation pro-

gressed.

Figure IV-10 The evolution of a curved grain

boundary

t=15 t=30 t=45 t=200

Before the simulation most students were unsure of what would happen.

As they started the simulation, they observed that the movement was

not smooth or unidirectional as the conventional grain growth equa-

tions would suggest, but that there was intense activity on both grains

with intense flipping of atoms. The following excerpt suggests that vi-

sualizing this evolution sparked some changes in Liz’s understanding,

but she still employs a top-down, aggregate-level mindset:

Interviewer: Can you describe what you see?

Liz: Just because one grain has a concave side and the other has a convex side, so it comes in towards the concave, because... [pause] does line tension apply in this situation?

Interviewer: Line tension?

Liz: That might be from dislocations... I might be mixing them up. Just because... when you have something... part of the grain is like, curving in, mostly likely other parts of the grain are curving in, so the tension of the grain boundary lines, so the force outside is greater

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than the force inside, so it will like shrink, it looks like that probably be like straight in the middle, rather than entirely red... just because if the red part also has some concave thing that is off the screen it will just like go together.

Liz is apparently referring to results of the Laplace-Young equation,

which relates surface tension and curvature – she is still thinking of the

boundary as a line. She cannot yet think in the “micro” level: to visualize

what is happening on the computer screen, she has to imagine a large

circle going off-screen, and think in terms of forces – all macroscopic

elements.

However, in the second activity, when Liz drew five grains (Figure

IV-11), her understanding was markedly different. Watching the evolu-

tion of this new microstructure was a crucial experience – she effectively

started to transition from memorized rules-of-thumb to a micro-

behavior-based reasoning.

Figure IV-11 Liz’ structure with five grains,

zoomed out (left) and zoomed in (right)

While observing this phenomenon, Liz was told to zoom the simulation,

both in and out, so as to also see what was happening at the micro level

(following a single atom.)

Interviewer: So what happens to growth speed?

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Liz: Eventually they will get like... two big ones... and then it will take forever.

Interviewer: So what could be the law?

Liz: It will eventually taper off... to some point... because if you have a lot or grains then you will... the rate of increase will be faster, but when average grain size increases it gets harder and harder to increase the rest of them, so it just goes...

Interviewer: Why is it harder and harder?

Liz: Just because there isn’t a distinct... [pause] being in this orien-tation is more favorable than this other one so you have to pick and choose... the grains are doing that, but it is not happening quickly just because you know, either one can happen.

In this very short time watching the model, Liz was able to understand

and generate hypotheses about two essential ideas (and oftentimes re-

ferred as hard to understand, see Krause & Tasooji, 2007): triple points

and logarithmic laws. Rather than trying to assemble statements pulled

from regular instruction, Liz departed from what she knew about other

phenomena and what she was actually seeing in the simulation. Even

without formally “mathematizing” the time dependency of grain growth,

she understood the reason for the triple point to be considered a “low-

mobility” point in a microstructure.

Analysis based on those categories were conducted with all seven stu-

dents chosen for the study.

COGNITIVE CHANGE IN BUILDING WITH MODELS

The second research question of this study purported to investigate

model-building, focusing on two aspects: (1) the nature of the cognitive

shift occurred during model building, particularly the perceived micro-

behavioral and structural similarities between apparently disparate phe-

nomena, and (2) how students made use of the affordances of the agent-

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based programming language. In the following, I will discuss examples

of data analysis of the model-building task.

In class, most phenomena were taught with different sets of equations

and modeling approaches, despite the similarities in their micro-

mechanisms. One focus of this study, therefore, was to evaluate if stu-

dents would successfully perceive the similarities across phenomena and

build working models based on those similar micro-mechanisms.

As an example of such analysis, let us examine Betty’s model. She built a

model to investigate grain growth with a novel and important feature:

taking into consideration the misalignment between grains. In her inno-

vative model, the more misalignment across the boundary, the harder it

would be for an atom to jump across that boundary. The construction of

this model presented Betty with many challenges. The first was to con-

vert the grain orientation’s angle, which could lie in any of the four qua-

drants, to a normalized quadrant-independent measure. Betty’s solution,

after much thinking, sketching and trying out different trigonometric

functions, was to use the arcsine function (see Figure IV-12). From her

drawing, we can observe that she was using geometrical analysis from a

“micro” level, taking into consideration the orientation of individual

atoms.

Figure IV-12 Betty’s sketches about angles,

sine and arcsine.

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She considered that the probability for an atom to jump to the next grain

should be dependent not only on the number of different atoms around

it, but also on the average misorientation between the two grains. Low

misorientation would promote easier migration. Apart from the initial

difficulty in figuring out the best trigonometric function for the angle

comparison, Betty did not resort to any of the textbook formulas, con-

versely, she was generating her own mechanistic theory from the

ground-up, as the triangulation of the videotaped model-building ses-

sions, her code, and her drawings reveal. Her operationalization of the

model shows that she did perceive that, at the micro-level, adding the

misorientation effect was trivial8. In her code, she simply added one

command to the original grain growth model, which was:

;;OLD PROCEDURE if future-free-energy <= present-free-energy [set heading (future-heading)]

The resulting code of her procedure just added one “if” statement:

;;BETTY’S NEW PROCEDURE if future-free-energy <= present-free-energy [ if (present-heading - ([heading] of one-of neighbors6) < miso-rientation) [set heading (future-heading)] ]

Betty’s model illustrates one of the main advantages of the agent-based

representation: at the micro level, the mathematical machinery required

to add new phenomena or parameters to an existing algorithm is much

lower than traditional representations. Instead of employing numerous

equations to add her ‘misorientation’ effect, just one line of code, at the

micro-level, was enough.

Almost every model built by students tells an interesting cognitive story

about levels thinking and the transformation afforded by the ‘discovery’

8 On a more advanced level, similar research was undertaken and published by researchers, such as Kimura, & Watanabe (1999)

146

of the micro behaviors and their ontology (Wilensky & Resnick, 1999).

I analyze those stories in detail, with special attention to these catego-

ries:

Idea to code transition: how easily students adapt their modeling ideas to the constraints and characteristics of computer code? I identify, in the video data, instances of seamless idea-to-model transitions. Examples:

- Easy transition: “atoms move around randomly, so I can just type fd 2 right-turn random 360”

- Difficult transition: “atoms try to minimize free energy, but I don’t know how to represent energy in the system.”

Uses of agent-based affordances: several authors have devised coding schemes for evaluating students’ understanding of complex systems phenomena, particularly, expert-novice studies (Hmelo-Silver & Pfeffer, 2004b; Jacobson, 2001), students interacting with models (e.g., Levy & Wilensky, 2008), or building models (Berland & Wilensky, 2006; Centola et al., 2000b; Wilensky, 2000b, 2001a; Wilensky & Reisman, 2006). However, in the literature there is still no established coding scheme to assess how students use the affordances of agent-based programming languages, or even some measure of complexity or sophistication of their models. In the following, I briefly describe four categories which were devised for this goal, based on the literature review and on my analysis of the data from all previous studies. This list is not exhaustive and the categories are not orthogonal. For example, foregrounding physical processes and one-to-many generativity can be closely connected—if we assume that the microscopic physical processes are similar, one-to-many generativity could be a direct consequence.

- One-to-many generativity: algorithms and rules which can be used to understand many phenomena.

- Formalization of intuitive understanding: students’ intuitive ideas about atomic behavior being encoded as a formal computer language.

- Foregrounding of physical processes: the model resemblance with the actual phenomena, graphically and in terms of the rules embedded in the code.

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- Model bending & model blending: the difficulty of combining micro behaviors (blending) as opposed to macro-behaviors, and of adapting micro-behaviors from other models.

An example of this analytic instrument is in Table IV-3, in which I iden-

tify, in Betty’s model (aforementioned), the instantiations of these four

affordances. Note that different students had different uses of these four

categories – some models, for example, did not make use at all of some

of them.

Table IV-3 Affordances of agent-based

modeling

One-to-many generativity

Formalization of intuitive under-

standing

Foregrounding of physical

processes

Model bending & blending

Betty Grain growth with misalign-ment

Neighborhood-based local count, energy minimiza-tion

“the more misaligned, the harder to jump”

Atoms vibrate and jump

GG algorithm + micro-level geometry

In the actual study, more details about those analysis categories are ex-

plained, alongside with the data.

IV.5. STUDY 3: LARGE STUDY WITH AN ENTIRE MATERIALS SCIENCE CLASS (2007)

IV.5.1. RESEARCH QUESTIONS AND DATA SOURCES The third study was designed to fit into the regular class schedule. In-

stead of volunteers, the study comprised all 21 students in the Micro-

structural Dynamics class in 2007. All students had to build a NetLogo

model as a regular, 4-week graded assignment. Additionally, two treat-

ments were employed. Approximately half of the students were intro-

duced to NetLogo from an ‘aggregate’ perspective (Figure IV-13, right),

while the other half was exposed to the agent-based approach (Figure

IV-13, left). I structured two tutorials and two sets of sample models,

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one for each condition, and both focused on the same phenomenon (so-

lidification.) As I will explain in the study, unexpected events made

some students move from one group to another, making the compara-

tive study more difficult. Namely, some students met after class to dis-

cuss the assignment and ended up moving from the ‘aggregate’ to the

‘agent-based’ group (interestingly, no agent-based to aggregate changes

were observed). In the end, only four students remained in the aggre-

gate group.

Figure IV-13 Agent-based (left) and aggre-gate (right) sample models of the same phenomena, used in

the NetLogo tuturial

For both groups, the study shared many characteristics with the pre-

vious one, in which many of the analysis categories, rubrics and metrics

employed in the studies with volunteer students will be used again. The

two research questions of this study are:

a. In a realistic classroom environment, with all its time and material constraints, would students be able to build a computer model of a phenomenon in materials science? What human and material sup-ports are needed to facilitate such task?

Data sources: field notes, models build by students, rating of models,

logfiles.

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b. Did the model-building process effect significant cognitive change (similar to the question in Study 2)?

Data source: field notes, materials generated by students (models,

drawings), video recording of model-building sessions, post inter-

view, post-survey, logfiles.

In the following subsections, I first describe in detail the whole study,

and subsequently hone on the two research questions and their data

sources.

IV.5.2. DESCRIPTION OF THE STUDY From the students’ point of view, this study followed the format of most

assignments in the Microstructural Dynamics class: an assignment was

posted on the course website, and a deadline was set. There were many

intermediary milestones, which I will explain in detail in this section,

and students had available one TA (myself) exclusively dedicated to this

assignment, for one month.

Differently from the previous studies, in which students were video-

taped during the entire model-building process, in the present study

students did part of the work at home. However, they were instructed to

run a research version of NetLogo which logs all of their interactions

with the environment, and tracks the evolution of their model, keeping a

snapshot of every instance of compiled code9. In addition, we video-

taped all of their sessions with the “modeling” TA, kept incremental ver-

sions of their models, and saved all email communication during the

study, which was structured as follows:

1. Introduction: I made a 15-minute presentation in class about the assignment (day 1), and students received the assignment via the online course management system (day 2).

9 Due to technical difficulties (some students accidently erased the logfiles and other could not transport them since some got to several hundred megabytes), just about 30% of the logfiles were retrieved.

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2. Students scheduled and attended an individual 45-minute NetLogo tutorial (days 3-7). At the beginning of the session, they were explained the IRB procedures and could opt-out of the study (those could still do the assignment, but were not videotaped or interviewed). Before the tutorial, there was a 30 minute pre-interview, which included: - Questionnaire about students’ familiarity with computers

and computer programming.

- Semi-structured interview with selected content-related questions from section IV.4.2.

- The following question: “Suppose you were hired as an engineer and you will be assigned to create mathematical models of some phenomena in materials science. For that task, you would be able to look at books and online materials. From this list of phenomena compiled from the course syllabus, please rate how comfortable you would be creating a model of them.” (5-point scale)

3. Model-building, divided into multiple milestones:

- 1 week after the tutorial (days 7-9), students had to send by email their desired topic for the model.

- After the tutorial, students had access to a wiki page (see Figure IV-14) in which they could freely schedule TA slots for help with the programming.

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Figure IV-14 Screenshot of the wiki page for

scheduling help, with names obscured for anonymity.

- 2.5 weeks after the tutorial (day 19), students had to send a first working version of the model.

- 3.5 weeks after the tutorial (day 26), students sent their final model with a detailed report (8 pages, on average) explaining the model, and comparing model data with established theoretical data.

4. Post interview: after having finished their model, students came back to the lab for a 30-minute interview. During this interview, they would:

- Explain the phenomenon they have just modeled (for a technical and non-technical person).

- Again, the following question: “Suppose you were hired as an engineer and you will be assigned to create mathematical models of some phenomena in materials science. For that task, you would be able to look at books and online materials. From this list of phenomena compiled from the course syllabus, please rate how comfortable you would be creating a model of them.” (5-point scale)

- Then, I asked the exact same question for a list of phenomena compiled from the following quarter’s course (Microstructural Dynamics II).

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- Form this list, the interviewer then chose two of the phenomena which were positively rated and asked students to ‘think on their feet’, explaining how they would build a computer model. In Figure IV-15 we have some of the materials generated by students during this part of the interview.

Figure IV-15 Examples of students’ work

during the post interview

- Students were asked to build a ‘motivation plot’, showing their own motivation at each of the five milestones of the project: (1) first tutorial, (2) choosing a topic, (3) model-building, (4) sending the beta version and (5) final report writing.

- Finally, students answered a web survey with the following items:

a. What did you like the most about this assignment? (Open-ended)

b. What did you like the least about this assignment? (Open-ended)

c. In general, how interesting was doing this project? (5-point scale)

d. In general, how motivating was the work? (5-point scale)

e. “I learned something new in *materials science* doing this project”. Do you agree? (5-point scale)

f. If you did learn something new in materials science, please mention the main topics, in order of how much you learned about each of them. (Open-ended)

g. “I learned something new *outside* of materials science doing this project”. Do you agree? (5-point scale)

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h. If you learned something new outside of materials science, please mention the main topics/skills, in order of how much your learned about each of them. (Open-ended)

i. How much time, in hours, did you spend in the following phases of the project?

thinking about your project idea Doing research about the "science" behind your

chosen phenomenon. Just learning the NetLogo language. Actually programming your model. Running ‘virtual’ experiments, plotting data. Writing up the final report. Getting help from the “NetLogo TA”. Getting help from the other TAs and the professors.

j. You were asked to come up with your own idea for a project. How important for your motivation was being able to pick your own topic for modeling, as opposed to being told to model a particular topic? (5-point scale)

k. Please rate how difficult the following phases of the work were (5-point scale):

Choosing a topic to model. Doing research about the "science" behind the topic. Learning the NetLogo language. Programming your model. Running 'virtual' experiments, plotting data. Writing up the final report.

l. How would you rate learning NetLogo as opposed to learning MatLab? (try to remember your first time using MatLab) (5-point scale)

m. In the programming projects which you have done for *other* classes at Northwestern, which were the most common activities?

plotting data transforming equations to computer code solving word problems using the computer optimization problems (finding a value that

optimizes a system) creating scientific models finding out new phenomena comparing lab data to computer-model data

n. “Creating computer models *in NetLogo* (such as the ones you did) could be a good activity for a course such as Microstructural Dynamics.” Do you agree? (5-point scale)

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o. If you were the MAT SCI 316-1 professor and were to redesign assignment #5 from the ground up, how would you do it? (Open ended)

5. Follow-up interviews (2008): The goal of this part of the study, which took place in 2008, was to assess if the cognitive change effected by the intervention had a long-term effect on students, after 12 months. I interviewed four volunteers students from the 2007 study. These semi-structured interviews lasted for approximately 30 minutes each, dealing with two of these three phenomena in materials science:

- Phenomenon 1: Solid-liquid transformations (from Microstructure Dynamics 1)

- Phenomenon 2: Martensitic transformation (from Micros. Dynamics 2)

- Phenomenon 3: Memory-shape alloys (new topic)

For each of those three phenomena, students were asked to:

- Describe their understanding of the phenomena, in a ‘recall and explain’ mode (see previous sections).

- Solve, qualitatively, an exam or homework problem comprising the phenomena.

- Explain how they would create a model of three phenomena.

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Figure IV-16 Experimental setup for the

tutorial and the model-building sessions. One camera was

mounted exactly on top of the drawing area, and the other is

pointing to the student.

IV.5.3. SUMMARY OF ANALYSIS PROCEDURES The data analysis of Study 3 has two major parts. First, I will present re-

sults for the entire class, including qualitative and quantitative metrics

about their computer models, the logfiles automatically recorded by

NetLogo, and data about students self-reported motivation, interest,

and time-on-task. The goal of this first part is to determine the viability

of agent-based modeling in real classrooms, the general learning out-

comes, and the differences across students, in particular the influence of

previous computer ability in student’s performance.

The second part of the study is an in-depth case study with two stu-

dents, in which I narrate and illustrate in detail narratives of students ex-

plaining their computer models, as well as creating theories to explain

phenomena they were not previously instructed. These narratives are

composed of multiple interviews, pre- and post-activity, including a one-

year follow-up interview with students. The purpose of the study is to

establish a more fine-textured analytical framework to comprehend stu-

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dent’s representational practices, cognitive trajectories when hypothe-

sizing about models and scientific phenomena, and epistemological re-

sources activated.

IV.5.4. DATA ANALYSIS FOR THE ENTIRE CLASS One of the key improvements of Study 3 in relation to Study 2 is the

depth and systematicity of the model analysis, so as to evaluate the

models’ quality and depth, with both programming and content matter

criteria. Probably the most well-known piece on the assessment of the

complexity of computer code is the Thomas McCabe’s (1976) paper on

“cyclomatic complexity.” McCabe conceived a method for counting

nodes and edges within the control structure of the program that would

correlate to its complexity, sophistication, and also manageability. A

simplified method for calculating the cyclomatic complexity M is:

M Number of closed loops Number of exit points= + (IV.1)

The problem with cyclomatic complexity for my particular purposes is

that the tools to measure it are language-specific, i.e., they need to

“know” about the language’s grammar (C++, Java, etc.) Even if I were to

develop from scratch a tool to access cyclomatic complexity of the Net-

Logo language, it wouldn’t capture the data I purport to extract from the

code – not its elegance or nesting level, but rather the uses that students

make of the language. Other standard, less sophisticated measures exist,

such as percent of comments (PoC), and lines of code (LoC). They are

also only partially useful, since, a priori, they are not necessarily related

to how well students use the language and build models. Therefore, as it

seems that there are no standard metrics for our purposes, I created two

rubrics, one quantitative and one qualitative. The goal of these rubrics is

to understand and quantify:

The modeling approaches used (agent-based, equational, or mixed)

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The quality of the model, given the approach used, previous programming experience, and the time and resources available.

Possible correlations between automatically-extracted data (e.g., frequency of use of a given set of commands, number of lines of code, number of interface widgets) and items in the qualitative rubric (e.g., sophistication and usage of the local rules).

QUALITATIVE EVALUATION OF MODELS

With that goal in mind, I created a qualitative rubric to assess the 21

available models created by the students. The rubric has four categories

(system, rules, visualization, and interface/reporting), as shown in Table

IV-4. For each of the 90 items in the rubric, a weight was assigned based

on my assessment of the difficulty of implementation, and its level of so-

phistication, accordingly to existing agent-based models and program-

ming practices. For example, a model with a hexagonal topology is in-

trinsically more difficult to program that one with a square topology.

Along the same lines, a model in which the agents’ properties are distri-

buted normally is more sophisticated than a model with uniform distri-

butions properties. The caveat here is that some scientific models might

not require a hexagonal grid or normal distributions, so it would be inac-

curately penalized. I am aware of such limitation, and it will be further

discussed in Study 3 and in future work.

To apply the rubric, closely examined the code of the models, as well as

the interface, and recorded the metrics in a custom-made database sys-

tem. An example of the data visualization tools to use examine the mod-

el coding is in Figure IV-17.

Table IV-4 Rubric for qualitative rating of

the models Dimension 1: System definition - how students code the modeling ‘world’, the setup procedures, and the initial distributions of agents. Total items: 36

1.1 topology square (default) hexagonal other (more compli-

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cated)

1.2 size default: standard NetLo-

go sizes

customized: the world’s size was customized

1.3 variables

number of globals use of globals number of locals use of locals number of patches-own number of turtles-own number of links-own

1.4 breeds use of breeds

number of breeds

1.5 initial distribution of agents

equal: all agents have the same properties

random-uniform: un-iformly distributed

random-normal: normal-ly distributed

number of classes of agents

1.6 initial construction

patch-only turtle-only patches and turtles turtles and links patches, turtles and links Boundary-check

1.7 initial activation of agents

all: all activated at the same time

local: based on agents' properties

local: based on local random rule

local: local rule global: global variable global: global rule global+local: local &

global rule

1.8 constants model-only: make sense

in the model

natural: from the natural sciences

1.9 types of agents used Patches behave? Turtles behave? Links behave?

Dimension 2: Rules – frequency of use of agents’ rules. Total items: 24

2.1 near neighborhood neighbors other-turtles-here

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distance at-points in-radius

2.2 far neighborhood distance in-radius/in-cone

2.3 iteration/trial and error use of finite element methods recursion push system to boundary condition

2.4 collision

distance other-turtles-here neighbors in-radius

2.5 energy gain/loss

gain/lose or lose energy arbitrarily gain/lose or lose based on own

behavior gain/lose energy as they interact

with agents

2.6 selective activation

n-of max-of one-of based on a property of agents

[breed, etc.]

2.7 links agents are not re-linked agents are re-linked arbitrarily agents are re-linked based on rule

Dimension 3: Visualization: shapes and color. Total items: 10

3.1 use of shapes

agents keep default shape agents have custom shapes agents change shape arbitrarily agents change shape based on

rule/variable

3.2 use of color

agents keep default colors agents have custom colors agents change colors arbitrarily agents change colors based on

rule/variable

3.3 palleting default palettes custom palettes

Dimension 4: Interface/Reporting: frequency of reporters, plots and monitors. Total items: 20

4.1 plotting

plot with multiple pens (total) plot with linear scale plot with non-linear scales (log,

exp) Histogram dynamic plotting

4.2 numerical output

print show to-report reporters

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monitors

4.3 interface

buttons sliders plots monitors chooser switch

4.4 automation/comparison

"Manual" experiments In-model comparison BehaviorSpace experiments BehaviorSpace + external tools

Total: 90 items

Figure IV-17 An example of the data visualiza-

tion tools to examine the model coding

QUANTITATIVE EVALUATION OF MODELS

For the quantitative evaluation, I created a suite of scripts and programs

to calculate several statistical data based on (1) the models created by

students and (2) a baseline comprised of a selected set of models from

the NetLogo models library and community models. The metrics are

described in Table IV-5.

Table IV-5 Rubric for quantitative rating of

the models Dimension 5: Quantitative metrics

5.1 Model size number of non-comment characters number of comment characters total number of characters

5.2 Language use frequency of certain commands: ask, set, neighbors, if, foreach, etc.

5.3 Interface number of buttons, plots, monitors, sliders number of other interface widgets

g y g y g g g39.6 24.9 17 28 55.1 38.1 47.6 40.4 38.2 42.8 52.3 41.4 39 35.3 42.9 39.3 35.5 54.8 30 42.5 27 53 45.3 total19.6 13.3 10.7 13.5 31.7 14.6 23.1 16.2 19 22.5 24.9 22.5 21.7 18 18.3 19.7 19.5 24 17.9 23.4 10.2 25.2 23.6 setup

8.5 0 0 8 12 5 12 3 9 14 8 13 10 7 10 9 8 12 3 8 5 20 11 rules3.5 1.5 1.5 1.5 1.5 3 6.5 6.5 3.5 3.5 5.5 3.5 1.5 2.5 6.5 5 1.5 1 1.5 5.5 5 3.5 6.5 visualization7.8 10.1 4.8 5 9.9 15.5 6 14.7 6.7 2.8 13.9 2.4 5.8 7.8 8.1 5.6 6.5 17.8 7.6 5.6 6.8 4.3 4.2 interface

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An example of the baseline for comparison is shown in Figure IV-18,

which shows the histogram of the number of non-empty lines of code

for the NetLogo models’ library.

Figure IV-18 The histogram for model length

based on all of NetLogo’s models library

To extract the metrics from the models, I used multiple procedures and

tools:

a. Design of regular expressions (a special computer language for string and text manipulation, also known as “regex”) to split the model file (.nlogo) into sections. The filters I designed split each model into five files:

o Code only (no comments)

o Comments only

o Code + comments

o Shapes

o Interface

b. Design of Mathematica programs to automatically open all files, ap-ply filters, and extract useful data. Below is one example of the code to count each occurrence of the words in the list “wordlist” wordlist={"ask ", "to ", "set ", "atoms ", "neighbor ", "neigh-bors ","neighbors4 ","in-radius ","of ", "if ", "ifelse "} d = Table[ StringCount

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[Import["C:\\data\\data-students\\models\\originals\\"<>ToString[students[[z]]]<>"-original.nlogo.code-pure"],t,IgnoreCase->True], {z,22}, {t, wordlist}]

In addition to the numerical output, I created a set of automated code

visualization techniques as to enable an ‘at-a-glance’ evaluation of stu-

dents’ models. These visualizations might reveal aspects that the sheer

numerical output might miss, for example, particular patterns in com-

mand usage. Below I show one example of such graphical analysis, which

employs “tagcloud” and “word tree” techniques. First, I show in Figure

IV-19 both visualizations for the baseline model, grain growth:

Figure IV-19 Word tree (left) and tagcloud

(right) visualizations of MaterialSim’s grain growth

model

In Figure IV-20, we can observe a relatively simple model built by a stu-

dent (Barton) to study recrystallization. Figure IV-21 shows the model

built by another student, Lin, to study the exact same phenomenon.

The sheer sizes of the models is very diverse (1032 vs. 132 terms), but

the visual comparison suggests that Barton’s model, for the most part,

used the command “set” to hardcode several variables (g, r, k, n) and

makes use of few agent rules. Lin’s model, conversely, uses “set” in the

context of agent rules (heading, color, breed, neighbors).

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Figure IV-20 Barton’s model, with 132 terms

(53 unique)

Figure IV-21 Lin’s model, with 1032 terms

(210 unique)

QUALITATIVE AND QUANTITATIVE EVALUATION OF MODELS, COGNITIVE CHANGE

The analysis categories for qualitative and quantitative evaluation of

models, as well as cognitive change afforded by the construction of

agent-based models were already described in item IV.4.3.

This study, however, collected extra data, such as students describing

modeling ideas, logfiles and survey data, which required new analysis

tools and rubrics. These new requirements also made me make im-

provements to the format of the transcriptions. I transcribed all the data

in a custom XML format (see Figure IV-22), which presents one consi-

derable advantage: timestamps, notes, and other “tags” can be added to

the transcript with multiple nesting levels without losing its readability

or integrity (they can be filtered out at any time.) Also, it is an extensible

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format quantitative which allows for future improvements (re-coding,

adding new codes) without losing any of the previous data.

Figure IV-22 A screenshot of the XML tool

used for the trancriptions

Departing from the XML files, I generated tables for further coding and

analysis, as shown in Figure IV-23 (left). Note, also, that the utterances

can be easily filtered and sorted (Figure IV-23, right), allowing for sev-

eral types of coding, data analysis, and summarization.

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Figure IV-23 One of the forms generated from

the data for easy coding, alongside with one of its filters

dialog box.

One of the important new elements of this study is the development of a

rubric to code students’ verbal utterances before programming a model,

i.e., when they were asked to ‘think on their feet’ and explain to the in-

terviewer the rules for a given model. In the following, I present a rubric

that will be used to code the rules described by students, both during the

construction of the model and in the post-interview. Attempts to devel-

op rubrics for complex system thinking have been made. Wilensky and

Resnick developed the first framework based on categories such as the

Decentralized/Centralized mindset (Resnick & Wilensky, 1998), and

levels confusion (Wilensky & Resnick, 1999). Jacobson (2001) devel-

oped the complex systems mental models framework (CSMM) to com-

pare novices’ and experts’ verbal explanations about several natural and

social phenomena (for example, “How does the slime mold, which gen-

erally exists as tens of thousands of individual amoebae cells, form into a

multicellular creature when food is not available?”.) His CSMM has

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eight categories of beliefs rated under two types of mental models

(“clockwork,” and complex systems.) Levy and Wilensky (2008) em-

ployed the same framework but added a “levels” dimension. Hmelo-

Silver (Hmelo-Silver & Pfeffer, 2004a) employed a ‘structure, behaviors,

function’ coding to determine differences between novices and experts

explaining the functioning of an aquarium, and built concept maps

representing prototypical cases.

Table IV-6 Pseudo-rules for describing

models

Pseudo-rules: how students verbally describe the model

1 Move

until collision until a particular target randomly until global event until user click

2 Look around if near

3 Feedback X has more energy, so it goes faster Y has less energy, so it dies off

4 Tendency tends to it wants to

5 Causality

X will do Y because so... that's why

6 Conditional if you X when...

7 Qualitative X is not good Y doesn't want to stay that way

8 Proportionality the X this is, the Y that is

9 Order then when... first this, then that

Below we have one example of how students’ transcripts could fit into

these codes, as well as the previous code for ‘system setup’ (see Table

IV-4).

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Figure IV-24 Examples of coding of students’

verbal utterances (yellow and blue boxes refer to two different

students)

I will also look at other constructs which emerged from the research it-

self, and which will be properly explained in subsequent chapters, such

as:

Recalling authority-delivered heuristics (for example, “they always want to go to a lower energy, that's how stuff works” and “I can't remember if it is the smaller ones that grow”).

Similarity triggers: common elements shared by two or more phenomena which trigger students to establish parallel when searching for an explanation.

Revisiting previous knowledge about similar phenomena and trying to infer similarities (“in a system that is this, recrystallization…”).

Asymmetric reversibility: measures if an explanation, when reversed, generate mechanisms that were not contained in the first explanation (e.g., I ask students about a liquid to solid transformation, and then a solid to liquid transformation)

DRAWINGS AND DIAGRAMS

Since students intensely used drawings and diagrams while explaining

the phenomena, I utilized Abrahamson & Fuson’s “transcliptions”

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(2005) to pair verbal and pictorial data. Transcliptions are side by side

transcriptions of dialogue or classroom events, and frames captured

from the viodeotaped material.

I extracted frames from the overhead camera only, since it was the one

showing the drawings and diagrams. I adopted a non-uniform capture

rate for different parts of the videos grabbing many frames per second

during periods with high density of gestures and diagramming by stu-

dents, and less frames when no activity was going on. In Figure IV-25 we

have the image manipulation software showing some of the frames cap-

tured, and below some examples of the “transcliption.”

Figure IV-25 A screenshot of the image

manipulation software showing some of the thousands of frames

captured

“Transcliption” example, Brickey

a I guess, [pause] using the same similar idea up here, start off all of these and give each one a…

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b so this is high temperature, this is low temperature,

c so for these ones on the edge, I guess I would give them a random kind of vibrational energy based on the temperature next to them,

“Transcliption” example, Liam

a And there would also be a probability that at any given time, a solid atom would leave the solid and become part of the liquid.

b And those probabilities would be due to the temperature.

LOGFILES

Logfile analysis is a new technique with relatively little literature availa-

ble, except for preliminary limited work (see, for example, Buckley et al.,

2004; Levy & Wilensky, 2005). The goal of my analysis with the logfiles

is twofold: (1) determine if any of the statistics extracted from the logs

correlate with the other dimensions of the study, such as quality of the

final model, and (2) for some selected students, investigate qualitatively

the evolution of their models.

Since students would do most of the work at home in their own com-

puters, some sort of record of what students were doing would be useful.

Coincidentally, just before the 2007 study, NetLogo’s logging module

was released for beta testing. This module logs user actions, such as key-

presses, button clicks, changes in variables and, most importantly for

this study, changes in the code.

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The logging module uses a special configuration file which specifies

which actions are to be logged. This file was distributed to students

alongside with instruction about how to enable logging, collect the log-

files, and send those files back for analysis.

However, the logistics of the logfile collection ended up being more

complicated than anticipated. Given that the logging module entered its

testing phase just weeks before the study, this was not a total surprise,

but the loss of some logfiles could not be avoided. The main issue was

that the logfiles were oftentimes automatically deleted on shutdown by

the operating system, which misinterpreted them as a temporary files.

Also, students sometimes did their work on multiple computers (some

of them public), and forgot to copy their logfiles before switching ma-

chines. In the end, I was able to collect logfiles from nine students, but

some of them were not complete, i.e., did not cover the entire modeling

process.The logfiles record several types of interaction “events” in Net-

Logo:

‘Code’: compilation (successful or not) of any type of code.

‘Buttons’: pressing and depressing of buttons in the interface.

‘Greens’: overall changes to the NetLogo environment (world size, size of patches, etc.)

‘Widgets’: creation or deletion of interface widgets.

‘Procedures’: a subset of the “Code” event, indicating compilations of code in the procedures tab only (not counting code inside buttons, etc.)

The following excerpts show the format of the logfiles (some pieces

were removed for simplicity), showing two types of events: changes in

variables (“INTERCEPTS” was changed to 5.0 and “GRAIN-

GROWTH-EXPONENT” was changed to 0.28), and a code compila-

tion (the actual code was removed). The timestamp uses the standard

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format of the Java programming language (number of milliseconds since

January 1st, 1970):

</event> <event logger="GLOBALS" timestamp="1179463524171" type="globals"> <name>INTERCEPTS</name> <value>5.0</value> </event> </event> <event logger="GLOBALS" timestamp="1179463574406" type="globals"> <name>GRAIN-GROWTH-EXPONENT</name> <value>0.2801480962249191</value> </event> <event logger=" CODE" timestamp="1179463511750" type="procedures"> <action>compiled</action> <code> [model’s code] </code>

Data mining the logfiles was non-trivial. I collected about 9 million data

points from nine users (see Table IV-7), and extracting meaningful in-

formation from such a voluminous dataset was challenging.

Table IV-7 Number of files and events per

participant Name Files Size (MB) Events

chuck 2 43.1 258036

che 6 2.3 5970

leah 2 0.7 2836

liam 12 657.4 4044723

leen 38 43.7 253112

luca 40 16.1 92631

nema 7 1.0 3690

paul 6 0.1 218

shana 45 692.0 4165657

Total 158 1456.4 8826873

For clarity purposes, a more detailed technical account of the data-

mining process is given in Study 3 itself, alongside with the data. The in-

formation which was determined from the logs includes:

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Variation in size of the code versus time. In Figure IV-26, we can clearly observe two different model-building patterns. The sudden peaks in Luca’s plot indicate that she briefly opened other models to copy code from them, or just examine them – a markedly different pattern from Liam, who worked on his model all the time. The idea of this exploratory analysis tool is to evaluate how frequently students open other models for inspiration, and copy and paste code between model.

Figure IV-26 Two example of size of the code

versus time plot, for two students over about a week.

Frequency of use of some key ‘agent’ commands over time (ask, neighbors, in-radius, etc.)

Frequency (and type) of compilation errors, and distribution over time. In Figure IV-27 a screenshot of the analysis tool is chosen – the query box allows easy filtering and counting of different compilation errors. The idea of this analysis was to detect typical errors and problems during the coding of the models.

20 40 60 80 100 120

1000

2000

3000

4000luca

10 20 30 40 50 60

4600

4800

5000

5200

5400

liam

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Figure IV-27 A summary table with consoli-

dades logfile data. Note that the query box allows the user to

filter and sort events for analysis.

Minute changes in the code. I created software tools to display and compare the differences between the code in two compilation events (also see Figure IV-27). It is also possible to detect which models students opened during the process, and which pieces of code were copied between models. In the example below, taken from one of the logs, we can observe that between interval between timestamps 1179890304937 and 1179890611140 (approximately 5 minutes), this students added an important agent-rule to the procedure.

timestamp="1179890304937" timestamp="1179890611140" to create-many-dislocations [x y] hatch-dislocation-atoms 1 [ set xcor x set ycor y set shape "circle" "square" set size 0.5 set color yellowgreen ask atoms in-radius 1.5 with-max [ycor] [ ask the-atom [let right-neighbor one-of atoms-on patch-at 1 0 let left-neighbor one-of atoms-on patch-at -1 0 ask link-with right-neighbor [die] ask link-with left-neighbor [die] ;let left-atom min-one-of atoms [xcor] ;let right-atom max-one-of atoms [xcor]

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;ask right-atom [ask link-with left-atom [die]] create-link-with myself ] ]

SURVEY DATA

The data from the post-survey and interview will be instrumental in

creating a collection of design principles for ‘real-world’ implementation

of agent-based computer modeling.

The data were organized into a relational database, which also included

data from other parts of the study (logfiles, verbal analysis), as to easily

generate aggregate data for statistical or qualitative analysis (see Figure

IV-28 and Figure IV-29)

Figure IV-28 Tables and data relationship in

the database

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Figure IV-29 Screenshot of the survey data

table

The survey data were analyzed with standard statistical tools, such as de-

scriptive statistics and correlations. Due to the relatively small number

of data points, the correlations were very sensitive to outlying students,

and a visual inspection of each correlation pair was necessary to quickly

determine them. I employed Mathematica and a custom-made SPLOM

(scatterplot matrix) tools10 for that purpose, and also the Latticist pack-

age in R (an open-source statistical package.)

The data analysis revealed that some apparently minor factors play an

important role in real-world classroom implementations. For example,

many students complained that the assignment was not worth enough

‘points’ in the final grade. Lack of time to complete the assignment was

another consideration, alongside with the usefulness of learning an en-

tirely new programming language for just one assignment. Also, the time

investment in each of the phases of the assignment deserves careful con-

sideration. The average time spent on the project was 20.7 hours

(SD=6.7h), of which 2 hours (SD=1.4h) were dedicated to research on

the ‘science’ behind the model, and 2.9 hours (SD=1.2) for learning the

NetLogo language. Those number reveal that NetLogo’s low-threshold

10 The Mathematica SPLOM tool was developed by Spiro Maroulis and Eytan Bakshy.

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design is effective in quickly getting students ‘up-to-speed’ to build

models, but that there could be more emphasis on the scientific research

before and while constructing the model (more of that data will be ex-

plained in the Study.)

MOTIVATION PLOTS

Finally, the motivation plots will provide yet another window to assess

students’ attitudes toward the modeling assignment. Students were

asked to represent their own motivation at each of the five milestones of

the project: (1) first tutorial, (2) choosing a topic, (3) model-building,

(4) sending the beta version and (5) final report writing.

One preliminary result is that there is a significant drop in motivation

when students had to start writing their final reports, but motivation in-

creases steadily while the model building process was taking place. Fig-

ure IV-30 shows two examples of such plots, in which this trend is very

clear.

Figure IV-30 Two examples of students’

motivation plots

Since all the plots were drawn on paper with an arbitrary scale, trans-

forming them back into numerical data is challenging. For that purpose,

I followed this procedure:

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1) I numerically estimated the minimum and maximum scales of the plot (allowing for negative numbers when the curve went below the x axis)

2) I recorded the approximate y coordinate of each point, within the scale estimated before.

3) I renormalized the data on a scale from 1 to 10.

This procedure allowed a reconstruction of a normalized average plot for the entire classroom, and the calculation of descriptive statistics on the data.

   

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V SOFTWARE DESIGN 

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V.1. SUMMARY This chapter describes the software design principles used throughout

the project. I describe the main programming platform (NetLogo), the

software and models developed especially for the learning activities

(MaterialSim), and discuss the principles and rationale employed in the

design.

V.2. NETLOGO NetLogo (Wilensky, 1999b) is a freely-available, integrated multi-agent

modeling environment, developed by Uri Wilensky at the Center for

Connected Learning and Computer-Based Modeling at Northwestern

University11. NetLogo is a unique system equally used by science re-

searchers and by educators. It achieves, by design, a balance between

learnability and power of the language; advanced features and a stream-

lined interface design (Tisue & Wilensky, 2004).

NetLogo is a direct descendant of the Logo language (Papert, 1980) and

the constructionist pedagogical tradition. Therefore, it has many tools

and features for building, experimenting with, visualizing, testing, and

refining models, such as a sophisticated and highly-customizable graphi-

cal user interface, as well as a multi-agent modeling language for author-

ing models (see, in Figure 1, NetLogo’s interface tab, on the left, and pro-

cedures tab, on the right)12.

11 http://ccl.northwestern.edu/netlogo

12 Many of those features were already explored in the Methods chapter, and some will be further explained in the next section, and throughout the dissertation.

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Figure V-1 The interface (left) and

procedures (right) of a NetLogo model (solid diffusion)

NetLogo was designed as a multi-agent modeling language (MAML).

Such languages are optimized to enable users to easily create and mani-

pulate thousands of computational entities (“agents”) with minimal

coding. For example, to create 100 agents (or ‘turtles’, in NetLogo’s lin-

go) on the computer screen, the user has to simply type:

create-turtles 100

To make all of those 100 turtles move 10 pixels forward, users would

type:

ask turtles [forward 10]

Users can also define simple rules that govern agents’ behavior. NetLo-

go agents can perform simple rule-based behaviors, such as to seek being

surrounded my equal neighbors, or to avoid being surrounded by differ-

ent agents. For example, to ask all turtles to check for neighbors (within

a one-patch13 radius) and move backwards in case there are at least two

neighbors around, we would use the following command:

13 The NetLogo screen in divided into a grid of patches. The size of the patches can be defined by the user.

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ask turtles [if count neighbors in-radius 1 > 2 [back 50]]

Apart from the language, NetLogo includes advanced visualization fea-

tures especially designed for agent-based modeling, such as multiple to-

pologies, 3D, and agent views. It also includes some specialized tools

such as BehaviorSpace (Wilensky & Shargel, 2002), which enables users

to explore a wide parameter space by automatically running multiple ex-

periments and logging the data.

V.3. MATERIALSIM From the Literature Review, it is apparent that most studies show that

even a simple interaction with agent-based models can effect dramatic

changes in conceptual understanding of the subject matter, particularly

topics in which multiple particles/elements interact (chemical reactions,

population dynamics, etc.) There is, however, a large variety of model-

based curricula and activities, each differing significantly from the other

with respect to the 12 dimensions analyzed. Even within the construc-

tionist tradition, some are based on interaction with pre-built models

and/or microworlds (Edwards, 1995) – which I termed interaction-

based constructionist (IBC), while some have model building and pro-

gramming at their core (building-based constructionist, BBC).

Within the IBC realm, Molecular Workbench, a model-based scripted

curriculum in chemistry, heavily relies on the idea that modeling is inte-

raction with models, with no need to gain insight into the algorithms.

Connected Chemistry (an agent-based chemistry curriculum), NIELS

(an agent-based curriculum in electromagnetism), and BEAGLE (ge-

netics and evolution), allow for more advanced interactions since they

enable learners to see and/or modify the underlying code and at least

minimally interact with it. In the BBC realm, in VBot (a multi-user visu-

al programming environment for building virtual robots), in the CoPeP

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project (middle school unit on complexity) and in the EACH project

(an agent-based curriculum for learning about the evolutionary dynam-

ics of cooperation and competition), students build models from scratch

(Berland, 2008; Berland & Wilensky, 2004, 2006; Centola et al., 2000a,

2000b).

Each level of interaction and each choice of modeling media call for dif-

ferent implementation strategies, support materials, and expected out-

comes. To locate my software design choices within the 12 dimensions

explained in the literature review, I examined several constraints and de-

sired outcomes:

Studies in which model-building took place (BBC, e.g., EACH, CoPEP, VBot) report impressive gains in understanding of deep principles within a domain. They also report that students were able to infer behaviors based on incomplete or sparse information. Since one key element of MaterialSim is to train students to see commonalities across phenomena and domains, having a strong programming component is a key design principle.

Although reporting positive results, studies of scripted curricula (e.g., Molecular workbench) or IBC modeling (e.g., Connected Chemistry, ProbLab, NIELS), for the most part, start out with a very well defined content coverage (gas laws, Ohm’s lab). In this more ‘convergent’ approach, they do not necessarily afford insights into other areas of their target domain (chemistry, or physics), nor allot large chunks of time for a deeper examination of the elementary “under-the-hood” behaviors. Since programming is not needed, it is understandable that students’ intimacy with the behaviors and rules will not be as well developed as in BBC modeling.

Creating models is not foreign to undergraduate engineering – it is common for engineering students to have modeling assignments and learn several programming languages along their degree. However, as shown in the Literature Review, traditional model-based activities in engineering oftentimes do not afford understanding of microscopic behaviors or elementary physical/chemical principles. Therefore, another key design principle is to build activities which foreground these micro-behaviors, and in

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which students develop a high level of familiarity with the language and the ABM paradigm.

Since engineering models not always come from first principles (i.e., fundamental laws of chemistry or physics), many models are purely empirical. Thus, data-driven model validation is a very common (and needed) practice in engineering. Another design principle, thus, is to include data validation as an integral part of the modeling activities.

The design constraints and learning outcomes point to a BBC design in

which students would individually build their own models with a special

focus on empirical or theoretical validation. In the following, I present a

summary of the design dimensions of MaterialSim based on the design

constraints and expected learning outcomes:

Dimension 1: Type of user experience – 1.6 (Building)Dimension 2: Curriculum navigation – 2.3 (Open-ended)Dimension 3: Emergent algorithms – 3.3 (High)Dimension 4: Media – 4.3 (On-screen with asynch. comp. physical artifacts) Dimension 5: Data Validation – 5.4 (Quant. validation with collected data) Dimension 6: Transparency of the code/rules – 6.4 (Code visible/changeable)Dimension 7: Modeling methodology – 7.2 (Mixed mode)Dimension 8: Data collection automation – 8.3 (User-defined automation) Dimension 9: Communication between users : 9.2 (Analog, non-simultaneous)Dimension 10: Participatory interactions : 10.1 (No participatory interactions)Dimension 11: Graphical realism:11.3 (Intermediate graphics) Dimension 12: Maximum visualization dimensions: 12.3 (3D)

These dimensions are useful to understand the appropriate software de-

sign focus. In IBC environments, the designer has to focus on a careful

design of sequences of models. In BBC, the designer’s foci are:

Programming exemplars as to present students with the important algorithms and coding examples which could be useful in the process of building several other models.

Support materials to help students in learning how to program.

Easily transportable code examples, which students could easily reuse across models. For example, students might want to copy and

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paste code between a sample model and their own models. The code examples should be general and “clean” enough: code tweaks, beautifying tricks, and overly specialized code should be avoided.

Readily-available validation tools, as to enable students to quickly verify the validity of their models.

My design was based on these principles and foci. Therefore, Material-

Sim is not a set of scripted models, but rather a set of exemplar models

built within the NetLogo environment. Since students are introduced to

just two models as a departure point for their own construction, the de-

sign of these models was the subject of careful consideration. Material-

Sim’s components were:

a. A very simple model (Solidification).

b. A feature-complete model (Grain Growth).

c. A persistent library of student-generated models from previous years, from which student could reuse code and get inspiration. This library was available for all participants, and I would occasionally re-fer them to particular models.

d. Support materials and tutorials: the NetLogo official documenta-tion, special purpose online materials, simple NetLogo “cheat-sheets.”

V.3.1. A VERY SIMPLE MODEL (SOLIDIFICATION) Most of the user studies in this dissertation were comprised of a short

NetLogo tutorial in which students learned the basics of the language, in

preparation for building their own models. The “Solidification” model

was used in those one-to-one tutorials – I would build the model to-

gether with students, step-by-step, during their first session.

One particularly useful feature of the Solidification model is that it can

be built incrementally, starting from one of the most elementary beha-

viors in NetLogo: making agents move randomly. By adding new beha-

viors on top of that base behavior, I was able to walk students through

the key ideas in NetLogo programming in just about 30 minutes: creat-

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ing agents, moving agents, inspecting agents, changing the states of

agents, interactions between agents, adding probabilistic rules, using

control structures (if-then) and implementing basic plotting/reporting.

This was accomplished in these seven steps14:

1. Create 50 particles. ask patches [sprout-liquids 1]

2. Ask particles to move randomly. ask liquids [ right random 360 forward 0.1 ]

3. Ask particles to stick together (solidify) if they collide. ask liquids [right random 360 forward 0.1 if any? solids in-radius 1 [set breed solids] ]

4. Ask particles to stick together (solidify) if they collide and depending on temperature.

ask liquids [right random 360 forward 0.1 if any? solids in-radius 1 and random-float 100 > temperature [set breed solids] ]

5. Ask particles to break apart (liquefy) depending on temperature. if any? liquids in-radius 1 and random-float 100 < temperature [set breed liquids]

6. If there is no solid, create a solid seed. if count solids = 0 [ask one-of liquids [set breed solids] ]

7. Plot the percentage of solid vs. liquid. plot count solids / (count liquids + count solids) * 100

After this short tutorial (see Figure V-2) and a brief discussion, students

were then introduced to the “feature complete” model, Grain Growth.

14 The code was slightly simplified for clarity – the complete code is in the Appendix.

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Figure V-2 A screenshot of the Solidifica-

tion model

V.3.2. A FEATURE COMPLETE MODEL (GRAIN GROWTH) 

The grain growth model is the central model in the project, for several

reasons. First, ABM modeling of grain growth is a widely accepted scien-

tific practice – it was in fact the first application of ABM in materials

science. Second, the grain growth model was conceived to present stu-

dents with a wide variety of features which they could use in their own

models. Also, the code was conceived so as to enable easy copy-and-

pasting of code to other models.

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Figure V-3 The interface of MaterialSim’s

grain growth model

These are the multiple interaction possibilities of the model:

1. One-dimensional exploration, and drawing structures: users can change variables, draw microstructures using the mouse, and observe their behavior over time.

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Figure V-4 The interface of MaterialSim’s

grain growth model – the normal setup (left), and a

structure created by a student, using the mouse to draw

microstructures

2. Multi-dimensional exploration: students can run experiments sweeping entire parameters spaces, as to find out critical points, system rules, mathematical relationships, and patterns.

Figure V-5 Sequence of screenshots from a

student’s experiment Particles = 8 Particles = 4 Particles = 1 Particles = 0

3. Bifocal exploration (Blikstein & Wilensky, 2006c) and data validation: Students can connect real-world and virtual experiments, importing digital pictures from real experiments, or using empirical data collected in the lab, or using published data for validation.

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Figure V-6 Plot generated by a student, showing his model data and

theoretical data

4. Model building: students can change, create or extend the system by coding their own procedures, modifying existing ones, or creating whole new models from scratch, using the NetLogo modeling language. And since NetLogo is a prototypical “low-threshold, high-ceiling” programming tool (Papert, 1980; Tisue & Wilensky, 2004), learners can achieve sophisticated results within a relatively short period of time.

5. Interface design: MaterialSim’s interface also contains several learning-oriented features – useful both to learn about the phenomenon itself and as an exemplar of programming models – summarized in the table below:

Simulation setup Matrix size/atom shape

hex circles lines

Users can start either from a random ar-rangement of atoms or from a pre-set stage, which can be drawn by the user using the mouse or converted from a digi-tal picture. This enables easy exploration of “what-if” scenarios. Important model-learning features: buttons, image import,

The appearance of the atoms can be changed for better visualization of particular phenomena (“lines” mode was very useful to understand the differences in crystallographic orien-tations). Important model-learning features: shapes, sliders, choosers

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V.4. SUMMARY OF THE CHAPTER In this chapter I described the software and the design principles em-

ployed in the studies. I first described NetLogo, the programming envi-

ronment utilized, and MaterialSim, a set of BBC activities in materials

science built within NetLogo.

My choice of a building-based constructionist environment is justified

by the expected learning outcomes (a deep understanding of micro-

behaviors within a scientific domain and their applicability across discip-

lines), and informed by previous research. In VBot “sharing, tinkering,

and performance were strongly correlated.” (Berland, 2008). In EACH,

it was not before Goeff (one of the participants) built his own model

that he gained the fundamental insight on the interaction between mul-

tiple factors in cooperation and competition (Centola et al., 2000a,

2000b).

Granted, BBC curricula require an ecology of activities and resources to

make it effective. In this chapter, I described my implementation of this

data import, setup-go dyad. Drawing tools Additional parameters

To investigate particular situations, users can “draw” their own microstructure, or retouch an existing one. Important mod-el-learning features: mouse draw, direct manipulation of the ‘View’ with the mouse, colors.

The annealing temperature slider allows for experiments with different levels of thermal agitation. The other slider can introduce a certain percen-tage of precipitates in the sample. Therefore, users can change the tem-perature and the type of material as to study their effects on grain growth. Important model-learning fea-tures: sliders, ‘add-on’ rules, mod-ularity of rules, probabilistic rules.

191

ecology and its main components: (1) automated data validation, (2)

exemplar models, (3) code transparency, (4) transportable code exam-

ples, (5) support materials, and (6) a persistent library of student-

generated model.

   

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VI STUDY ONE 

193

VI.1. SUMMARY OF THE CHAPTER This chapter will describe and analyze data from classroom observations

in a sophomore-level materials science course, over three quarters

(2004, 2005 and 2006). The first part of the study will discuss current

teaching and representational strategies using as data sources classroom

field notes, teacher transcriptions, class handouts, textbooks, and

homework assignments. The second part of the study will analyze data

from “recall and explain” content-oriented interviews with a selected

group of students. I conclude by identifying aspects of current instruc-

tion practices that affect the data from the students’ interviews.

VI.2. REPRESENTATIONAL PRACTICES IN A MATERIALS SCIENCE CLASSROOM

VI.2.1. A DAY IN AN ENGINEERING CLASSROOM What is the typical routine of an engineering student? How do his/her

classes look like? What kinds of teachings strategies and techniques in-

spire his/her teachers and textbooks authors? My goal in the following

sections is to answer these questions.

I have already discussed how the several reform initiatives in engineer-

ing schools have deeply influenced design courses, but neglected theo-

retical courses. In fact, my classroom observations revealed that little has

changed from the much-criticized ‘traditional’ undergraduate STEM

classroom. I observed a very typical theoretical course in materials engi-

neering: “Microstructural Dynamics.” Over the three years of observa-

tions, two different professors taught the class, although they used the

same transparencies, handouts, and textbooks.

Students attend class twice a week for 80 minutes, and instruction is al-

most entirely in a lecture-format. The class also has a biweekly lab ses-

sion, taught by a different teacher, which is approximately synchronized

194

with the theoretical session. During class, students are exposed to sever-

al pages of theory, derivations, and some examples of practical applica-

tions. From 2006 on, students were assigned to present in class a 5-

minute summary of the previous class. Along the 10-week quarter, there

were two exams and five homework assignments.

Both professors employed the classical lecture style: approximately 80%

of the time was occupied with explanations of transparencies. The other

20% was dedicated to the 5-minute student presentation at the begin-

ning of each class, and some more participative moments in which the

professor would ask the class some questions. Some questions were

merely rhetorical, as a bridge to another part of the explanation, others

actually generated brief discussions between students and the professor.

VI.2.2. WHAT KIND OF WORK ARE STUDENTS SUP‐

POSED TO DO? One striking observation since the very first year of the study was the

sheer amount of mathematical content matter that was covered in the

80-minute periods. But given the complexity and breadth of the topics

in the course, this should not come as a surprise. The overall goal of each

instructional unit is to prepare students to solve exercises which require

a solid mastery of the derivation process leading to the ‘final’ equation or

result. My analysis of the homework assignments and exams revealed

the following six prototypical exercises (all snippets were extracted from

actual homework assignments; note that some were extracted by the

professor from textbooks which were not referenced):

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a. Proof

b. Plug numbers into an equation and solve

c. Plot and infer

d. Draw

e. Define theoretical constructs

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f. Derive

To find out the most common exercises and tasks students were ex-

pected to do, I analyzed several homework assignments, plus review

handouts, totaling about 60 exercises. Table VI-1 shows the distribution

of exercises throughout a 10-week quarter15. Although the numbers are

approximate, there is clear indication that “proof”, “derive” and “plug

and solve” account for 57% of all exercises. If we also include also “plot

and infer,” we reach 73%. In other words, the vast majority of the work

required by all assignments involved sophisticated mathematical mani-

pulation. Theoretical and drawing questions account for only 27%.

15 Note that not all assignments were collected, due to the fact that some were sent electronically and, for some time, I was not in the correct list to receive them.

197

Table VI-1 Occurrence of different types of

exercises Exercise type %Proof 5%Draw 11%Plot and infer 16%Theoretical constructs 16%Derive 26%Plug and solve 26%

These results confirm our observation that mathematical manipulation

was a principal part of instruction. As we can see from the excerpts of as-

signments reproduced above, mathematical derivation was not only a

classroom artifact to present equations in a more elegant way, but a skill

that students were supposed to master in order to move forward in the

course. For example, question 4, under the Derive category above, asks

students to derive “equation 3.13” from the textbook in order to get

another equation as a result. This final equation is a well-known rela-

tionship that explains why hexagonal grains are stable. The question,

however, focuses on the derivation process without referring back to its

physical significance. The analysis suggests that rather than an excep-

tion, this is the rule – as the students progress in their courses, there is an

increasing separation between the mathematical formulation and the

physical phenomena. But how is that reflected in the teaching strategies

and artifacts used?

VI.2.3. TEACHING ARTIFACTS The goal of next part of this study is to further my analysis as to under-stand the types of representations and teaching artifacts employed dur-ing instruction. Those artifacts could be, for example, equations, plots, drawings, or pictures. For one quarter (fall of 2005), I logged and time stamped such artifacts (see Table IV-1 for one example of the data col-lected). After cleaning up and discarding incomplete data, I selected

198

seven classes approximately 10 days apart from each other, with 109 da-ta points in total. Figure VI-1and Figure VI-2 show plots (1) grouped by type of artifact, and (2) groups by date. Note that I counted only new equations and not small manipulations as steps of a derivation.

Table VI-2 Example of the logging and time

stamping of ‘artifacts’ Date Time type: variables minute/variable minute/equation 28-Nov-05 10:12 equation: 5 vars 0.20 1.00 28-Nov-05 10:13 equation: 6 vars 0.33 2.00 28-Nov-05 10:15 equation: 5 vars 1.00 5.00 28-Nov-05 10:20 plot 28-Nov-05 10:21 drawing

Figure VI-1 Teaching artifacts per type, with

the grey bars indicating the average

0

5

10

15

20

plot drawing other equations

Teaching artifacts per typeClass 1

Class 2

Class 3

Class 4

Class 5

Class 6

Class 7

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Figure VI-2 Teaching artifacts per date

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Teaching artifacts per date

Equation

Other

Drawing

Plot

These data confirm what the analysis of the exercises already suggested:

representing materials science phenomena mathematically and manipu-

lating those representations are a considerable part of what instruction

is. Not only is the “equations” cluster in Figure VI-1 extraordinarily larg-

er than any of the other ones, but Figure VI-2 shows that in 6 out of 7

classes equations were substantially predominant. And if we consider

that equations and plots are usually tied together in one explanation,

they account for more than 80% of all teaching artifacts.

This result does not come as a complete surprise – after all, engineering

is a mathematically-oriented field. Arguably, if you have an equation-

centered curriculum and sufficient time to explain those equations, it

might not be problematic to student learning. Therefore, the last part of

the analysis was dedicated to finding out how much time was spent in

each equation (or per variable within an equation). Figure VI-3, Figure

VI-4, and Table VI-1 show the results of this analysis.

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Figure VI-3 Plot showing the time spent per

equation

Table VI-3 Average number of variables and

equations per minute for the focus classes

Class # # variables Min/variables Min/equations Class 1 60 0.76 2.7 Class 2 9 1.08 6.0 Class 3 95 0.24 1.3 Class 4 40 0.54 2.9 Class 5 16 0.58 2.5 Class 6 40 0.62 2.2 Class 7 34 0.52 2.6 Weig. Avg. 0.60 (σ = 0.43) 2.4 (σ = 1.5)

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Figure VI-4 Histogram of the number of minutes spent per equation

1 2 3 4 5 6 7

Frequency 18 16 12 2 4 2 1

0

2

4

6

8

10

12

14

16

18

20

Histogram - minutes per equation

The data are quite consistent: the average time spent per equation is 2.4 minutes, and the histogram shows that 84% of the equations fall into the 1-3 minute bracket. Figure VI-3 shows that the dispersion is relatively low (even more if we were to discard outlying data points), in other words, the frequency of equations is approximately constant during each class and throughout the quarter, with few exceptions.

Up to now, the data demonstrate that mathematical derivations and proof, at least in quantitative terms, play a crucial role in the course. In the last chapter, I discussed how representation schemes based on diffe-rential equations can generate such “equation overload,” since they rely on a many-to-one approach requiring multiple equations to explain each phenomenon. The next step in this study was to understand more deeply the nature and consequences of this process, i.e., how the current representational approaches are generating instruction that consists of showing one equation after another at such incredible speeds and, also, how these representations are generated. That is the goal of the next sec-tion.

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VI.2.4. A QUALITATIVE DIVE INTO THE MODELING AND REPRESENTATION IN THE CLASSROOM 

The reasons behind the ‘equation overload’ described in the previous section are deeply tied to the representational approaches used throughout the courses materials. My goal is to take a ‘deep dive’ into some of the pivotal topics in the course and analyze the modeling ap-proaches employed, extending what has been done in the previous chap-ter (Representation Comparison) about grain growth, and diffusion. Particularly, I will show how such representations are constructed, and what aspects of the phenomena they foreground.

The intensive use of equational representations in the textbook, class-notes, and during instruction, is just part of the story. Surprisingly, the prototypical explanations of a phenomenon would almost never start with equations, but with qualitative descriptions of the phenomenon based on atomic micro behaviors, simple rules, and agent-based heuristics. The mechanism of grain growth, for example, is explained in the official text-book in the following excerpt:

“In the case of the cells in a soap froth the higher pressure on the con-cave side of the films induces the air molecules in the smaller cells to diffuse through the film into the larger cells, so that the small cells eventually disappear. A similar effect occurs in metal grains. In this case the atoms in the shrinking grain detach themselves from the lattice on the high pressure side of the boundary and relocate themselves on a lattice site on the growing grain” (Porter & Eas-terling, 1992, p. 131)

The phenomenon of solidification, also, is introduced to students also using local behaviors, as the following paragraph, together with Figure VI-5, show:

“If a single atom attaches itself to a flat close-packed interface it will raise the interfacial free energy and will therefore tend to de-tach itself again. It can thus be seen that continuous growth […] will be very difficult.” (Porter & Easterling, 1992, p. 178)

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Figure VI-5 An illustration of the process of

solidification from the textbook.

Both examples show that agent-based heuristics are used to introduce the topics to the students – both textually and graphically. But how can textbook authors and instructors get from those micro behavior to differen-tial equations in just some minutes? In what follows, I will show a slightly simplified version of Porter & Easterling’s (1992, pp. 63-65) explanation of the fundamental equation for diffusion (Fick’s First Law). The goal of the analysis is to illustrate this radical representational transformation during the modeling process, which I divided into four phases.

1. Textual explanationNormally a substitutional atom in a crystal oscillates about a given site and is surrounded by neighboring atoms on similar sites. […] Normally the movement of a substitutional atom is limited by its neighbors and the atom cannot move to another site. However, if an adjacent site is vacant it can happen that a particularly violent oscillation results in the atom jumping over on to the vacancy […] the probability that any atom will be able to jump into a vacant site depend on the probability that it can acquire sufficient vibrational energy.

The process starts with a textual ex-planation which is based on probabil-istic micro behavior of atoms,

2. Atomistic graphical representation

The second step is a graphical repre-sentation of the micro behavior, with minimal labe-ling.

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3. Transitional graphical representationThe third step is a hybrid represen-tation, in which the graphical represen-tation is first ‘matched’ to a plot, and then to a diffe-rential expression (note a version of Fick’s law to the right of the curve).

4. Inscription

2

2

J Dx

Dt x

f

f f

¶=-

¶¶ ¶

=¶ ¶

Finally, after a series of deriva-tions, we arrive at the final equation for diffusion.

The process between the transitional graphical representation and the inscriptions has also many sub-steps, which I explain in the following. Figure VI-6 (enlarged) is the starting point of the derivation. In the text, taken from the textbook, I highlighted in boldface many of the assump-tions of the mathematical formulation of the problem, and I will com-ment on those later.

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Figure VI-6 The picture supporting Porter &

Easterling’s derivation of the diffusion equations

“To answer this question [of diffusion] consider the exchange of atoms between two adjacent atomic planes such as (1) and (2) in Fig. 2.5a. Assume that on average an interstitial atom jumps

BG times per second […] and that each jump is in a random di-rection, i.e. there is an equal probability of the atom jumping to every one of the six adjacent sites. If plane (1) contains

1n B-

atoms per m2 the number of atoms that will jump from plane (1) to (2) in 1 second ( )J will be given by:

-2 11

1J atomsm s

6B Bn -= G (VI.1)

During the same time the number of atoms that jump from plane (2) to (1), assuming

BG independent of concentration, is given

by:

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-2 1

2

1J atomsm s

6B Bn -= G (VI.2)

Since 1 2

n n> there will be a net flux of atoms from left to right given by:

1 2

1( )

6B BB B

J J J n n= - = G -

(VI.3)

where 1

n and 2

n are related to the concentration of B in the lattice. If the separation of planes (1) and (2) is the a concentration of B at the position of plane (1) 3

1(1)

BC n atoms ma= . Likewise 3

2(1)

BC n atoms ma= . Therefore,

1 2( ) ( (1) (2))

B Bn n C Ca- = - and from Fig. 25b it can be seen

that (1) (2) ( )B B B

C C C xa d d- =- . Substituting these equa-

tions into [the previous one] gives:

2 2 11

6B

B B

CJ atoms m s

x

da

d- -

æ ö÷ç ÷= - Gç ÷ç ÷çè ø (VI.4)

The partial derivative BC

x

dd

has been used to indicate that the con-

centration gradient can change with time. Thus in the presence of a concentration gradient the random jumping of individual atoms produces a net flow of atoms down the concentration gradient. Subs-tituting

21

6B BD a= G (VI.5)

yields:

BB B

CJ D

x

dd

=- (VI.6)

This equation is identical to that proposed by Fick in 1855. B

D is known as the diffusion coefficient of B.”

At first glance, this constitutes an elegant and general the derivation of Fick’s law. Fick’s law is indeed very general, exact, and comprehensive,

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but its elegance and “exactness” came at a price: obtaining a predictive mathematical expression was only made possible by taking a series of as-sumptions into consideration. Its very compact formulation encapsu-lates crucial simplifications which are opaque in the final inscription, such as:

“Assume that on average an interstitial atom jumps”: the atomic jump rate is an average

“each jump is in a random direction”: jumps are on average also directionally random

“there is an equal probability of the atom jumping to every one of the six adjacent sites”: each atoms has six symmetrically positioned adjacent sites.

“assuming B

G independent of concentration”: the jump frequency does not change with concentration, which is not always true.

“Since 1 2

n n> there will be a net flux”: the model assumes that the flux happens in one dimension, from left to right.

the concentration gradient can change with time: although the picture is static, concentration is constantly changing.

We assume that atoms have six neighbors, as the expression for the

diffusion coefficient shows: 21

6B BD a= G

To understand the possible learning implications of the encapsulation of these assumptions, let us consider each of them. The probabilistic beha-vior of atomic jumps is backgrounded in the very beginning. Then, we also rule out any directional effects, and a possible change in atomic jump rate due to concentration variations during diffusion. Unidimen-sional diffusion is assumed, i.e., it only happens horizontally.

Fick’s law, albeit a hallmark of modern science, is a simplification. It’s generality, compactness, and elegance are certainly impressive, but in order to achieve such features, several elements from the actual pheno-mena had to be stripped down. In particular, the probabilistic behavior of atoms could cognitively “neutralized” as we represent the random

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jumps as a static inscription which is simply an arbitrary symbolic con-vention from which those behaviors cannot be directly inferred.

This is important: Tristan Ursell, among many other authors, recognizes

that:

“Given a group of non-interacting particles immersed in a fluctuat-ing (Brownian) environment, the movement of each individual par-ticle is not governed by the diffusion equation. However, many iden-tical particles each obeying the same boundary and initial conditions share statistical properties of their spatial and temporal evolution. It is the evolution of the probability distribution underlying these sta-tistical properties that the diffusion equation captures.” (Ursell, 2007)

The same type of trajectory was present in the professor’s lecture and the text in the transparencies (see example in Table VI-4). We can clear-ly see that the epistemic form of the verbal explanation is object-based (see text in green – “for an atom to detach itself from this grain”, “prob-ability that this atoms surmount this barrier”, “the frequency with which this atoms attacks the barrier”, “atoms in a favorable position to make the jump”), but the formalization of such ideas bears no resemblance with such intuitions about how atoms ‘detach’, ‘jump’, or ‘surmount bar-riers’. Again, in accordance with the textbooks’ representations afore-mentioned, micro behaviors are used to explain conceptually the phe-nomenon, and gradually abandoned in favor of differential equations. In the text below, we can precisely observe how speech and inscriptions are intertwined in the process of extracting from micro behaviors ‘differen-tiable’ elements, and how equations come to dominate the teaching dis-course.

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Table VI-4. Side-by-side comparison between the professor’s transcription and class notes he handed out […] Delta-G*A here,  we  are  going  to  take  that  to  be,  uhh,  the energy involved, the free energy change involved for an atom to detach itself from this grain  here,  grain-1,  and  move  into grain-2. And then once it finds a home in grain-2, it has a lower energy than this atom in grain-1, a lower free energy, so we can write  this down as,  it  involves, of course, a Boltzmann expres‐sion, this is the flux of atoms from grain-1 to grain-2,  involves this  Boltzmann  factor  involving  this  free  energy  change  here, delta-GA over RT,  and  then  you  have  a  free  factor  which  you know from your physics,  this  is  just  the probability,  this  is  the probability that this atoms surmount this barrier. NU-1  is the frequency with which this atoms attacks the barrier, ok, so  you’d have,  and  that  you’re  familiar with  from your  course on  diffusion,  and NU-1  here,  as  I  said,  is  the  vibrational fre-quency, N-1 now, this  is the number of atoms per unit area  in grain-1  that are in a favorable position to make the jump, and  I  showed  you what we meant  by  favorable  position,  that they have to be at the end of an atomic type ledge in this simple model, and then A-2, you see, note the difference here, this is A-sub-2  because  this  is  the  probability of it being accommo-dated in grain-2, everything else refers to grain-1 whereas here A-2 is referring, I’m sorry, everything here refers here to grain-1with the exception of a-2, which is a probability, not an area, of it being accommodated  in grain-2. We surely, we are going  to, we  don’t  know  what  this  number  is,  we  are  going  to  shortly take it equal to 1, let’s wait a minute before doing that. Now, it is going to be a reverse flux of atoms, and that reverse flux will involve a Boltzmann factor, but a Boltzmann factor involves the sum  of  these  two  energies,  delta-g  and  delta-ga,  because  the atoms sitting over here  in grain-2 have  to surmount the bar-rier which is higher than the previous barrier, to make this reverse  jump, ok?, now the pre‐factor  involves once gain a vi-brational frequency, we call this the test frequency and n-2 is the number of atoms in grain-2 that are in a favorable position to make the jump, and notice over here that you have an a-sub-1 and that the probability of this atoms being accommodated in grain1. Now when delta-g is 0, then this two local minima, are the exact same energy level, and then you get that the flux in both directions are the same, and the expression becomes quite simple,  just  as  the  a-1 * a-2 * nu-2, a2 * nu-1 * nu-1,  the Boltzmann  factor disappears  completely,  and  if we are  talking about a high angle grain boundary, a high angle grain boundary with, say, above 15 degrees, I asked you to make a calculation of when  the  cause of  a dislocations,  in  a  tilt  boundary  touch one another, and you will see you should get a number somewhere around 15 degrees. Now when delta-g is  greater  than 0,  there will  be  a net flux  from grain-1  to grain-2,  and  then you just take the difference in those two fluxes to get the net flux and I’m going to take a-1 to be approximately a-2, we are going to take it to be 1 finally, and then you see this factor here, this factor is out, this exp-delta-GA over RT and then the curly brack‐ets  you  have  1-minus-exp-little-delta-g,  that’s  the  delta G over here,  by  how much  an  atom  in  grain-2  sits  below  an  atom  in grain-1. Ok. Now we want the grain boundary velocity. How fast is  this grain moving as a result  from of  fact  that  there  is a net flux of atoms from grain-2  to grain-1. Let B be the grain boun‐dary velocity. […]

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It is not surprising, after this analysis, that students are exposed to one equation every 2.4 minutes: the labor of transforming micro-behaviors to differential equations is considerable and involves multiple levels of modeling. Figure VI-7, for example, shows additional examples of how graphical representations have to be repeatedly “hammered” into diffe-rentiable shapes: (i) in the top picture, grains were reduced to rectangu-lar prisms so as to graphically generate a “dx”, (ii) the second picture shows the initially “atomistic” grain boundary becoming a solid object more amenable to geometrical modeling; (iii) finally, the bottom pic-ture shows the complexity of geometrically modeling a liquid seed in contact with a solid surface, as well as the many needed simplification.

Figure VI-7 Three examples of graphics

representations leading to differential equations

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Our classroom observations, therefore, suggested that the ever-growing intricacy of college-level content in materials science poses a difficult challenge to traditional teaching approaches. While discursive descrip-tions of the phenomena extensively employ agent-based approaches, their formalizations do not. What is the impact of this fact on students’ understanding?

VI.3. INTERVIEW EXPLANATIONS The second part of this chapter analyzes data from “recall and explain”

content-oriented interviews with a selected group of students. As de-

scribed in the Methods chapter, the interviews were semi-structured,

and students could draw pictures to illustrate their explanations. It was

an “open-book” interview, i.e., students could resort to any class materi-

al, book or website to answer the questions (a complete list of questions

is described in the Methods chapter.)

Below we have a commented transcription of some excerpts of Question

1. The goal in this section is to show and discuss students’ explanations

of some core content in materials science, to which they were exposed

during their regular classes one or two weeks prior to the interview.

Interviewer Q1: How would you explain what a grain is? [Conventional explanation: “A grain is a solid substance in which the atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions.”]

Bob A grain is just an orientation of a crystal structure, a group of atoms in a crystal structure, a specific orientation, it is just molecules aligned [pause] in one direction and then you have various grains and each grain has its own direction and when they meet [there is a] grain boundary.

Erika A grain is just when you have got everything the same, same structure and everything, and then you have a boundary around it

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and it doesn't line up with the neighboring crystals. [...] One is oriented differently but basically they are the same.

Betty If you have a metal and you are looking at it under a microscope, at the surface of the metal, where different [pause] what I call grains grow, and these grains are just areas where the atoms collect and the boundaries in between the grains are [pause] sinks and sources for dislocations and [pause] vacancies and so.

Liz It is so hard to explain... When I think of grain, those kinds of pictures that we see, what comes to [my] mind […] I feel that it is a word that we use in the English language and you always associate with something small, that is individual, you can see its limits and stuff like that. So when you use it in class, you just associate it with... like... I mean, a grain of rice... it is just one, out of many, that you can see right now.

Ken A grain is basically a region of materials where there are no dislocations to it.

Ella A grain? There is the material... A material is just made up of grains... I guess if you... Like, I could say something about the boundaries, grain sizes are different, they can change, with temperature and other variables... I guess I’m not really explaining what a grain is.

These first excerpts illustrate how dissimilar students’ explanations

were. This may at first seem surprising, as the idea and description of a

grain or crystal is a fundamental notion in materials science, and do not

even involve dynamic processes. The understanding of grains is a build-

ing block for further understanding of a variety of concepts in the field.

Also, students had just been exposed to the topic in class just a week

prior to the interview. We might expect that if any concept would yield

uniformity in student response, it would be this one.

However, based both on the literature on prior conceptions and on our

own classroom observations, the diversity of students’ explanations is

213

not surprising. The literature is replete with examples where even simp-

ler ideas are not learned by students in unison, and that their under-

standing is strongly influenced by previous knowledge, phenomenologi-

cal primitives (diSessa, 1983) and ad-hoc theories. Moreover, our class-

room observations showed students were overloaded with a multitude

of phenomena, equations, and representational modes, without neces-

sarily making a clear distinction between the atomic behaviors them-

selves and the mathematical descriptions of those micro behaviors.

Bob and Erika offer a reasonably complete explanation, close to what we

would find in a textbook. Most of the other students diverge from that

version. This divergence is also not coherent: the starting points for the

answers are rather different, as well as students’ approaches to it. Betty

based her explanation on the visual appearance of a grain seen under the

microscope. Liz utilizes her previous knowledge about the morphology

of a “real-world” (a grain of rice). Ken uses one idea related to an earlier

topic in the course, ‘dislocation theory.’ Ella apparently understands

what a boundary is, but has difficulty explaining what exactly they en-

close. Students resort to a variety of metaphors and explanations for

characterizing a grain, at multiple levels: the surface under the micro-

scope, a grain of rice, or atoms with same orientation. Many responses

to this first question did not diverge completely from the acceptable

concept. However, as the interview progressed and questions started to

address more complex and dynamic phenomena, the diversity of expla-

natory models increased, and those initial difficulties to explain what a

grain is unfolded in significant ways. In the following excerpts, students

try to explain the phenomenon of grain growth:

Interviewer Q2: How would you explain what grain growth is? [Conventional explanation: “Grain growth refers to the increase in size of grains in a material at high temperature. This occurs when

214

recovery and recrystallization are complete and further reduction in the internal energy can only be achieved by reducing the total area of grain boundary.]

Bob Grain growth is just when a grain, when more molecules [pause] come into one grain and line up that same direction. The driving force is [long pause]…

Interviewer Why don’t they stay the way they are?

Bob Well, I mean [pause] I know the method of it, it is diffusion.

Interviewer But what is the reason they grow?

Bob Well, grains grow through diffusion, through vacancy diffusion, and atomic diffusion, for one, it is all over the place, temperature increases, molecules move around faster and they just... [pause] but the reason that they would grow [pause] I guess they grow... the driving force is to lower the free energy, overall, there is excess free energy due to dislocations and impurities in the grains, so by growing out, they can get rid of those and thus lower the free energy.

Betty So when you heat-treat a metal, so when you deform a metal first the grains shrink and become compacted, you get all sorts of dislocations then, like twin boundaries, stuff like that, so if you do a high temperature anneal, then the grains all grow because you increase the energy of the system when you heat it, and so it tends to decrease its internal energy, so the grains become bigger and anneal out the dislocations because [pause] there is a high mobility for the atoms to move, and so they move to the lower energy positions which is into the grains and the grain decrease.... ah... the grain size increases, and the total area of the grain boundaries decrease, which decreases to decrease the overall energy of the system.

Liz It is because, it wants to be more energetically stable, or have less energy in the crystal, so it will grow, just to form one big grain, because that’s the least energy configuration, and it does this because, by the whole radius of curvature idea, where it starts shrinking.

215

Chris Grain growth is... The smaller grains have higher curvatures and higher curvatures is not good, so they will want to shrink and become smaller and smaller, and bigger grains, with a lower radius of curvature will want to expand and so sooner or later will consume the smaller grains.

Peter Molecules with high energy, which are over here, will jump over to the low energy spot and that's a more desirable position, and that's why grain growth grows.

Interviewer Ok, when you say high energy or low energy, is it a general kind of energy, or are you talking about a specific kind?

Peter It's called “free energy”, but I don’t really know how to explain that.

This question brings about at least three different ways to explain grain

growth. The diversity of models and explanation paths is even more ap-

parent than when students were explaining what grains are. Bob, for ex-

ample, uses the metaphor of free will (“molecules come into the grain

and line up”), and employs ideas about diffusion, dislocations, and im-

purities in contradictory ways. He does not resort to the Laplace-Young

equation, for instance, to explain the process of decreasing free energy

by simply increasing the curvature radius. To him, excess free energy is

due to impurities or imperfections in the crystal structure (known as dis-

locations). “Purity” is taken as a synonym for low energy, and grain

growth as a “cleansing” mechanism by which grain boundaries would

“sweep out the dirt”. However, the Laplace-Young equation (studied in

class) states a very different idea. Namely, the driving force is the curva-

ture or pressure difference – impurities are not eliminated by grain

growth, and growth can exist in 100% pure materials. Here we can again

notice that students “mix-and-match” models that appear superficially

to be related, such as “grain growing” and “grains boundaries pushing

216

impurities out”. Betty goes even further searching for explanations. The

phenomenon she describes (deformation and recrystallization) was

taught in a previous section of the course but is, in fact, very different

from grain growth. In recrystallization, similarly, crystals grow, but for a

different reason and with different kinetics. During the pre-test, when

presented with a printed picture of grains, she incorrectly indicated that

the small ones would grow (which would happen in recrystallization).

Moreover, she mentions that grains “all grow” to decrease the internal

energy of the system, whereas in fact some grow and some shrink (oth-

erwise, evidently, the material would expand). Liz’s explanation, on the

other hand, is more coherent, relying on the idea of having “less” energy

in the crystal being correlated to the “whole radius of curvature idea,”

but without demonstrating how those things connect. Ken, similarly,

was more coherent in his explanation, although using overly qualitative

expressions such as “curvature is not good, so they will want to shrink.”

Bob and Ken provided good additional examples of the model “mix-

and-match.”

Interviewer What is the effect of dispersed particles?

Bob I think that... I feel that particles constrict grain growth, and when a grain boundary meets a particle it bends around it, it kind of molds around it, it will slow it down, it won’t make it stop completely, but it will slow it down. It hits the particle, it goes around it, and as it happens, there is a pull on the opposite direction that the grain boundary is moving. They slow... every time the grain boundary is moving out it slows down the growth.

Interviewer Is it good?

Bob It depends on how big you want your grain. You know, more particles, the closer they are together, the smaller the grains will end up being, in that case it will be a harder and strong material

217

Betty If you have a lattice around the impurity and that increases the energy of the system, and then that is bad, but if you have a lattice and you add particles of similar grain size, or, similar atom size, you can strengthen the material, because this small grains or atoms act to stop dislocation movement, and so it becomes harder and harder to push dislocations through so the plastic deformation becomes harder. The more particles you put [pause] in a system, the harder it is, [pause] the closer the spacing, the harder it will be to put dislocations through, so the harder the material will be.

Liz Basically, if there is an impurity, the grain boundary will just go around it so it will just do like this, viewing it from a top angle, this will be a grain boundary [showing a drawing]

Interviewer Will more particles affect grain growth?

Liz [looks at her class notes for several seconds] As for now, I don’t think it does anything to grain size.

Interviewer What is the effect of dispersed particles?

Ken if you have two precipitations and if you have a dislocation line, you need to exert a force Tau on it, to move the dislocation line, but once it gets to the precipitation, it has to bow out and that will cost more energy so if you have precipitations it will strengthen the material and that depends on the density of precipitations.

Interviewer So grain growth slows down or is faster?

Ken That I am not very sure.

Again, students tried to employ a variety of micro-models: a force-

feedback model, where particles pull boundaries away, slowing grain

growth (Bob); a classical mechanics model, in which boundaries can “hit”

a particle and slow down (Bob), a dislocation movement model (Betty),

and a purely geometrical model, with no consequences for the behavior of

the material (Liz). Betty’s explanation has relevant elements of disloca-

218

tion theory (another topic explored in class weeks before), but does not

address completely the question about grain growth; Liz does not see

any relationship between grain size and dispersed particles; Bob only

sees it as a factor that may decrease speed, but never “stop it complete-

ly.” Ken offers a reasonable explanation but fails to say if dispersed par-

ticles accelerate or slow down grain growth. His statement is very similar

to Peter’s, and suggests that they might know a considerable part of the

theory, but lack fundamental understanding of the basic atomic beha-

viors within a material. Ken knows how to recite back the theory about

grain growth, but cannot articulate the physical meaning of the formu-

laic representation.

The pre-interviews, therefore, suggest that students’ explanations, sewn

together on-the-fly, leverage a variety of models, admix different topics

(recrystallization, dislocations, grain growth), and often use the stan-

dard vocabulary and rules-of-thumb of the field, but express a weak

sense of the interconnectedness, relationship, and possible contradic-

tions amongst these components which could be describing different

aspects of atomic movement.

VI.4. FINAL REMARKS This chapter was comprised of two main parts: one study about current

explanation and representational strategies in a materials science class-

room, and a set of preliminary semi-clinical interviews with students.

The results from the first study suggest an overall pattern for such expla-

nation and representational strategies. The prototypical explanation of a

phenomenon is divided into five explanatory events:

a. Description of a micro-behavior.

b. Graphical representation of the micro-behaviors.

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c. Series of intermediary graphical representations toward mathemati-zation.

d. Blended representations: graphics and inscriptions superimposed.

e. Mathematical inscriptions.

Such an approach suggests an existing teaching rationale and underlying

cognitive theory. The belief is that micro-behaviors are a good introduc-

tion to most phenomena in materials science, a necessary part of the ex-

planation, and easier to understand. A second belief is that the micro

behaviors per se are not powerful enough to predict phenomena – and

predicting is core to the engineer’s ethos – thus, ‘conceptual’ explanation

and predictive mathematical apparatus are dissociated. Those micro-

behaviors need to be transformed into manipulable representations

which can ultimately predict behaviors.

Therefore, the data suggest that micro-behaviors are powerful as expla-

natory artifacts, but not powerful enough as a mathematical language.

Then, during several ‘mathematization’ phases, the micro behavior is

translated into representations of decreasing levels of adherence to the

physical phenomena, and increasing conventional mathematical sym-

bolism. The differential nature of most of these representations presup-

poses the subdivision of matter, forces, fields, vectors, and fluxes into in-

finitesimal pieces – as we observed, the initial graphical representations

are repeatedly fitted into a “calculus-friendly”, symmetrical graphical

shape which, for students, could be a difficult cognitive transition.

Indeed, the data of the second part of this study suggested sizeable diffi-

culties in students’ understanding. First, students’ responses were con-

ceptually very dissimilar – for example, while a small minority of stu-

dents correctly viewed grains as orderly groups of atoms, the other ex-

planations barely resembled one another – even for the most basic of

topics in the course. The representational and teaching strategies used

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in the classroom impacted students’ understanding in three ways. First,

the focus on equational representations leaves little time and resources

for in-depth classroom discussions about the micro-behaviors, and those

behaviors were not given much consideration as a language to make

predictions. Second, even when students claimed to know a topic, their

explanations were oftentimes a verbal reproduction of inscriptions with

no sense of causality. Third, the fragmentation of the content into a my-

riad of loosely connected, phenomenon-specific, mathematical artifacts

made their reconnection difficult for students, as the data show – fre-

quently, equations or ideas from one content topic were used to explain

another topic due to superficial similarities and not common behaviors.

      

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 VII STUDY TWO 

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VII.1. SUMMARY This chapter describes and analyzes data from laboratory studies with

students from a sophomore-level materials science course, over three

quarters in 2004, 2005, and 2006. The first part of the study, using data

sources of semi-structured videotaped interviews, shows results from

students interacting with pre-built computer models in materials

science. The second part of the study describes a selected group of stu-

dents building and running their own computer models. Data sources

for this second part of the study include videotaped interviews and arti-

facts created by students. I conclude by (1) identifying aspects of model

interaction which generated deeper understanding of key concepts in

materials science, and (2) discussing affordances of the model-building

activity which enabled students to identify ‘kernel’ materials science

principles and apply them across phenomena.

VII.2. INTERACTION WITH PRE-BUILT MODELS

VII.2.1. OVERVIEW AND EXPLANATION OF THE PHE‐

NOMENON The first part of the study was dedicated to the exploration of one par-

ticularly important model in materials science: grain growth. As I pre-

viously explained, the relevance of grain growth for the studies in this

dissertation is due to both its centrality within materials science content,

its simple yet powerful rule set, and the excellent acceptance of its agent-

based model within the research community.

The first activity proposed to students was simple: observe and reflect

on curvature as a driving force for grain growth. Within the study of

grain growth, curvature is a canonical example of a micro-macro discon-

nect and, and a case of slippage between levels (Wilensky & Resnick,

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1999). Curved surfaces are considered to have higher energy than flat

surfaces, due to the effect captured by the Laplace-Young equation,

which is commonly used in fluid dynamics to calculate surface tension

in liquid-gas interfaces (such as a drop of water). It states that the sur-

face tension in one particle (a drop of water, or a grain) grows as the

pressure difference is increased, and as the radius of curvature decreases:

2p p

Rb a g= + (VII.1)

where pa and pb are the outside and inside pressures, R is the spherical

particle radius, and g the surface tension. In other words, if R ¥ ,

the pressure difference p pb a- goes to zero, and an infinite curvature

radius corresponds to a rectilinear interface. Conversely, for 0R ,

the pressure difference goes to infinity, and thus the interface is highly

unstable.

However, a different yet standard approach to the same phenomenon is

to look at the interaction between individual molecules in the liquid and

in the gas, as we can observe in this example from a standard fluid dy-

namic curriculum:

“Let us first consider a free surface, for example that between air and water. A water molecule in the fluid bulk is surrounded by attractive neighbors, while a molecule at the surface is attracted by a reduced number of neighbors and so in an energetically unfavorable state. The creation of new surface is thus energetically costly, and a fluid system will act to minimize surface areas.” (Bush, 2007)

The grain growth situation is just slightly different, since it is a solid-

solid interface – still, the creation of interface between grains is energeti-

cally costly. At an atomic level, atoms on the concave side of a curved in-

terface will have less equal neighbors than atoms at the convex side. In

Figure VII-1 (left), we observe how a curved interface can be seen as a

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simple sequence of discrete atomic “bumps” into the other side. The yel-

low/red “curved” surface, thus, exhibits yellow atoms with less average

equal neighbors (3) than the red atoms (4 or 5). Conversely, on the right

side of Figure VII-1, the rectilinear interface shows the same average

number of neighbors for either red or yellow (4). Since the number of dif-

ferent neighbors indicates how many broken bonds the atom has, it fol-

lows that atoms with many different neighbors are more unstable, and

so are curved surfaces.

Figure VII-1 The evolution of a curve

boundary in the simulation

→

→

However, what most of the students knew from their previous class-

room instruction were not those principles, but rules of thumb about

how interfaces and grains evolve. Students mentioned, for example, that

large grains consume small ones, grains grow toward their center of cur-

vature, and high-curvature boundaries tend to disappear. However,

those concepts appeared to be monolithic and isolated ideas, hardly

connected to the Laplace-Young equation, and even less to the atomistic

explanation.

VII.2.2. DESCRIPTION OF THE ACTIVITIES The goal of the activity was twofold. First, assess students’ pre-existing

understanding of the phenomenon. Secondly, carefully observe the cog-

nitive shift as the simulation progressed within very small time intervals

(Siegler & Crowley, 1991). The activity consisted of:

1. Open the NetLogo software.

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2. Open the “Grain Growth” model within NetLogo.

3. Using the “Draw Grains” feature, draw two grains divided by a curved surface (see Figure VII-2).

Figure VII-2 Two grains divided by a curved

surface

4. Make an oral prediction of what would happen.

5. Run the model and observe its behavior. The pictures below are snapshots of the typical evolution students observed.

Figure VII-3 The evolution of a curved grain

boundary

t=15 t=30 t=45 t=200

6. Erase the two grains and draw a new configuration: a microstructure with five grains, but one of them a lot smaller than the others, as we

226

can see in Figure VII-4. This type of microstructure will exhibit many triple points, which are (theoretically) immobile points in the material (a more complete explanation is offered within the next few paragraphs).

7. Make an oral prediction of what would happen.

8. Run this second configuration and observe its behavior.

Figure VII-4 Four large grains (yellow, green,

light and dark blue) surround a small red grain (left), and a

zoomed-in view showing a triple point (right)

9. Restart the grain growth model and design a simple experiment using the model. Students were free to pick a topic, but these experiments did not focus on visualization and drawing microstructures anymore, but on quantitative outcomes of several runs of the model. Topics included, for example, investigating grain size over time and the effect of different percentages of impurities. For gathering data, students were instructed to use BehaviorSpace, a built-in experiment-automation tool within NetLogo.

The discussion of the data will follow the three subgroups of activities:

(i) drawing two grains (steps 1-5), (ii) drawing five grains (steps 6-8),

and (iii) designing and running the experiment (step 9).

When invited to make predictions of that would happen to the first con-

figuration with two grains (step 4), most students were unsure of what

would happen. Approximately half thought that the larger grain would

grow at the expense of the smaller, regardless of the curvature of the

boundary separating them, while the other half considered concavity, ra-

227

ther than size, as the main criterion. As they started the simulation (step

5) and saw the grain boundary moving towards its center of curvature

(Figure VII-3), most were surprised that the movement was not smooth

or unidirectional, but that there was intense activity on both grains with

random flipping of atoms. The following excerpt suggests that visualiz-

ing this evolution could have sparked some changes in Liz’s understand-

ing of the phenomenon:

Interviewer Can you describe what you see?

Liz Just because one grain has a concave side and the other has a convex side, so it comes in towards the concave, because... [pause] does line tension applies in this situation?

Interviewer Line tension?

Liz That might be from dislocations... I might be mixing them up. Just because... when you have something... part of the grain is like, curving in, mostly likely other parts of the grain are curving in, so the tension of the grain boundary lines, so the force outside is greater than the force inside, so it will like shrink, it looks like that probably be like straight in the middle, rather than entirely red... just because if the red part also has some concave thing that is off the screen it will just like go together.

Liz is apparently mentioning results of the Laplace-Young equation,

which relates surface tension and curvature (“other parts of the grain are

curving in” and “the force outside is greater than the force inside”.) Howev-

er, she cannot yet think at the “micro” level: to visualize what is happen-

ing on the computer screen, she has to imagine a large circle going off-

screen – which is probably a consequence of what she remembers from

class, where grains were always approximated as spheres. In her explana-

tion, she still employs macroscopic geometrical elements, such as

spheres, circles, lines, boundaries. She does not yet construe the local in-

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teractions along the curved interface as mechanisms for those macros-

copic outcomes, but only aggregate level effect of curvature.

Steps 6-8 of the activity (configuration with five grains) was a crucial ex-

perience for Liz. She started to transition from the memorized rules-of-

thumb to micro-level reasoning. The following excerpt took place when

she was observing a triple point – a region where three grains meet and

the probability to flip to any of the surrounding grains is the same, as

there are two atoms of each grain around the central element – see Fig-

ure VII-4. While observing the model, Liz was told to zoom in and out

NetLogo’s “view,”16 so as to also see what was happening at the micro

level, following a single atom.

Liz Right here there is an equal position for red, yellow and blue, but it just happens to be that blue won, it keeps winning.

Interviewer How would you explain that?

Liz Because... it you look at one of those points, either of the three colors, they all have the same number of other colors around it, so it is not favorable to choose one or the other...

Interviewer What angle is here?

Liz Oh, so this is the 120 degree angle between the... [pause]

Interviewer Did you talk about it in class?

Liz Briefly. He [the professor] said that when you reach a triple junction, it will become 120 degrees.

Interviewer So are you saying that there is an equal probability?

Liz

16 NetLogo’s “view” is the main graphic window of the software, where users can see the agents in action.

229

Well, I just don’t understand why blue is doing so much better, in general. Eventually just one has to become bigger, because this is the most energetically favorable thing, so maybe... blue was bigger, but now yellow is coming back, so maybe next time blue gets bigger again, and they will just keep going. Maybe it will just be like that for a long time.

Interviewer So what happens to growth speed?

Liz Eventually they will get like... two big ones... and then it will take forever.

Interviewer So what could be the law?

Liz It will eventually taper off... to some point... because if you have a lot or grains then you will... the rate of increase will be faster, but when average grain size increases it gets harder and harder to increase the rest of them, so it just goes...

Interviewer Why is it harder and harder?

Liz Just because there isn’t a distinct... [pause] being in this orientation is more favorable than this other one so you have to pick and choose... the grains are doing that, but it is not happening quickly just because you know, either one can happen.

In this very short time watching the model, Liz was able to understand

and generate hypotheses about two key ideas: triple points and loga-

rithmic laws (the literature refers to these ideas as particularly hard to

understand, e.g. Krause & Tasooji, 2007). Rather than trying to assem-

ble a response concatenating rules of thumb pulled from classroom in-

struction, now Liz departed from what she knew about other phenome-

na and what she was actually observing in the simulation. Even without

formally mathematizing the time dependency of boundary migration

during grain growth, she understood the reason for the triple point to be

considered a “low-mobility” point in a microstructure. The central atom

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has two atoms (out of six) of each of the surrounding grains as neigh-

bors, so the switch probability is the same (1/3), and there is no pre-

ferred growth direction. She also realized that the time dependency is

not linear: growth speed decreases over time and eventually tapers off.

Rather than being told, Liz arrived at this conclusion on her own, by draw-

ing microstructures on the computer, changing variables and observing

the dynamics within a microworld with known rules. Particularly, when

asked about the fundamental reason for the “tapering off” of grain

growth, she affirmed that “[…] because there isn’t a distinct orientation

[which] is more favorable” – she was getting at the very core of the expla-

nation. This same idea could be useful to explain other phenomena in

materials science – we will see how students applied such generative

ideas to other phenomena in the next section.

Similarly, Peter and Elise, notwithstanding their initial difficulties in ex-

plaining grain growth during the pre-interview (see previous chapter),

understood exactly the logarithmic nature of the grain growth law:

Interviewer What could be the rule for grain growth speed?

Peter As the grains get bigger, each grain is increasingly hard to take away from because it's bigger, so the interfaces start to be between two large grains, instead of small grains, so an interface between a large grain and a large grain is less likely to have a lot of movement because both grains are large and they are already in a state where they don't want to shrink.

Interviewer What will happen to this surface [between two grains]?

Elise [It’ll] shift up to be vertical. [looking at the simulation] Yes, it’s just getting flatter.

Interviewer Why do you think it wants to get flat?

Elise

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It's like the nearest-neighbor thing, these want the most nearest green neighbors, the red ones want the most red ones.

Interviewer [some minutes later, she is looking a triple point] What’s happening here?

Elise It has the same number around each other, so, the red, the angles are all at equilibrium, they are all a stable formation.

Interviewer And what's that angle there?

Elise It's a hexagon, I guess it's 360 divided by three, 120.

Generally, most students knew that the small red grain in Figure VII-4

was going to disappear. From their reactions while observing the simula-

tion, they seemed to be expecting a unidirectional animation of the grain

being gradually consumed by the surrounding ones and disappearing.

This was consistent both with the heuristics and the types of results of

aggregate tools, animations, and equations commonly learned by stu-

dents in class – as a consequence of the urge to fit discrete stochastic

events into the traditional representational scheme (see the example of

diffusion in the last chapter), the aggregation of these stochastic events

are represented as unidirectional processes (Stieff and Wilensky (2003)

detected a similar process in undergraduate chemistry). However, in

this case, what students observed was different: behaviors emerging

from local stochastic interactions. As a result, at times, the small grain

would grow, but most of the times it would shrink. Some of the students

wanted to slow down the simulation and use the zoom tool to see the

process in more detail. But in doing that, students could only see the mi-

cro-level phenomenon (atoms flipping to different orientations). By

zooming out again, they could observe the emergent behavior: curved

surfaces disappearing as the Laplace-Young equation would predict.

Words commonly used in the classroom, such as “shrink,” “consume,”

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and “growth” acquired a new meaning. Those metaphorical terms, as

our pre-test data suggested (see the last chapter), can mislead students

to interpret literally their meaning – interacting with the grain growth

model, students realized the main phenomenon taking place was not

grains growing or shrinking but atoms switching places, and the meta-

phors were just describing the aggregate effect of such behavior. This

was a central element of the whole experience and, as we will observe,

deepened as students progressed in the user study.

The last activity (step 9) of the study was a “BehaviorSpace” (Wilensky

& Shargel, 2002) experiment. This NetLogo feature enables users to run

tenths or hundreds of simulations automatically, each with different pa-

rameter settings, sweeping entire parameter spaces. Students ran at least

one set of experiments, plotted the data, and came up with theories to

describe the phenomenon. Most students chose to model the influence

of dispersed particles on grain growth. The textbook explanation of this

phenomenon takes approximately four pages. It begins with an account

of how a force P appears when a boundary attempts to go through a par-

ticle, and then calculates the drag force by means of geometrical approx-

imations (see Figure VII-5).

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Figure VII-5 The textbook picture explaining

how dispersed particles affect boundary migration

Departing from those geometrical approximations, the formula is ob-

tained with a series of derivations (Porter & Easterling, 1992, pp. 141),

which relates the fraction of dispersed particles f, the mean radius of the

particles r, and the maximum particle size after grain growth, Dmax:

max2

3 3 2 3 4

2 2 32

f f f rP r D

r r fr D

g g gp g

p= ⋅ = = = (VII.2)

The algorithm in the grain growth model ignores the existence of this

formula. Bob was somewhat skeptical that the ‘official’ equation could

be matched by the simulation. Thus he programmed NetLogo to run a

series of simulations with percentages of particles varying from 0% to 8%

(see screenshots and individual plots of grain growth speed in Figure V-

5). He also constructed a plot to aggregate the results across all experi-

ments, and subsequently tried to compare their own curve with the

theoretical data (dotted line in Figure V-5’s lower plot). To his surprise,

the two curves had a reasonable match. Other students, with slight varia-

tions, undertook the same project, or selected different aspects of the

234

phenomenon. By exploring entire parameters spaces, and having not on-

ly the dynamic visualization but also actual numerical data to base their

explanations on, they were able to further generate original hypotheses

and find correlations.

Figure VII-6 Sequence of screenshots from

Bob’s experiment Particles = 8 Particles = 4 Particles = 1 Particles = 0

VII.3. BUILDING THEIR OWN MODELS The second session was the model construction part of the study. Stu-

dents had two and a half hours to learn the basics of the NetLogo lan-

guage and program a new model of a materials science phenomenon.

For this session, which took place two or three days after the first ses-

sion, students were asked to bring one idea for a new model of a mate-

rials science phenomenon. They pursued questions of their interest or

problems that they did not understand during regular instruction. By au-

thoring new models or new features for the existing models, they could

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elaborate on answers to their research questions. A comparison between

the pre-interview data, when students relied on ready-made statements

about the phenomenon, and their performance on the last day of the

study, when they built models relying on fundamental atomic behaviors,

suggests that designing those behaviors promoted a significant cognitive

shift. Even more than exploring the existing models, constructing their

own models was a cognitively significant experience for most. In this

section we will narrate and analyze some of those learning trajectories,

focusing in particular on four affordances of the agent-based modeling

approach:

a. One-to-many generativity: algorithms and rules can be used to understand many phenomena.

b. Formalization of intuitive understanding: students’ intuitive ideas about atomic behavior can be directly encoded into a formal computer language.

c. Foregrounding of physical processes: the model, both graphically and encoding-wise, resembles the actual phenomena.

d. Model “blending”: micro behaviors are easier to combine and “blend” than their ‘macro’, aggregate counterparts.

VII.3.1. BETTY’S MODEL Betty built a model to investigate grain growth with a new and impor-

tant feature: taking into consideration the misalignment between grains.

In her innovative model, the more misalignment across the boundary,

the harder it would be for an atom to jump from one grain to another. In

Figure VII-7 we have an example of two grains with very different crys-

tallographic alignment (on the left, low misalignment, on the right, high

misalignment) – Betty wanted to investigate how the misalignment an-

gle would influence the activity across the boundary.

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Figure VII-7 Betty’s model: grain growth with variable misalignments

The construction of this model presented Betty with many challenges.

The first was to convert the grain orientation’s angle, which could lie in

any of the four quadrants (but would be equivalent for the purposes of

the algorithm), to a normalized quadrant-independent measure. Betty’s

solution, after much thinking, sketching and trying out different trigo-

nometric functions, was to use the arcsine function. The following pic-

ture shows some of her reasoning. From her drawing, we can observe

that she was using geometrical analysis from a micro level, taking into

consideration the orientation of individual atoms.

Figure VII-8 Betty’s sketches about angles,

sine and arcsine

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She considered that the probability for an atom to jump to the next grain

should be dependent not only on the number of different atoms around

it, but also on the average misorientation between the two grains. Low

misorientation would promote easier migration, since the two grains

would be almost the same. Apart from the initial difficulty in figuring out

the best trigonometric function for the angle comparison, Betty knew

what she needed to do, without resorting to any of the textbook formu-

las. For her, at the micro-level, adding the misorientation effect was

quite easy17. She simply added one command to the original grain

growth model to implement her change – previously, in the traditional

equation-based materials science, making such a change would require

long and demanding derivations. The resulting code of her misorienta-

tion calculating function was:

;;calculate the absolute value of the arcsin to-report misorientation [angle] report asin (abs (sin (angle))) end ;;calculates the absolute value of the sum of the two arcsins to-report calculate-misorientation [angle1 angle2] report abs (misorientation (angle1) + misorientation (angle2)) end ;;reports the average misorientation for a given atom to-report compare-misorientation let i 0 ask neighbors6 [ ;;calculates the misorientation between the current atom ;;and each of its 6 neighbors set total-misorientation (total-misorientation + calculate-misorientation heading (heading-of neighbors6)) set i i + 1 ;update counter ] ;;returns the average misorientation report (total-misorientation / i) end

17 On a more advanced level, similar research was undertaken and published by researchers, such as Kimura, & Watanabe (1999)

238

Then, having her reporters calculate how much each given atom would

differ from its neighbors angle-wise, she changed the original grain

growth procedure, adding one extra simple “if” statement:

Old procedure if future-free-energy <= present-free-energy [set heading (future-heading)]

Betty’s new procedure if future-free-energy <= present-free-energy [ if (present-heading - ([heading] of one-of neighbors6) < miso-rientation) [set heading (future-heading)] ]

Whereas the aggregate and macroscopic mathematical models did not

afford insights as Betty’s, the agent-based approach provided a “low-

threshold” entry point for Betty to implement her ideas by constructing

models. Her model was very consistent with known theory, even though

she was not cognizant of this theory prior to the interventional study.

Betty’s model illustrates one of the main advantages of the agent-based

representation, which I will discuss more in the conclusion of this chap-

ter: at the micro level, the mathematical machinery required to add new

phenomena or parameters to an existing algorithm is much simpler than

in traditional representations. Instead of employing numerous equations

to add her ‘misorientation’ effect, looking through atomic glasses, just

one line of code was enough.

VII.3.2. BOB’S MODEL: GRAIN GROWTH WITH HETE‐

ROGENEOUS PRECIPITATES Bob wanted to include a new parameter in the grain growth model: the

size of the dispersed solid particles. The idea was to enable users not on-

ly to change the percentage of particles (which was already imple-

mented in the grain growth model), but also the radius of the particles.

Bob realized that this seemingly simple change was in fact challenging.

239

Given a certain percentage (in mass) of particles, their number had to be

adjusted to compensate for the increased mass of each particle. That in-

volved the calculation of the area of each particle (in a hexagonal grid)

and the total area of the sample, to determine how many hexagon seeds

would be necessary for a specific percentage. The first problem involved

the conception of an algorithm for calculating the area of polygons

placed in the hexagonal grid, which turned out to be an interesting ma-

thematical exercise: particles with different radii, in a hexagonal grid,

have different shapes (see Figure VII-9). Bob realized that a recursive

procedure would be adequate; a radius increase by one unit would simp-

ly add one layer of near-neighbor atoms to the existing particle.

Figure VII-9 Bob's attemps to understand

how to calculate the particles' areas, first “hard-coded” in

NetLogo (top), and then figuring out a formula to

accomplish it (bottom)

Finally, Bob found a way to code his formula in NetLogo:

repeat element-size [ set element2-individual-area element2-individual-area + (6 * m) set m m + 1 ]

After completing the model (see Figure VII-10), he investigated the in-

fluence of particle size on grain growth: maintaining the same percen-

tage in mass, how is growth affected by changing each individual precipi-

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tate’s size? He concluded that the granularity of the particles has a

strong influence on the final grain size – in other words, having fine or

coarse particles (even with the same overall amount in mass) would

have a dramatic effect on the final grain size. He was able to run large

batches of simulations in BehaviorSpace, chart the data, and explore

possible explanations. By constructing his own model, he went even fur-

ther than his previous experiment, on the first session, with different

percentages of particles (see Figure V-5). Having previously addressed

the f variable (percentage of particles), Bob’s new model enabled him to

also manipulate the other part of the equation, the r variable (radius of

the particles18), thus fully re-creating the max4

3

rD

f= equation within

an agent-based approach.

Figure VII-10 Bob's model for particles with

varying size

VII.3.3. ANAND’S MODEL: INTERFACIAL ENERGY Anand did not want to investigate anything related to grain growth, and

built a completely different model from scratch. His idea was to explore

18 On a more advanced level, similar research was undertook and published by many researchers, such as Gao, Thompson, & Patterson (1997) and Hassold & Srolovitz (1995).

241

in detail interfacial energies due to atomic misalignment. In other words,

his model meant to determine how much energy was stored in an inter-

face between two grains that did not match in terms of atomic spacing.

We can observe his model in Figure VII-11: one of the grains (in red),

has a very large spacing between the atoms compared to the “blue”

grain. This causes strain in the interface between the two. Anand built

this model using the same “kernel” as the grain growth model: atoms

look around and check the state of their neighbors, deciding what to do

based on the number of equal and different neighbors. Even though this

topic, in the regular curriculum, was completely separate from grain

growth, he was able to identify a “transferable” micro-level model be-

tween the two phenomena. He calculated the final energy of each atom

with a reporter that simply counted the number of connected atoms

within a certain distance.

to calculate-interfacial-energy ask element1 [ set interfacial-energy (count turtles in-radius 2 with [color = blue]) ] end

Figure VII-11 Anand’s model for detailed

study of interfacial energies

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VII.3.4. JIM’S MODEL: POLYMER CHAINS Jim was taking a polymer science course at the time, and just some classes before he had learned about polymer chains and how they moved around. Polymer chains can move and expand, but not if that process ends up breaking the chain itself. When he was choosing the idea for his authored model, he very quickly realized that the neighbor-hood based grain growth algorithm could be a good start for a polymer model. After all, per Jim, what atoms were doing was:

1. Moving randomly

But

2. Not breaking the chain

3. Not crossing the chain

His NetLogo implementation followed these three simple steps.

to move ;; choose a heading, and before moving the monomer, ;; checks if the move would break or cross the chain set heading 90 * random 4 if not breaking-chain? and not crossing-chain? [fd 1] end

To check if the monomer movement would break the chain, he simply

built a procedure that searched atoms at the four orthogonal directions.

In case there were any atoms there, the procedure returned ‘false’ and

that atom did not move.

to-report breaking-chain? ;; checks if moving the turtle would break the chain report ( heading = 0 and any? atoms at-points [[-1 -1] [0 -1] [1 -1]] ) or ( heading = 90 and any? atoms at-points [[-1 -1] [-1 0] [-1 1]] ) or ( heading = 180 and any? atoms at-points [[-1 1] [0 1] [1 1]] ) or ( heading = 270 and any? atoms at-points [[1 -1] [1 0] [1 1]]

243

) end

A similar reporter was done for crossing chain, but with a different set of

neighborhood points. The model’s interface (and typical initial setup)

can be seen in Figure VII-12.

Figure VII-12 Jim’s “Polymer Chains” model

But the model worked only in a very limited way, because if there were

too many atoms “clumped” together, they would never get a chance to

move, because any movement would either break or cross the chain.

One reason for this problem is that it failed to incorporate the attractive

and repulsive forces between atoms. Therefore, even though some

atoms could move, the chain would not greatly expand because most

atoms were within a “one” radius of each other. Jim needed a spring-like

repulsive force activated at particular time steps to relax the system, and

an attractive force to keep the atoms close to each other. His answer was

to create the one extra procedure with just a single line of code:

layout-spring atoms links .4 1 0.1

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By blending two algorithms, Jim got his model to work exactly as the

animation shown in class by the professor – but in a short program of

about 15 lines of code. In Figure VII-13 we have a typical evolution of a

polymeric chain. On the last frame (bottom, right), the “movement”

procedure was turned off, so just the spring-like forces were in place, ge-

nerating a smoother chain.

Figure VII-13 The evolution of a polymer

chain in Jim’s model

Jim’s model is another example of the easy blending of algorithms (in

this case, spring-behavior and restricted movement), and the one-to-

many generativity (again, a neighborhood-checking mechanism was at

the core of the model).

VII.3.5. PETER’S MODEL: DIFFUSION VS.  INTERFACE CONTROLLED PROCESSES & SOLIDIFICATION 

Peter’s model was another example of the transferable affordances of the

agent-based representation. In the pre-survey, he identified diffusion

control as one of the hardest topics in the course. In the second session,

that was precisely his choice for building a model. Peter started the

model from scratch, since it was significantly different than most of the

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pre-built models. In less than two dozen lines of code and two hours, he

had a model the complexity of which is far beyond what is expected

from typical assignments in the Microstructural Dynamics course, con-

sidering the classroom observations and analysis of class materials. Peter

used the agent-based approach and some micro-rules from grain growth

to create a diffusion model. Even though the two phenomena have dif-

ferences, he managed to identify the common micro-rules and copy

them from one model to the other, with the necessary adaptations, in

the same way as Anand did with his interfacial energy model.

Figure VII-14 Comparison of the two algo-

rithms

In materials science, it is particularly important to tell apart transforma-

tions that are interface-controlled (i.e., the slowest phase happens at the

interface of the two materials) from diffusion-controlled (the slowest

part is for atoms to “travel” to the interface, where the actual reaction is

fast). Knowing the slowest phase of a given process, engineers can great-

ly optimize that process. Peter’s purpose was to build a model to investi-

gate this phenomenon and compare diffusion- and interface-controlled

reactions. The textbook explanation of this phenomenon is a 5-page

narrative with five different equations, which are put together to show

that the driving force (referred to as ∆μBi ) is:

246

( )lni i

B i ee e

X RTRT X X

X XmD = @ -

(VII.3)

where Xi and Xe are the chemical compositions of the two materials, T is

the absolute temperature, and R is the ideal gas constant (Porter & Eas-

terling, 1992, pp. 177).

Again, Peter ignored the existence of this long sequence of equations.

He concentrated in the micro-rules concerning the phenomenon, and

realized that the rules were not very different from other models. After

all, atoms were just moving randomly and “bumping” into a solid, stick-

ing to the solid according to a certain probability. Just as Bob did, Peter

was concerned with the correctness of his work. He generated a series of

plots and screenshots so as to match his data with the textbook plots,

part of which are shown in Figure VII-15.

Figure VII-15 Results of Peter’s model with

diffusion control (top), interface control (bottom), and

the chart from the textbook, where we can identify a similar

shape (rotated for clarity)

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Peter’s algorithm was straightforward:

1. If an atom in the liquid bumps into a solid, it attaches itself to the bulk and “becomes” solid (with a certain probability, dependent on their chemical properties), hence: if ((breed = element1-liquid) and (neighbor-breed = solid) and (element1-probability > random-float 100)) [ set color neighbor-color set breed neighbor-breed ]

2. If the atom is in the liquid (breed different than solid, or “!=solid”), and it meets an atom different than itself, the atoms switch places – in other words, diffusion is taking place:

if ((breed != solid) and ;;if you are in the liquid (neighbor-breed != solid) and ;;and one neighbor is liquid (diffusion-speed > random-float 100)) ;;and depending on diffu-sion speed [ set [color] of random-neighbor color ;;switch neighbor’s color set [breed] of random-neighbor breed ;;switch neighbor’s breed set color neighbor-color ;; switch the atom’s color set breed neighbor-breed ;; switch the atom’s breed ]

In a dozen lines of code, Peter was able to model both diffusion and so-

lidification, exclusively manipulating local rules. At the end of the ses-

sion, I asked Peter about the next steps in his model’s implementation,

had he more time to work on it – again, he demonstrated a solid under-

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standing of how to manipulate those basic rules to generate new models

without great difficulty:

Peter I did a liquid to solid model, now I want to be able to invert it, do a solid to liquid algorithm.

Interviewer And how would you implement it?

Peter It’s simple. I’ll just invert the probability. It’s just the opposite probability. I don’t have to change much.

[…] Interviewer

And how would you implement, for example, dispersed particles in a grain growth model?

Peter I would put in molecules that have zero probability to change to anything else, and zero probability of another molecule to change into them.

Peter’s response demonstrated a level of understanding of the process

that was in great contrast with his pre-interview data, in which although

he correctly identified and explained some phenomena, he failed to see

how those explanations could be put to use to further his own know-

ledge about a particular topic.

VII.4. FINAL REMARKS My purpose in this chapter was to investigate the learning outcomes of

students interacting with and building models. In the first part, I showed

how by foregrounding micro behaviors, the design of the grain growth

model enabled students to identify the mechanism for the non-linear

(logarithmic) growth rate of the grain, and understand it as an emergent

property of elementary local rules. Students were able to infer the

growth law even without resorting to any equational manipulation or to

their class notes. This was in stark contrast with Study 1, in which stu-

249

dents had difficulties explaining even very basic ideas in the course (i.e.,

‘what is a grain?’). Also, in Study 1, I showed how the representational

practice of turning pictorial representations of discrete processes into

differential equations made the content opaque to most students. The

agent-based representation, conversely, maintained the fidelity between

the actual mechanism and the computational representation. When vi-

sualizing the grains grow, students had in mind the algorithm individuals

atoms were following, and could infer aggregate behaviors from them

(i.e., the growth slows down because “as they grow, it is increasingly

hard to take away from them, or “either one can happen”.)

Then, students ran batches of experiments with the model, plotted the

data, and went back to their textbooks for validation. After doing re-

search on their regular class materials, they were able to reconnect their

own empirical results to the traditional formulas and descriptions of the

phenomena. Yet, throughout that process, they did not lost touch with

the actual atomic behaviors that the grain growth models encoded.

In the second part of the study, when students built their own models,

we observed that the agent-based representation was also useful to

extrapolate from the initial phenomenon (grain growth) to other phe-

nomena as well, by means of extracting, customizing, and combining the

atomic micro rules.

The main affordances of the agent-based representation which were in-

stantiated in the last part of the study were:

a. One-to-many generativity: algorithms and rules can be used to understand many phenomena.

b. Formalization of intuitive understanding: students’ intuitive ideas about atomic behavior can be directly encoded into a formal computer language.

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c. Foregrounding of physical processes: the model resembles the actual phenomena both graphically and in terms of the rules em-bedded in the code.

d. Model blending: micro behaviors are easier to combine and super-pose than their ‘macro’, aggregate counterparts.

The following table shows how each of the projects instantiated such af-

fordances.

Table VII-1 Affordances of the agent-based

representation One-to-many

generativity Formalization of intuitive under-

standing

Foregrounding of physical processes

Model blending

Betty grain growth with misalignment

Neighborhood-based local count, energy minimization

“the more misa-ligned, the harder to jump”

Atoms vibrate and jump

GG algorithm + micro-level geometry

Bob grain growth with heterogeneous precipitates

Neighborhood-based local count, energy minimization

Atoms vibrate, jump, and collide

GG + incremental area calculation

Anand interfacial energy

Radius-based local count, energy minimi-zation

“an interface be-tween different structures is less stable”

Simplified GG + radius-based instead of neighborhood-based

Jim polymer chains

Neighborhood- and radius based re-stricted movement, repulsion/attraction

Atoms are con-nected by springs

Atoms in a polymer chain move but keep the integrity of the chain

Restricted movement, diffusion-like + spring-like repul-sion/attraction

Peter diffusion vs. inter-face controlled processes & solidi-fication

Neighborhood-based local count, energy minimization

“I’ll just invert the probability.” – melting and solidifi-cation are symme-trical.

Diffusion and solidification as probabilistic phe-nomena

GG adapted for solidi-fication + diffusion

The one-to-many generativity of the agent-based approach is evident in

almost all projects. The grain growth algorithm was present in almost all

of these projects, with the needed modifications. Betty and Bob added

new features to the original model, making it far more sophisticated by

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just adding a few lines of code. Peter went further, and by just making

atoms mobile ended up modeling an entirely different phenomena with

very similar rules, just like Jim was able to model polymer departing

from a simple neighborhood-checking algorithm.

The other powerful aspect of one-to-many generativity is that it enables

easy model blending. Jim’s polymer model, for example, combined a

modified diffusion model and springs, in order to model freely moving

(but interconnected) atoms. Peter also made use of model blending, by

putting together a solidification and a diffusion algorithm.

The foregrounding of physical processes and the formalization of intui-

tive ideas about atomic behavior are two intertwined affordances of the

agent-based approach. As we saw throughout this chapter, students were

able to depart from very elementary ideas about atomic behavior in or-

der to build complex models, even about phenomena they had not been

instructed about before. Bob’s model about particles of varying sizes, for

example, is not even in the textbook. After the next chapter, I will return

to this discussion in greater length with new data .

Despite students having successfully built agent-based models in a very

short period of time (2.5 hours), and the evidence about the affordances

and features of the agent-based approach, this study took place in a la-

boratory environment. Students were taken out of the classroom into a

artificial environment, in which I was always present to help. Would that

design work in a regular engineering classroom? Can students achieve

the same level of sophistication in their models with far less support?

And, also, would the learning outcomes I observed in this study survive

the test of the ‘real world’? The goal of the next study was exactly to ad-

dress these questions.

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VIII STUDY THREE 

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VIII.1. SUMMARY In Study 1, we investigated the typical knowledge encoding infrastruc-

ture in a materials science classroom, as well as students’ understanding

of some basic concepts seen in class. In Study 2, I showed how agent-

based modeling could generate a shift in students’ understanding to-

ward more generative epistemic forms.

In Study 3, my goal is twofold:

a. Present a proof-of-existence of agent-based modeling activities in a regular engineering classroom, under relatively common con-straints, and investigate students’ motivation and engagement in the activity.

b. Further the research about the representational affordances of agent-based modeling, and assess if it constituted a better match for students’ intuitive ideas about atomic behavior in materials.

In the end, I hope to have a reasonable case for the usefulness and prac-

ticality of agent-based simulation for learning materials science. And,

more importantly, a proof of existence of the content-representation-

pedagogy ‘fit’ which is one of the main contributions of the dissertation.

VIII.2. BRIEF DESCRIPTION OF THE STUDY This study followed the format of most assignments in the Microstruc-

tural Dynamics class: an assignment was posted on the course website

and a deadline was set. A special TA (myself) was assigned to help stu-

dents with their modeling assignment. Differently from the previous

studies, in which students were videotaped during the entire model-

building process, in the present study students did part of the work at

home. However, they were instructed to run a special version of NetLo-

go which logs all of their interactions with the environment, and tracks

the evolution of their model, keeping a snapshot of every instance of

compiled code. In addition, I videotaped all of their sessions with the

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TA, kept incremental versions of their models, and saved all email

communication during the study, which was structured as follows:

1. Introduction: I made a 15-minute presentation in class about the assignment (day 1), and students received the assignment via the online course management system (day 2).

2. Students scheduled and attended an individual 45-minute NetLogo tutorial (days 3-7). Before the tutorial, there was a 30 minute pre-interview, and questionnaires to assess students’ familiarity with computers, computer programming, and modeling.

3. Model-building, divided into multiple milestones:

- One week after the tutorial (days 7-9), students had to send by email their desired topic for the model.

- After the tutorial, students had access to a wiki page in which they could freely schedule TA slots for help with the programming.

- 2.5 weeks after the tutorial (day 19), students had to send a ‘beta’ version of the model.

- 3.5 weeks after the tutorial (day 26), students sent their final model with a detailed report (8 pages, on average) explaining the model, and comparing model data with established theoretical data.

4. Post interview: after having finished their model, students came back to the lab for a 30-minute interview. During this interview, they would:

- Explain the phenomenon they have just modeled (for a technical and non-technical person).

- Answers questionnaires about their familiarity with computer modeling in materials science.

- Chose two materials science phenomena and, ‘thinking on their feet’, explain how they would build a computer model of them.

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VIII.3. IS MODELING VIABLE? ASSESSING THE ACTIVITY

VIII.3.1. FAMILIARITY WITH COMPUTERS Students’ familiarity with computers and programming was an impor-

tant variable in the study, since programming was a principal part of the

assignment. The pre-survey had several questions around familiarity

with computers and programming, which are shown in Figure VIII-1

and Table VIII-1, below. Students were asked to rate their (a) familiarity

with computers in general (top left), (b) familiarity with programming

(top right), as well as (c) the size of the longest program they have ever

wrote (bottom). Also, Table VIII-1 shows students’ “first” programming

language and how familiar they reported to be with it.

Figure VIII-1 Various measures of students’

familiarity with computers

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Table VIII-1 First programming language and

students’ familiarity First programming language Number of students MATLAB 16 (84%)C++ 2 (11%)Meta 1 (5%)

Rate your familiarity with the language Number of students I barely remember anything 1 (5%)Superficial, just the basics 1 (5%)I can write small programs 14 (74%)I can write long programs 3 (16%)I am an expert programmer 0 (0%)

The distribution of students’ programming ability is approximately

normal, and the length of the longest program is very concentrated on

the 51-200 range (74%), which corresponds to a typical MATLAB as-

signment. 58% reported an “average” familiarity with computers, while

14 out of 19 reported to be able to write “small programs” in MATLAB

(which was cited by 84% of students as their first programming lan-

guage).

The data suggest, thus, that perhaps counter to stereotype, engineering

students are not “programming wizards” but rather have a relatively ba-

sic knowledge of programming languages and techniques. Only three

students did not mention MATLAB as their first language. Given that

they had a MATLAB course in college just some quarters before, it is

reasonable to claim that the great majority of students have had at most

a one-quarter exposure to computer programming, and therefore are far

from being programming experts. The other relevant piece of data is

that just a small number of students (3) reported being expert pro-

grammers.

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VIII.3.2. TIME ON TASK Another important consideration for the assignment was the number of

hours or work it would require from students. Differently from the lab

studies of 2005, 2006, and 2007, this study was conducted in a real class-

room environment in which practical considerations such as students’

workload were important. Therefore, in the post-survey, students were

requested to report the number of hours they spent on each part of the

project:

“Thinking about your project idea.”

“Doing research about the science behind your chosen phenomenon.”

“Just learning the NetLogo language.”

“Actually programming your model.”

“Running 'virtual' experiments, plotting data.”

“Writing up the final report.”

“Getting help from the NetLogo TA.”

“Getting help from the other TAs and the professors.”

The results are in Table VIII-3, Figure VIII-3, and Figure VIII-4. Consis-

tently, programming was the task that consumed most hours (24%), fol-

lowed by getting help from the NetLogo TA, and writing the final re-

port. The mean total hours on the project was 20.2, which averages

about 5 hours per week.

The official course evaluations (filled by students at the end of the quar-

ter) provide evidence that the new assignment, with all of its new re-

quirements, did not impact significantly the total number of hours stu-

dents spent out of class. In Table VIII-2 and Figure VIII-2 we have a

comparison between the (self-reported) number of hours spent in out-

of-class work.

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Table VIII-2 Hours spent on out of class

coursework, reported in the course evaluations (2007, n=18,

2008, n=23)

Out-of-class work (hours/week) 2007 2008

Less than 3 6% 9%

4h–7h 67% 52%

8–11 17% 35%

12–15 6% 0%

16–20 6% 0%

>20 6% 4%

Weighted average 8.60 7.20

Figure VIII-2 Hours spend on out of class

coursework. The bars indicate the percentage of students in

each range, per their responses in the official course evalua-

tions.

It is important to note that both in 2007 and 2008, the same professor

was assigned to the course, and the same course materials used. Enroll-

ment was also very similar: 22 students in 2007 and 23 in 2008.

259

If on average students spent between 7 and 8 hours weekly on course-

work, 5 hours for the modeling assignment is perfectly inside this range,

leaving extra hours for other activities as well. Also, the increase in week-

ly hours from 2008 (7.2) to 2007 (8.6) is modest, considering that the

modeling assignment was intrinsically more complex—the assignment

it replaced was just a list of exercises.

However, a real issue was that the assignment was more complex but

still only worth 3% of the final grade, which, as several students noted,

was incompatible with the 20.2 hours. In the post-survey, I asked stu-

dents about the correct percentage that the assignment should be worth,

and the mean response was 13.9% (std. dev. = 8.1), with values ranging

from 5% (5 students, or 28%) to 30% (2 students, or 11%). That seems

compatible with the number of hours they reported for out-of-class ac-

tivities. If they normally spend 80 hours a quarter on those activities, and

the exams are worth approximately 50% of the final grade, a 20-hour as-

signment should be equivalent to approximately 12.5% of the final grade

(80/20 * 50%).

The data also show that “programming” was the most time consuming

part of the assignment, but still within the normal weekly requirements.

Students took 2.9 hours to learn NetLogo from scratch, even given that

their initial knowledge of programming was not advanced. Even if we

put that together with “Learning NetLogo” and “Help from the NetLo-

go TA,” the total time somehow related to programming and learning

the language goes to 56%, or approximately 11h, equivalent to 1.5 weeks

worth of out-of-class work, thus still compatible with the expect weekly

workload (considering that in those 11 hours they were both building a

model and learning the language). Although that number is higher than

the more “conventional” tasks in the modeling assignment (writing a re-

260

port, doing literature research, running experiments) it seems a very rea-

sonable number if we consider:

Students took a quarter-long MatLab course (approximately 30h of lecture per quarter, plus homework hours) and still most have not programmed anything longer than 200 lines of code. So it seems that spending 11 hours (within another course) to learn an entirely new language and build a scientific model was an efficient use of time and speaks to NetLogo’s low threshold design.

Traditionally, NetLogo workshops conducted by the Center for Connected Learning and Computer-Based Modeling last from 16–40 hours (2–5 days). An 11h learning period, perhaps made more efficient due to the availability of one-to-one help (the “NetLogo TA”), does not differ greatly from that.

Table VIII-3 Mean hours for each task

Task Mean (h) Percent Std. dev. (h) total hours 20.2 6.7

Programming 4.8 24% 2.1

Help from the NetLogo TA 3.4 17% 2.3

Writing final report 3.3 17% 1.4

Learning NetLogo 2.9 15% 1.2

Research about the science 2.1 10% 1.5

Running virtual experiments 2.1 10% 1.3

Thinking about project idea 1.4 7% 1.1

Help from the other TAs 0.1 0% 0.2

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Figure VIII-3 Percentage of time spent on

each task

Figure VIII-4 Hours for each task

VIII.3.3. STUDENTS’  FEEDBACK To finish the section on the viability of modeling in an engineering

classroom, it might be useful to comment on students’ feedback on the

assignment, provided via a computer-based survey just after their final

262

interview. The answers were recorded online and subjects were re-

minded that there would be no impact on the grading since (1) the pro-

fessor would not see the data and (2) the model’s grades had already

been submitted.

Overall, students’ reactions to the activity were positive: 61% consi-

dered NetLogo modeling a “good activity for the course,” and just 17%

disagreed.

Figure VIII-5 Students’ view of the usefulness

of the assignment

Students were also asked to point out suggestions for improvement in

the assignment, which are transcribed in their entirety in Table VIII-4.

Departing from students’ reactions, I built a simple rubric with 10 items,

which is summarized in Table VIII-5, to capture the essence of students

suggestions.

Table VIII-4 Students’ suggestion for

improvement Students’ comments (unedited) Summary codesGive us more time to do it, teach how to use NetLogo during classes or TA sessions.

More timeInitial NetLogo training

I would make it a group project, and require a more complex model. I felt what was done was too simple, and most of us picked projects that we already knew

Group project

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how it worked in real life. It would be done over the same period of time. Don't make it interfere too much with other major assignments & tests.

Interference with other assignments

The only real change I would make would be to include more initial training with NetLogo.

Initial NetLogo training

more time .. more weight on the project.. more guidance and support

More timeMore weight More support

More time, earlier start and more people available to provide assistance.

More timeMore support

Make the basic sessions to learn about Netlogo more complete with examples.

Initial NetLogo training

I would eliminate this project. As I said before, the majority of the time I spent on it was just trying to learn the programming language. I didn't feel I learned anything new about the phenomenon I was modeling.

Eliminate

have more background knowledge on the program, and maybe show some previous examples of the assignment so we know exactly what we are attempting to do.

Initial NetLogo training Work from previous terms

I might make it a group or partner project. Group projectI think overall it was fairly well designed. I personally did not like doing the model, because I dislike computer programming. I don't think much needs to be changed about the project though. Have an organized session in which all students learn the basics of NetLogo (what is a patch, a turtle, etc.).

Initial NetLogo training

I would make the learning process start before it did with maybe an in-class beginning tutorial and maybe have an interactive video or list of previous terms that are common to use and how to use them.

Initial NetLogo training Work from previous terms

Scheduling: List the assignment in the syllabus. Take about 5% from the homework or labs and make that the weight of this project. Introduce NETLogo to the students as a class, so that we can ask questions together. Assign phenomena that we have already covered in class and lab. Have lab experiments available that we can compare data to. While we are working on the projects, have two TA's available during a smaller span of hours. A lot of us wanted to sign up for the same slots or go in together.

More weightInitial NetLogo training More support Pre-assigned phenomena

Good help schedule already, don't need more with that. Perhaps pick a series of phenomena that will help with the second midterm instead of only things that we had technically learned before. Final report was good way to analyze the project

Pre-assigned phenomena

Give more time, use a different programming language.

More timeOther language

Give a longer time to work on it, worth more of the grade, and more required meetings with TA.

More timeMore weight More support

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Table VIII-5 Feedback from students about

the assignment Code OccurencesInitial NetLogo training 7More time 5More support 4More weight 3Group project 2Pre assigned phenomena 2Eliminate the assignment 1Interference with other assignments 1Other language 1Work from previous terms 2

Therefore, it seems that the overwhelming majority of students’ re-

quests called for more collective “NetLogo classes,” more time to com-

plete the project, and more support. Considering that the assignment

was given to students in the last month of class, and its deadline coin-

cided with several others, those types of requests were expected.

Another piece of data that speaks to students’ reactions were the official

course evaluations. They are of limited usefulness since they refer to the

course as a whole and not only the assignment, but given that the 2007

and 2008 version of the course only differed by the modeling assign-

ment, there was a positive change as large as 18% in “Amount learned in

course”, and 8% overall, as Table VIII-6 and Figure VIII-6 indicate.

Table VIII-6 Average scores in the official

course evaluation for 2007 (n=18) and 2008 (n=23)

Item 2007 2008 Change (2008 → 2007)

Instruction: overall rating 2.8 2.7 +4%

Course: overall rating 3.6 3.1 +16%

Amount learned in course 3.9 3.3 +18%

Level of intellectual challenge 3.9 3.8 +3%

Interest stimulated in course 2.6 2.7 -4%

Average 3.36 3.12 +8%

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Figure VIII-6 Average scores in the official

course evaluation for 2007 (n=18, with implementation)

and 2008 (n=23, without implementation)

This summary of students’ feedback speaks to three issues about model-

ing in real-world engineering classrooms:

Just one student mentioned “disliking” computer modeling, but mentioned that it was just a personal preference and not a problem with the assignment. This very low number was also surprising, given that few of the students were experienced programmers. Also, course evaluations went up 8%, even though we cannot attribute that to the modeling assignment.

Just one student mentioned that the project should be conducted using “another language.” There is some concern in engineering schools about teaching tools that cannot be directly used in the job market (such as MatLab, Mathematica, or Java). I expected more negative reactions from students about using a non-standard engineering tool such as NetLogo, but the data suggest that students did not consider that a problem.

The requests for support are mostly quantitative (“more support”), suggesting that the “NetLogo TA” model was effective, but perhaps more hours would be needed.’

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VIII.4. GRADING THE MODELS To assess how students were making use of the affordances of the Net-

Logo language, and also the quality and sophistication of the models, I

developed a specialized rubric (presented in more detail in the Methods

chapter.) The rubric has four main components: system definition (35%

of the total points), rules (42%), visualization (8%), and inter-

face/reporting (15%). These components were defined based on the

typical activities comprised in creating an agent-based model—defining

the “setup” procedure with creates the NetLogo “world,” defining the

rules of the agents, creating a visualization scheme and an interface.

These percentages were defined based on the relative importance of

each dimension for the complexity of the models. For each sub-item, a

weight was assigned based on the difficulty of implementation. For ex-

ample, creating a model in which agents have uniform properties is

worth 2 points, whereas creating a normal distribution of properties is

worth 4 points (due to the level of difficulty in coding such a distribu-

tion). The weights of the rubric, as well as aggregate results, are shown

in Table VIII-7. The third-to-last column denotes the weight, the

second-to-last the average occurrence of that rubric per student, and the

last the count of occurrences of the rubric across all students. For exam-

ple, item [111 - topology - square] is worth zero points, and was used

0.7 times by each student, and was used by 15 students. Some items can

be used multiple times per student: for example, [131 - variables -

number of globals] indicates the number of global variables per stu-

dents, therefore the average is 4.5 (globals/student) and the occurrence

of globals is 15 (i.e., the number of students who used this language fea-

ture). This analysis will enable insights into students’ usage of certain

language structures. Comparing those structures with the ones from the

exemplar models and some canonical agent-based structures, I will as-

sess (1) if students’ models have the minimum features to be considered

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agent-based models, and (2) how well students explored and made use

of those features and affordances of the language. As a minimum crite-

rion for considering a model “agent-based,” I defined one minimum re-

quirement for each of the four dimensions of the rubric.

1. Setup: at least one type of agent with different properties at setup (location is considered to be a property).

2. Rules: agents need to perform actions based on their own state, or their neighborhood’s state.

3. Visualization: at least one graphical representation of the states of the main group of agents in the system.

4. Interface/reporting: at least one interface element conveying the states of the main group of agents in the system.

After Table VIII-7 I will summarize the data and comment on these cat-

egories.

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Table VIII-7 Rubric for qualitative rating of

the models

Weight Average Occurences

40.6

61.2 20.6 111 square (default) 0.0 0.7 15.0

112 hexagonal 2.0 0.3 7.0 113 other (more complicated) 3.0 121 default: standard NetLogo sizes 0.0 0.2 6.0 122 customized: the world’s size was customized 1.0 0.8 18.0 131 number of globals 0.1 4.5 15.0 132 use of globals 1.0 0.7 15.0 133 number of locals 0.1 3.9 11.0 134 use of locals 2.0 0.5 11.0 135 number of patches-own 0.4 0.0 1.0 136 number of turtles-own 0.4 1.0 10.0 137 number of links-own 0.4 0.1 3.0

141 use of breeds 2.0 1.5 20.0

142 number of breeds 0.3 2.7 19.0 151 equal: all agents have the same properties 0.0 0.5 12.0 152 random-uniform: uniformly distributed 2.0 0.4 8.0 153 random-normal: normally distributed 4.0 0.0 1.0 154 number of classes of agents 2.0 1.8 17.0 161 patch-only 0.0 0.0 1.0 162 turtle-only 1.0 0.1 3.0 163 patches and turtles 1.5 0.7 13.0 164 turtles and links 3.0 165 patches, turtles and links 5.0 0.2 5.0 166 Boundary-check 4.0 0.1 3.0 171 all: all activated at the same time 0.0 0.2 4.0 172 local: based on agents' properties 1.5 0.5 11.0 173 local: based on local random rule 2.0 0.2 5.0 174 local: local rule 3.0 175 global: global variable 1.0 0.2 5.0 176 global: global rule 3.0 177 global+local: local & global rule 5.0 0.1 2.0 181 model-only: make sense in the model 1.0 0.8 18.0 182 natural: from the natural sciences 4.0 0.2 5.0 191 Patches behave? 1.0 0.0 1.0 192 Turtles behave? 1.5 0.9 19.0 193 Links behave? 3.0 0.0 1.0

72.0 8.3 211 neighbors 2.0 0.5 11.0 212 other-turtles-here 3.0 0.0 1.0 213 distance 3.0 0.0 1.0 214 at-points 3.0 0.4 8.0 215 in-radius 3.0 0.3 7.0 221 distance 4.0 222 in-radius/in-cone 4.0 0.1 2.0 231 use of finite element methods 4.0 232 recursion 4.0 0.1 2.0 233 push system to boundary condition 4.0 241 distance 3.0 242 other-turtles-here 3.0 243 neighbors 3.0 0.0 1.0 244 in-radius 2.0 0.0 1.0 251 gain/lose or lose energy arbitrarily 2.0 252 gain/lose or lose based on own behavior 3.0 0.0 1.0

253 gain/lose energy as they interact with agents

5.0 0.0 1.0

261 n-of 3.0 0.0 1.0 262 max-of 3.0 263 one-of 2.0 0.3 6.0 264 based on a property of agents [breed, etc.] 3.0 0.6 14.0 271 agents are not re-linked 0.0 272 agents are re-linked arbitrarily 2.0 273 agents are re-linked based on rule 4.0 0.3 6.0

13.0 3.5 311 agents keep default shape 0.0 312 agents have custom shapes 1.0 0.9 20.0 313 agents change shape arbitrarly 1.5 314 agents change shape based on rule/variable 3.0 0.4 8.0 321 agents keep default colors 0.0 0.0 2.0 322 agents have custom colors 0.5 0.8 18.0 323 agents change colors arbitrarly 1.0 0.1 3.0 324 agents change colors based on rule/variable 2.0 0.5 11.0 331 default palettes 0.0 1.0 21.0 332 custom palettes 4.0

26.6 8.0 411 plot with multiple pens (total) 0.5 1.7 18.0 412 plot with linear scale 0.0 1.2 16.0 413 plot with non-linear scales (log, exp) 2.0 0.1 2.0 414 Histogram 3.0 0.0 1.0 415 dynamic plotting 3.0 0.0 1.0 421 print 0.3 422 show 0.3 423 to-report 1.0 0.2 4.0 424 reporters 0.4 0.0 1.0 425 monitors 0.0 431 buttons 0.2 4.5 22.0 432 sliders 0.4 2.8 19.0 433 plots 2.0 1.3 17.0 434 monitors 0.5 2.1 14.0 435 chooser 1.0 0.5 5.0 436 Switch 1.0 0.0 1.0 441 "Manual" experiments 0.0 0.0 1.0 442 In-model comparison 2.0 0.1 3.0 443 BehaviorSpace experiments 4.0 444 BehaviorSpace + external tools 5.0

1.6

Dimension 3: Visualization

Types of agents used1.9

3.1

3.2

use of shapes

use of color

2.7 links

far neighborhood

2.3 iteration/trial and error

2.1 near neighborhood

4.1 Plotting

3.3 palleting

Dimension 2: Rules – frequency of use of agents’ rules

2.2

2.5 energy gain/loss

2.6 selective activation

Dimension 4: Interface/Reporting: frequency of reporters, plots and monitors

Variables1.3

initial construction

Dimension 1: System definition - how students code the modeling ‘world’, the setup

1.1 topology

1.2 size

Interface4.3

4.4 Automation/comparison

Breeds1.4

1.7 initial activation of agents

1.8 constants

1.5 initial distribution of agents

2.4 collision

4.2 Numerical output

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The following summary takes into consideration that there are 22 mod-

els, 19 of them were agent-based, and 3 equational.

Topology: 15 models used a square topology, and 7 a hexagonal topology. Most hexagonal models used the code from the grain growth model’s hexagonal grid.

Variables & breeds: 15 students used global variables, 11 local variables, 10 turtle variables, and 20 used breeds (on average, 2.7 breeds per model). Since breeds and turtles variables are ABM-specific concepts, the facts that almost all used breeds and half used turtle variables is relevant.

Initial setup: most models (13) used patches and turtles, while 5 used also links. Each model had on average 1.8 classes of agents (i.e., solid and liquid atoms). In 12 models, agents were created with the same properties, in 9 models the distribution was random. The creation of models with random agent properties is also a very important ABM technique that was mastered by students.

Rules: all ABM models (19) used some sort of near-neighborhood rule, 8 of which employing fixed relative coordinates (at-points) and 7 the in-radius command. Just 2 models used far neighborhood (looking at agents which are further than the immediate neighborhood).

Collision, energy gain/loss: just 2 models used collisions, and 2 models employed some sort of energy gain/loss algorithm—which might be a consequence of the content of Microstructural Dynamics.

Selective activation: 14 models used some sort of selective activation—6 went further by using the NetLogo primitive one-of to select a random agent within a group of agents.

Links: six models used links with embedded behaviors.

Visualization: almost all models (20) used custom shapes, and 8 tied the agents’ shapes to their behavior.

Interface /reporting: models had on average 1.7 plot pens (18 models used plotting), buttons were the most popular widgets (4.5 per model), followed by sliders (2.1), and monitors (2.1)

270

Considering the “minimum” threshold aforementioned, the data sug-

gest that 18 of the 19 models were successful in having (1) at least one

type of agent with different properties at setup, (2) agents perform ac-

tions based on their own state, or their neighborhood’s state, (3) at least

one graphical representation of the states of the main group of agents in

the system [color, for the most part], (4) at least one interface element

conveying the states of the main group of agents in the system (normal-

ly, a plot).

This analysis is not considering, or course, the correctness of the model

or content-related issues, but that is not the goal of this section. Here the

goal is to establish that given all the constraints of the assignment, stu-

dents did applied at least the most basic principles of agent-based mod-

eling to their projects. It is also possible to verify that even advanced fea-

tures, such as the use of links, complex topologies, and multi-layered be-

haviors, were present in a large number of models.

In Table VIII-8 we have the average for each of the four dimensions of

the rubric, showing that the overall standard deviation was 20% of the

average, and that the core dimensions (dimensions related to the algo-

rithm itself) had a much lower standard deviation than non-core dimen-

sions such as interface and visualization, which reinforces the claim that

most students made use of the ABM-related features of NetLogo lan-

guage. In Figure VIII-7 we have a bar graph with all models and their re-

spective grades (top), and then broken down by category (bottom).

271

Table VIII-8 Average and standard deviation of the four dimension across all

models

Dimension Average Std. dev.

Total 40.6 8.1 (20%)

Setup 20.6 5.5 (27%)

Rules 8.3 3.8 (46%)

Visualization 3.5 2.0 (55%)

Interface 8.0 4.4 (56%)

Figure VIII-7 Students’ grades as calculated by

the rubric (top), and the contribution of each dimension

in the overall grade (bottom).

272

In Figure VIII-8 we have a smoothed histogram of the total time spent

on the project, time spent with the TA, final model grade, final exam

grade, and final grade in the course, and in Figure VIII-9 a scatter plots

of these variables, and finally in Table VIII-9 correlations between sev-

eral variables.

Figure VIII-8 Smoothed distributions of total time spent on the project, time spent with TA, final grade, and grades in the course and in the

exams

20 40

total_time

0 5

time_ta

20 40 60

model_final

80 100

exam_total

60 80 100

final_grade

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Figure VIII-9 Matrix of scatter plots of various

measures (time spent on the project, time spent with TA,

final grade, and grades in the course and in the exams)

Table VIII-9 Correlations between various

metrics of the modeling assignment

These data complement the model grades by allowing some initial anal-

ysis on correlations between time on task, model complexity, and the

grades in the other portions of the course. Some of the important find-

ings from the data are:

total_time

time_ta

model_final

exam_total

final_grade

274

I evaluated students’ ability to report their work hours correctly by comparing my TA “hourly log” with students’ estimated TA time (correlation is 0.88.).

The quality and complexity of students’ models were more uniformly distributed than students’ initial programming ability. Therefore, it seems that the initial programming ability might help some students but is not a predictor for good performance in the modeling assignment.

Instead, there was a much stronger correlation between model grade and exam grade (0.44) and final grade in the course (0.36), which suggests that students with good overall performance tend to be better at the modeling assignment.

Model grade, nevertheless, was poorly correlated with total time on the assignment (0.20).

The number of hours with the NetLogo TA was not correlated with model grade, suggesting that, perhaps, students with more difficulty came to TA office hours. The total number of hours doing the project was not correlated to model grade.

In this section, therefore, the data show that:

a. Students’ familiarity with programming, even after one MatLab course, was just basic. Only a few students were experienced pro-grammers.

b. The number of hours and the allocation of time were adequate, with some outstanding issues (probably more time should be spent on experiments and doing research on the content, and more time should be given to students to complete the assignment).

c. Students were in general satisfied with the assignment—suggestions that are more frequent refer to the need of more NetLogo “classes,” and more time to complete the assignment. In general, students saw the activity as valuable (only 17% disagreeing), but wanted it to be “worth” more in the final class assessment. There was almost no complaint from students about NetLogo not being an industry-standard language such as MatLab.

d. Some assumptions about the good performers in modeling or pro-gramming assignments might not hold, namely, that good pro-grammers generate better models (model = programming + discip-linary content + agentification skill), or that spending more time on the assignment would result in better models.

275

e. Better students tend to perform better at the modeling assignment too, although we have no data so far to go beyond the correlation.

VIII.5. LOGFILE ANALYSIS The goal of the logfile analysis was to identify patterns in the model building process, which comprises two distinct (but intertwined) tasks: learn the NetLogo language itself, and learn to “agentify” a given scien-tific phenomenon and program it using the NetLogo language. The la-boratory studies prior to this classroom study offered just a partial view into the process, since in the lab students were never building the model alone, but with assistance.

For the classroom study, since students would do most of the work at home using their own computers, a record of what students did would be useful. Fortuitously, just before the 2007 study, NetLogo’s logging module was released for beta testing. This module logs to an XML-style file all (or a subset) of the user’s actions, such as key presses, button clicks, changes in variables and, most importantly for this study, changes in the code.

The logging module uses a special configuration file, which specifies which actions are to be logged. This file was distributed to students alongside with instruction about how to enable logging, collect the log-files, and send those files back for analysis.

However, the logistics of the logfile collection ended up being more complicated than anticipated. Given that the logging module entered its testing phase just weeks before the study, this was not a total surprise, but the loss of some logfiles could not be avoided. The main issue was that the logfiles were oftentimes automatically deleted on shutdown by the operating system, which misinterpreted them as a temporary files. Also, students sometimes did their work on multiple computers (some of them public), and forgot to copy their logfiles before switching ma-chines. In the end, I was able to collect logfiles from nine students, but some of them were not complete, i.e., did not cover the entire modeling process.

276

Yet, the data revealed interesting patterns in model-building. In what follows, I will conduct two exploratory analyses: one general statistical analysis for the whole group, and one more detailed analysis for one stu-dent. My approach assumes that this type of analysis could be done semi-automatically in the future, so first I will try to lay out an initial framework for detecting anomalies or missing data. In addition, given the limitations of a purely data-driven statistical analysis, I will try to show how the data collected can, rather than completely elucidate the problem, point researchers to instances during the model-building process in a more in-depth qualitative analysis could be worthwhile.

VIII.5.1. INITIAL DATA PROCESSING AND VALIDATION  I was able to successfully collect 158 logfiles in total, from 9 students.

Using a combination of XQuery (the standard XML query language)

and regular expression processors (such as ‘grep’), I was able to process,

parse and analyze the voluminous amount of data generated (1.5GB and

18 million lines of uncompressed text files). Below is a summary of the

collected data (in this order): number of files collected by students, the

total size in megabytes for the set of files, total number of events logged,

total number of global variable changes, and its proportion in relation to

the total number of logged events (in percent and in absolute numbers).

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Table VIII-10 Number of events collected per

student Name Files Size (MB) Events Globals not Globals not Globals

Chuck 2 43.1 258036 257675 99.9% 361

Che 6 2.3 5970 928 15.5% 5042

Leah 2 0.7 2836 525 18.5% 2311

Liam 12 657.4 4044723 4041123 99.9% 3600

Leen 38 43.7 253112 241827 95.5% 11285

Luca 40 16.1 92631 86708 93.6% 5923

Nema 7 1.0 3690 649 17.6% 3041

Paul 6 0.1 218 15 6.9% 203

Shana 45 692.0 4165657 4159327 99.8% 6330

Total 158 1456.4 8826873 8788777 99.6% 38096

Clearly, the overwhelming majority of events collected were of global

variable changes (99.6% of the total, and 60.8% on average per student.

Note that in Table VIII-10, “Globals” refer to the number of events con-

taining only a variable change, while “Not Globals” refer to all other

events.) This particular kind of event takes place when students are run-

ning models – every single variable change gets recorded, what accounts

for the very large number of events (almost 9 million.) Since the analysis

of students’ interactions with models is out of the scope of this disserta-

tion, all the “Global” events were filtered out of the main dataset. The

remaining events were:

‘Code’: compilation (successful or not) of any type of code.

‘Buttons’: pressing and depressing of buttons in the interface.

‘Greens’: overall changes to the NetLogo environment (world size, size of patches, etc.)

‘Widgets’: creation or deletion of interface widgets.

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‘Procedures’: a subset of the “Code” event, indicating compilations of code in the procedures tab only (not counting code inside buttons, etc.)

Below we have a summary of these data: a table and a plot grouped for

each student, and a more detailed plot of successful and unsuccessful

code compilations.

Table VIII-11 Logged events per participant

Name Code Buttons Greens Speed Widgets Procedures

chuck 34 110 189 12 16 2

che 2320 920 1562 240 0 216

leah 681 844 763 9 14 7

liam 1635 818 1002 8 129 70

leen 2980 7812 375 118 0 555

luca 1948 1358 1432 430 755 142

nema 1237 522 1183 30 69 27

paul 131 36 3 26 7 16

shana 2696 1445 1212 328 649 152

Total 13662 13865 7721 1201 1639 1187

35% 35% 20% 3% 4% 3%

Figure VIII-10 Types of logged events, and

correct code compilations

0

2000

4000

6000

8000

10000

12000

chuck che leah liam leen luca niger paul shana

Types of logged NetLogo events WidgetsSpeedGreensButtonsCode

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

chuck che leah liam leen luca niger paul shana

Types of logged NetLogo events

279

This preliminary aggregation cannot shed light on any particular pat-

terns in model-building, but it is helpful as an initial attempt to find use-

ful data within millions of data points. First, it helps find out which log-

files contained richer data. For example, Table IV-7 shows that the vast

majority of events were just variable changes, and thus the size of the

logfiles was misleadingly large. Processing 18 million lines of log was a

difficult task in itself. When these data were filtered out, I realized that

the distribution of events was not uniform for different students (Table

VIII-11 and Figure VIII-10). Some logs hardly contained any code

compilation data (Chuck, or Leah,) while others were simply too small

to represent the entire process (Paul.) This indicates that those logfiles

were probably incomplete. The remaining files, therefore, appear to

represent at least a considerable part of the model building process. In-

deed, crossing that data with the number of days recorded in the logs,

Chuck, Leah, and Paul have only one day worth of logs, compared to 14

days of Shana or 9 days of Luca.

VIII.5.2. CODING STRATEGIES  Luca

Luca built a model of recrystallization. Her model grade was slightly be-

low the group’s average, and she had modest previous experience with

computers. Her grade in the class was also around the average, which

makes her a good example for an in-depth analysis of logfiles. Also, her

logfiles were complete, which makes such analysis more reliable.

0%

20%

40%

60%

80%

100%

che liam leen luca niger shana Total

Correct code compilationsw/ errors

no errors

280

Figure VIII-11 summarizes Luca’s model building logs. The red curve

represents the number of characters in her code, the blue dots represent

the time between compilation (secondary y-axis to the right), green dots

placed at y=1800 represent successful compilations, orange dots placed

at y=1200 represent unsuccessful compilations.

Figure VIII-11 Code size, time between

compilations, and erros, for Luca’s logfiles

1. Luca started with one of the exemplar models seen in the tutorial (the “very simple” solidification model). In less than a minute, she deleted the unnecessary code and ended up with a skeleton of a new model, containing setup, go and do-plots procedures (see point A in the graph, and Figure VIII-12).

281

Figure VIII-12 Phase 1: Luca departs from the

exemplar model, and deletes unrelated code

2. She spent the next half-hour building her first procedure, called go-site-saturated, which was one of the two types of crystallization she purported to include in the model. During this time, between A and B, she has numerous unsuccessful compilations (see the orange dots), and goes from 200 to 600 characters of code. (Figure VIII-13, left side, in blue)

282

Figure VIII-13 Phase 2: Luca copies-and-pastes

the code from her first proce-dure to create the second

procedure

3. The size of the code remains stable for 12 minutes (point B), until there is a sudden jump from 600 to 900 characters (just before point C). This jump corresponds to Luca copying and pasting her own code: she duplicated her go-site-saturated procedure as a basis for a new procedure, go-constant-growth. (Figure VIII-13, right side). During this period, also, she opens many of the sample models.

283

4. Luca spends some time making her new procedure work (go-site-saturated). The frequency of compilation decreases (see the density of orange and green dots in Figure VIII-11), the average time per compilation increases, and again we see a plateau for about one hour (point D).

Figure VIII-14 Phase 3: Luca copies-and-pastes

the code from the grain growth model

284

5. After one hour in the plateau, there is another sudden increase in code size, from 900 to 1300 characters (between D and E). Actually, what Luca did was to open the Grain Growth model (one of MaterialSim exemplar models), and copy the procedure that generates the hexagonal grid. Hexagonal grids are better adapted for models with radial growth, since they are radially symmetrical (see Figure VIII-14). Note that code compilations are even less frequent.

6. After making the “recycled” code from the Grain Growth model work, Luca got to her final number of 1200 characters of code. She then spent about 20 minutes “beautifying” the code, fixing the indentation, changing names of variables, etc. No real changes in the code took place, and there are no incorrect compilations (see Figure VIII-15).

285

Figure VIII-15 Phase 4: Luca beautifies the

code, fixes indenting, names of variables., etc.

Luca’s narrative suggests, thus, four prototypical modeling events:

a. Stripping down an existing model as a starting point.

b. Long plateaus of no coding activity, during which students browse other models (or their own model) for useful code.

c. Sudden jumps in character count, when students import code from other models, or copy and paste code from within their working model.

d. A final phase in which students fix the formatting of the code, inden-tation, variable names, etc.

This initial analysis, despite based on Luca’s logfiles, is a useful lens to

examine other logfiles as well. In the following, I show plots (character

count vs. time) from five different students (Luca, Che, Liam, Leen, and

Shana), which include all of students’ activity (including opening other

286

models—the “spikes”—note that the plot in Figure VIII-11 did not

show all of Luca’s activities, but only her activities within her model, i.e.,

excluding opening and manipulating other models).

Shana, Lian, Leen, Che

In Luca’s plot, it is apparent that during her initial explorations, she

opens other models several times. This was also true, for example, for

Shana.

Figure VIII-16 Code size versus time for Luca,

Shana, Che, Liam, and Leen

However, after many ‘spikes,’ there is a sudden jump (at time=75) from

about 200 to 4,000 characters of code. A closer, systematic examination

revealed that Shana employed a different approach. After some attempts

to incorporate the code of other models into her own, she gave up and

decided to do the opposite: start from a ready-made model and add her

20 40 60 80 100 120

1000

2000

3000

4000luca

20 40 60 80 100 120

1000

2000

3000

4000

5000

6000

shana

50 100 150 200

1500

2000

2500

3000

3500che

10 20 30 40 50 60

4600

4800

5000

5200

5400

liam

100 200 300 400 500

1000

2000

3000

4000

leen

287

code to it. She then chose the grain growth model and built her model

on top of it. The sudden jump to 4,000 characters indicates the moment

when she opened and started making the model ‘her own,’ by adding her

own procedures. She seamless integrated the pre-existing model into her

new one, adding significant new features. Shana wanted to model recrys-

tallization, but she needed “grown” grains as a starting point. So ran the

grain growth model for a given amount of time, until grains were large

enough for recrystallization to occur, and then started her own proce-

dures on top of the grown grains.

Leen, on the other hand, had yet another coding style. He did open oth-

er models for inspiration or cues, but did not copy and paste code. In-

stead, he built his procedures in small increments by trial-and-error. In

Table VIII-12, we can observe how he coded a procedure to “sprout” a

variable number of white vacancies in his model (during a 30-minute

period). The changes in the code are indicated in red.

Table VIII-12 Leen’s attempts to write the

“InsertVacancies” procedure to Insert-Vacancies to Insert-Vacancies

sprout 2 [ set breed vacancies set color white ] ] end

Initial code

to Insert-Vacancies ask patches [ sprout 2 [ set breed vacancies set color white ] ] end

to Insert-Vacancies ask one-of patches [ sprout 2 [ set breed vacancies set color white ] ] end

Ask patches is intro-duced, and then one-of

to Insert-Vacancies ask one-of patches [ sprout 1 [ set breed vacancies set color white ] ] end

to Insert-Vacancies ask 5 patches [ sprout 2 [ set breed vacancies set color white ] ] end

Experiments with differ-ent number of patches

to Insert-Vacancies ask patches-from [ sprout 2 [ set breed vacancies set color white ] ] end

to Insert-Vacancies loop [ ask one-of patches [ sprout 2 [ set breed vacancies set color white ] ] ] end

Tries patches-from and then intro-duce a loop

288

to Insert-Vacancies while [ ask one-of patches [ sprout 2 [ set breed vacancies set color white] ] ] end

to Insert-Vacancies while n < Number-of-Vacancies [ ask one-of patches [ sprout 2 [ set breed vacancies set color white ] ] ] end

Tries anoth-er loop ap-proach, with a while command

to Insert-Vacancies ask one-of patches [ sprout 2 [ set breed vacancies set color white ] ] end

to Insert-Vacancies ask 35 of patches [ sprout 2 [ set breed vacancies set color white ] ] end

Gives up looping, tries a fixed number of patches

to Insert-Vacancies ask n-of Number-of-Vacancies patches [ sprout 2 [ set breed vacancies set color white ] ] end

Gives up a fixed num-ber, creates a slider, and introduces n-of

His trial-and-error method had an underlying pattern: he went from

simpler to more complex structures. For example, he first attempts a

fixed, “hardcoded” number of events (sprout), then introduces control

structures (loop, while) to generate a variable number of events, and fi-

nally introduces new interface widgets to give the user control over the

number of events. Leen reported having a higher familiarity with pro-

gramming languages than Luca and Shana, which might explain his dif-

ferent coding style.

Liam and Che, with few exceptions, do not open other models during

model building. Similarly to Leen, they also employ an incremental, tri-

al-and-error approach, but we can clearly detect many more long pla-

teaus in Liam’s graph.

Therefore, based on these five logfiles, some canonical coding strategies

can be inferred:

a. Stripping down an existing model as a starting point.

b. Starting from a ready-made model and adding one’s own proce-dures.

289

c. Long plateaus of no coding activity, during which students browse other models (or their own model) for useful code.

d. Long plateaus of no coding activity, during which students think of solutions without browsing other models.

e. Period of linear growth in the code size, during which students em-ploy a trial-and-error strategy to get the code right.

f. Sudden jumps in character count, when students import code from other models, or copy and paste code from within their working model.

g. A final phase in which students fix the formatting of the code, inden-tation, variable names, etc.

Based on those strategies, and the previous programming knowledge of

students, the data suggest three coding profiles:

1. “Copy and pasters:” more frequent use of a, b, c, f, and g.

2. Mixed-mode: a combination of c, d, e, and g.

3. “Self-sufficients:” more frequent use of d, e.

The empirical verification of these canonical coding strategies and cod-

ing profiles has important implications for design, in particular, build-

ing-core (BBC) constructionist environments. Each coding strategy and

profile might entail different support strategies. For example, students

with more advanced programming skills (many of which exhibited the

“self-sufficient” behavior) might require detailed and easy-to-find lan-

guage documentation, whereas “copy and pasters” need more working

examples with transportable code. This validates our initial design

choice to offer exemplar models of increasing levels of sophistication to

cater to various coding profiles, and it shows that students in fact are rel-

atively autonomous in developing strategies for learning the program-

ming language.

Despite these differences, one behavior seemed to be rather similar

across students: the frequency of code compilation. Figure VIII-17

shows the moving average of unsuccessful compilations (thus, the error

290

rate) versus time, i.e., the higher the value, the higher the number of un-

successful compilations within one moving average period (the moving

average period was 10% of the overall duration of the logfile—if there

were 600 compilation attempts, there period of the moving average

would be 60).

Figure VIII-17 Error rate versus compilation

attempts (time)

291

For all four students, the error rate curve follows an inverse parabolic

shape. It starts very low, reaches a peak halfway through the project, and

then decreases reaching values close to zero. Also, the blue dots on top

of y=0 (correct compilations) and y=1 (incorrect compilations) indicate

the actual compilation attempts. Most of them are concentrated in the

first half of the activity—approximately 2/3 in the first half to 1/3 in the

second half. This further confirms the previous logfiles analysis in which

the model-building process is not homogenous and simple, but complex

and comprised of several different phases: an initial exploration charac-

terized by few unsuccessful compilations, followed by a phase with in-

tense code evolution and many compilation attempts, and a final phase

of final touches and smaller fixes. Together with the code size plots pre-

viously analyzed, we can trace a reasonable approximation of each pro-

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totypical coding profile and style—such an analysis has three important

implications for the design of BBC environments:

1. To design and allocate support resources, moments of greater difficulty in the modeling process should be identified. Our data indicate that those moments happens mid-way through the project.

2. Support materials and strategies need to be designed to cater to diverse coding styles and profiles.

3. By better understanding each student’s coding style, we have an extra window into students’ cognition. Paired with other data sources (interviews, tests, surveys), the data could offer a rich portrait of the model-building process and how it affects students’ understanding of the scientific phenomena and the programming language.

VIII.6. MOTIVATION PLOTS Programming the models was not the only activity students undertook

during the assignment. They also had to research an interesting pheno-

menon for the model, run several experiments, and write a final report.

To access students’ relative motivation during the other parts of the

process, I asked them to draw a “motivation plot” at the end of the activ-

ity (see the Methods chapter for more details). This plot had five data

points corresponding to these project milestones:

1. Reading the assignment.

2. Choosing a phenomenon to model (1st week).

3. First tutorial (1st week).

4. Sending the beta version of the model (3rd week).

5. Final report writing (4th week).

Figure VIII-18 shows six random examples of the 21 plots collected.

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Figure VIII-18 Samples from the motivation

plots

Since all the plots were drawn on paper with an arbitrary scale, for con-

verting them into a numerical data I followed this procedure:

1) I numerically estimated the minimum and maximum scales of the plot (allowing for negative numbers when the curve went below the x axis)

2) I recorded the approximate y coordinate of each point, within the scale estimated before.

3) I renormalized the data on a scale from 1 to 10.

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This procedure allowed a reconstruction of a normalized average plot for the entire classroom, as seen in Figure VIII-19.

Figure VIII-19 Average of all motivation plots

The motivation plots show that their peak of motivation took place

when they finished their first working version of the model (point 4).

This is consistent with previous work on constructionist learning, which

show that learners experience a deep sense of accomplishment and em-

powerment when they get their projects to work (Cavallo, 2004; Kafai,

1991; Papert, 1991; Wilensky, 2003). However, perhaps not so

straightforward is the dip in motivation after the first version of the

model was handed in (point 5). Students’ next task was to refine their

models, run experiments, and write a report—when some of the most

important and deep learning opportunities would take place, such as

fine-tuning parameters and algorithms, comparing model and real-world

data, and writing scientific justifications for discrepancies in the data.

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There are two important implications of such decrease in motivation

(both of which will be further explored in the Discussion chapter):

Typically, due to a common misinterpretation of constructionist learning environments, designers oftentimes emphasize the work leading to getting a working prototype done. Further refinements, reports, or careful data comparisons are not as common.

It is during that second half of the project that many of the important analytical tasks take place (particularly, some very important for engineering students). Also, it is when motivation goes down. It seems to be crucial, thus, to design support and facilitation strategies in the “post-artifact” phase of the project. Those strategies are relatively less researched by constructionist researchers.

VIII.7. DIVING INTO STUDENT’S COGNITION: CASE STUDIES

VIII.7.1. SCENE ONE: BENEDICT’S PRE‐INTERVIEW I will start this section with a case study about Benedict, an undergra-

duate student in a highly ranked materials science department in a re-

search university. He was a sophomore in 2007, when he participated in

the study for the first time, and a junior in 2008 when he came back for

the follow-up study. In 2007, Benedict ranked in the bottom half of his

class in the Microstructural Dynamics course. Since he came back for

the follow-up study, his story illustrates well the different stages of the

study. The first of these stages was the individual NetLogo tutorial,

which was given to all students. A short pre-interview preceded the tu-

torial. This interview followed approximately the same format as in pre-

vious years, i.e. students were asked about standard content questions

(“what is a grain?”, “what is grain growth?” – see Study 1 for a complete

protocol).

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Figure VIII-20 Benedict in the interview setting

My first question to Benedict was about the definition of grain.

Benedict A grain is just any small section of a substance where all the, it is a regular crystal pattern, like, and, at areas where there is a new grain, it just means, like, these are oriented this way, and then others would be oriented opposite to that, and so on, so forth, [pause] well, yeah. […] I mean, that's the basics of it. The interfaces between them can move as the dislocations... [thinks] I guess... I mean, a grain boundary is really just a series of dislocations [thinks] they can move as dislocations move as vacancies diffuse in and out.

Similarly to interviews conducted in previous years, Benedict’s explana-

tion is not incorrect, but its path is not deductive or coherently con-

structed, but instead an assemblage of several pieces of explanation, each

departing from a different approach. He starts by attempting a scale-

based approach (“a small section of a substance,” i.e. grains are some-

thing small’), then moves to a micro-structural rationale (“a regular pat-

tern”), and then finally a micro-dynamic view (“they can move as dislo-

cations move”). Also relevant is the number of times that Benedict

stopped to think, and how hesitant he was during this brief passage – as

if he was struggling not only to remember the definitions, but also to de-

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cide between different sources: the “classroom definition” (a regular

crystal structure), his own naïve idea about the appearance of grains as a

“small thing”, or a more mechanistic mental model involving diffusion,

atomic movement, and dislocations.

The interview continued with a question about a dynamic process: grain

growth.

Interviewer And then how would you explain what grain growth is?

Benedict Grain growth is as the larger, not necessarily larger, as the grains grown to minimize the energy like, with each grain boundary there is a certain energy associated with that and as they always want to go to a lower energy, that's how stuff works and as grains grow, their surface area to volume ratio decreases, which decreases the energy, so systems naturally want to move in that direction.

Interviewer For example, let's say this, this is a picture from a microscope [I show him a picture of grains], which grain [do] you think should grow and which grain would shrink?

Benedict Some are definitely going to grow. [thinks] I'm just not sure which ones, I can't remember if it is the smaller ones that grow, they just nucleated, hum…[thinks] I guess… in a system that is this, recrystallization, like it's liquid, or everything, like obviously the points that nucleate are going to grow first, but, and in a completely crystalline system [thinks] hum... [thinks] I couldn't actually tell you which ones is going to grow. I should be able to.

It might sound surprising that, even after showing a reasonable grasp of

what a grain is, Benedict fails to indicate, in the picture I showed him,

which grains would grow and which would shrink – even he acknowl-

edges this surprise (“I should be able to”). So why was not he able to do

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it? I hypothesize that in his explanation, he tried to access two types of

knowledge derived from different epistemological resources:

a. Recalling authority-delivered heuristics (for example, “they al-ways want to go to a lower energy, that's how stuff works” and “I can't remember if it is the smaller ones that grow”).

b. Revisiting previous knowledge about similar phenomena and trying to infer similarities (“in a system that is this, recrystalliza-tion…”).

Both resources are used problematically. First, the authority-delivered

heuristics (especially in the case of engineering rules-of-thumb), do not

carry enough information about the mechanisms involved, which causes

the inter-phenomena connections to be difficult. Also, revisiting pre-

vious phenomena can be deceiving if the similarities are at a superficial,

non-mechanistic level. The elements which triggered the perceived si-

milarities, in Benedict’s case, were (1) the existence of ‘small’ circular

shapes within a larger material, and (2) the fact that something was sup-

posed to ‘grow.’ None of these two potential similarities carried infor-

mation about mechanism. Not surprisingly, Benedict’s explanation for

lowering the energy of the grain boundaries was incorrect in the context

of grain growth (“their surface area to volume ratio decreases”), but abso-

lutely correct in the case of recrystallization. Benedict apparently did not

have the correct lens to look at recrystallization in a way that would give

him resources to also tackle grain growth. He correctly said that “ob-

viously the points that nucleate are going to grow first,” which is accurate,

but he does not mention why or how they grow. The lack of deeper me-

chanistic explanations makes it difficult for him to extract parallels with

grain growth. Let us note, also, that in the second explanation (after my

question) he does not pursue some of the key ideas of the first one, such

as “grains grow to minimize the energy” or “their surface area to volume ra-

tio decreases,” but attempts yet other avenues for explaining the pheno-

mena. So far, some of the constructs emerging from this analysis are:

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Knowledge derived from different epistemological resources: Benedict made use of authority-delivered heuristics and previous knowledge (“stored and retrieved,” in Hammer’s taxonomy, Hammer & Elby, 2003; Rosenberg, Hammer, & Phelan, 2006) about a similar phenomenon (once the similarity is established).

Similarity triggers: common elements shared by two or more phenomena which trigger students to establish parallels when searching for an explanation. For example, for establishing the parallels between grain growth and recrystallization, Benedict indentified “growth” and “small shapes amongst much larger shapes.”

The interview went on, and I asked Benedict about grain growth in pure

materials versus in materials with a fine dispersion of particles. In most

cases, particles (‘precipitates’) dispersed in a material will slow down or

impede grain growth, which is known as “Zener pinning” (in homage to

Clarence Zener, who published a famous paper on the phenomenon in

1948).

Benedict The precipitates are going to hinder the grain growth because it's harder for the interface to move when there is [sic] precipitates in a way, so the interfaces that don't have precipitates, they are going to move far more readily. Yeah, because, normally you have to move dislocations, and in the interface you also have to move the dislocations around the precipitate, and [pause] it's harder because it's something blocking the path of the dislocation movement.

This time, Benedict resorts to a mechanistic approach – precipitates im-

pede grain growth by blocking grain boundaries. Absent from this an-

swer are statements such as ‘it will lower the energy’ or ‘it is always like

that’, or direct comparisons with other phenomena. He just dives into

the phenomenon itself – at the atomic level – and offers a reasonable ex-

planation. Then I asked him to further his explanation:

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Interviewer And, so, let's say the precipitates can change in radius, there are really big or really small. Which configuration would result in smaller grains - a lot of precipitates, small precipitates, or let's say, we maintain the mass of precipitates constant, so a lot of small precipitates or fewer bigger precipitates?

Benedict The way I understand it is a lot of small precipitates will cause grain size to decrease because as the precipitates get larger, they become more and more like separate grains in themselves, I mean, they are going to make the interfaces move, even more slowly than the small precipitates, but there are few enough of them that it really outweights them being so massive […] so everything moves closer to as if there are no precipitates than if there are a lot of small ones.

In this passage, Benedict was able not only able to correctly describe the

trade-off between large and small precipitates, but even offered a ratio-

nale for his explanation: if the precipitates are too big, they are almost

like grains themselves, so the effect of having a fine dispersion of smaller

particles in a bigger matrix tends to disappear. Differently from the pre-

vious passages, he did not resort to sweeping assertions about energy or

engineering heuristics – the basis of his explanation was the collision be-

tween grain boundaries and precipitates. Departing from that very sim-

ple element, he was able to explain the phenomena and extend his ex-

planation for new phenomena (precipitates with different sizes). My

hypothesis here is that the question gave Benedict an opportunity to

dive into the micro-level (the “collision” level) of the problem, activat-

ing a different kind of resource: his knowledge about how two classes of

objects would collide, and how one class of object would cease to exist if

its distinctive characteristic (the smaller size) was to disappear.

After the pre-interview, I showed Benedict NetLogo’s grain growth

model. I started with an arrangement with a large number of small grains

and let the system evolve into bigger, less numerous grains (the full in-

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terface on the top of Figure VIII-21 and a similar sequence of 6 screen-

shots seen by the students at the bottom).

Figure VIII-21 Several screenshots of the grain

growth model

I then asked Benedict for his guess on the equation behind that model.

Benedict The equation behind it? It is certainly [pause] natural log, and obviously it starts up very quickly as it goes like where it is now, starts to level off, eventually I would assume it would just be one

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big grain and just level off completely. [pause] But yeah, the visualization helps, a lot, [pause] Well, actually, it doesn't seem to be. I just get the impression that it would level off, because, first, few hundred grains there and now there is three, [pause] but then, I guess, it makes sense with the just random interactions that would never completely level off, there is always going to be fluctuations, [pause] Is this plot based on the visualizer window, or is it over a much larger overview?

Interviewer It’s based on the window.

Benedict It's kind of leveling off right now. Oh. Spoke too soon. [pause] This way it looks like it is going to be completely green at some point.

Interviewer Why is the green taking so long?

Benedict Hum... At the beginning, a grain can be pushed out just immediately, because it is so small, doesn't have a whole lot of… [pause] oh, there we go. Level off. As they get larger, they start pushing back, [pause] each one, it's like a [pause] it's kind of like “Risk”, like the game, if you have a lot of people against you on all sides, you are obviously going to have a harder time defending, and then, like, if you have just two people next to you, you have to kind of fight less… like with the grains, like, grain boundaries moving on all sides based on everything around you, when there are fewer larger grains the interactions are much easier to deal with. They are a lot slower, more stable.

The difference between his initial answer to the same question (just

about ten minutes earlier, “I couldn't actually tell you which ones is going to

grow”) and the last transcript is striking. Let us then recapitulate his ex-

planation:

1. At first, he mentions that “is certainly natural log […] it starts up very quickly […] starts to level off […] eventually […] it would just be one big grain,” but at the same time is concerned with the “random interactions that would [make it] never completely level off.” Here Benedict is trying to make sense of the three perceived speeds of the phenomenon: a quick start, a slowing rate of growth, and a stable phase.

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2. Them, he goes on to say that “At the beginning, a grain can be pushed out just immediately […] it doesn't have a whole lot of… […] As they get larger, they start pushing back […] it's kind of like [the board game of] “Risk19.”

Even though in (1) he is trying to fit the behavior onto a known mathe-

matical function, he acknowledges that his initial theory might be wrong

due to the random interactions – he is thus actively trying to make sense

of the perceived behaviors, rather than using knowledge handed down

by authority, or simply using stored information. His own theory is in

flux. But it is in (2) that the difference in the epistemological resources

employed becomes even more apparent. The NetLogo model (see Fig-

ure VIII-21) was set to a zoom level which enabled students to see the

overall pattern evolving, but also to realize that the material was com-

posed of thousands of smaller units. Without any previous explanation

from me, Benedict quickly realized that small grains were shrinking and

disappearing, and larger ones were growing, and offered a causal expla-

nation for it, without even mentioning any of the class materials, but in-

stead referring to a board game he had played. His explanation was that

small grains have a lot more neighbors to ‘fight with,’ and thus tend to

disappear – just like in the Risk board game, in which smaller armies

tend to disappear (note also that the Risk game has a built-in random

element as well, since players throw dice to decide the winner of each

battle). That idea is exactly congruent with the grain growth neighbor-

hood-based algorithm – even though he had not seen the actual code.

Again, an element of the model triggered the perception of similarity –

and thus the possibility of using ideas from other phenomena to explain

the problem at hand. Previously, when he was trying to explain grain

growth but erroneously traced some similarities with recrystallization, 19 http://en.wikipedia.org/wiki/Risk_(game)

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Benedict did so based on two similarity triggers: (a) some form of

“growth” was taking place, and (b) “there were small shapes amongst

much larger shapes.” Because those two triggers were not causal, but re-

lated to an aggregate behavior, Benedict was unable to make the connec-

tions at a deeper level. Conversely, in the second scenario, the similarity

trigger between grain growth and the “Risk” board game was causal, i.e.,

what reminded Benedict of the board game was the algorithm of the

model, and not just its geometrical or morphological aspects. That

enabled Benedict to use the ideas from the “Risk” game in an effective

way to understand grain growth.

Between these two scenarios, there was a considerable difference in re-

presentational infrastructure. In the first dialogue, about grains and grain

growth, the representation of the phenomena (drawings on paper) ex-

posed only some particular elements of grain growth – namely, that

some ‘shapes’ were changing its size. Those exposed representational

elements activated certain epistemological resources, and also influ-

enced which similarities triggers were activated. When the representa-

tion changed, however, the exposed aspects of the phenomena were dif-

ferent. In the agent-based representation, the micro-behaviors were ex-

posed, rather than the aggregate behaviors. That enabled Benedict to

use those exposed elements to construct an explanation based on his

previous causal knowledge. In the next examples we will dive deeper in-

to this issue.

VIII.7.2. S C E N E T W O: B E N E D I C T’ S M O D E L B U I L D I N G Stories like Benedict’s are not uncommon in the literature. Sherin's

(2001) review of physics problem solving discusses a number of models

that informed the data analysis. Some students identified some of the

questions as belonging to a certain schema, and then tried to activate the

resources that they believed to be related to it. In these examples, I will

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try to better understand what makes students recognize problems to be

of a certain kind, and that perception could change.

After the first interview, I conducted a 30-minute NetLogo tutorial for

Benedict. I randomly picked approximately half of the students and

taught them NetLogo in a non-agent-based fashion, i.e. using NetLogo

as an aggregate modeling tool (such as MatLab). In the tutorial, we

would look at equational representations of one phenomenon (solidifi-

cation), and create a model based on that representation. In the case of

solidification, we had equations for the surface energy, the volume ener-

gy, and the combination of both (see Figure VIII-22).

Figure VIII-22 Solidification model showing

surface energy, the volume energy, and the combination of

both

A week after the tutorial, Benedict picked his phenomenon to model:

recrystallization (not surprising given that he demonstrated a good

command of it). For his first TA session, about a week after he started

on the project, Benedict had a simple model that created multiple par-

ticles and made them grow according to the known laws of recrystalliza-

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tion. The core of his code was the following algorithm, which increases

the size of the particles at every time tick (for clarity, I first present the

entire procedure, and then explain each line of the code):

to go set G B * e ^ (- Q / (8.314 * T)) set r r + (G * delta-t) ask particles [set size r] set total-volume n * (4 / 3 * pi * r ^ 3) set total-surfacearea n * (4 * pi * r ^ 2) do-plots end

to go Every procedure in NetLogo must start with “to”, followed by the name of the procedure.

set G B * e ^ (- Q / (8.314 * T))

Sets the variable “G” (Gibbs free energy): 8.314

Q

TG B e-

= ⋅

set r r + (G * delta-t) Sets the variable r (radius): ( )r r G t= + ⋅ D

ask particles [set size r] Asks all the agents from the “particles” breed to set their sizes to r (calculated in the previous stp)

set total-volume n * (4 / 3 * pi * r ^ 3) Sets the variable total-volume to be the product of the number of particles and the volume of each based on their radius, using the

formula for spherical volume: 34

3n rp

æ ö÷ç ÷⋅ ç ÷ç ÷çè ø

set total-surfacearea n * (4 * pi * r ^ 2) Sets the variable total-surfacearea to be the product of the number of particles and the surface area of each based on their radius, using

the formula for surface area: ( )24n rp⋅

do-plots Updates the plots

end Every NetLogo procedure must end with the “end” keyword.

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It was very similar to the solidification model from the tutorial, but with

some modifications. He seemed to understand that both solidification

and recrystallization have “growing” entities (see ‘similarity triggers’

above), and reused the algorithm. However, the algorithm was not caus-

al in the agent-based sense, as it just applied known formulas to predict

deterministic outcomes. And it raised a fundamental problem for him --

the particles were overlapping (as we can see in Figure VIII-23).

Figure VIII-23 Benedict’s recrystallization

model showing the overlaps of crystals

The red particles were not “instructed” to stop when they meet another

particle, so they would just overlap all around. This constituted a consi-

derable problem because Benedict meant to calculate how much ma-

terial would recrystallize at different times, and now his idea of adding

up the areas of the circles would not be accurate at all.

We then spent 12 minutes studying the geometry of the problem, and

trying to find an equation that would detect and discount the overlaps

between arbitrarily-sized and positioned particles. But then he had an

insight:

Benedict Well, if you had a grid, couldn't it count [pause] everything that has one thing over it, it could count as one, everything that has two things over it, it could count as zero? Is there a way to do that? Easily? Well, relatively easily? That could [work] for surface area

overlaps

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too, in that if one of these points has a surrounding point that is not covered then it counts as a surface.

Benedict realized that if he divided the screen into a grid, and could in-

spect the state of each patch within the grid, he would automatically

have a precise way of calculating the overlaps (in other words, patches

could look “up” and see how many particles were over it.) If two (or

more) particles were covering a particular patch, there was overlap on

that patch, so the software would not count it as a “valid” area – as Bene-

dict said, “it could count as zero” (actually, the correct algorithm would

be to count it as one and not zero). This insight was a fundamental de-

parture from his previous algorithm as it was, for the first time, based on

micro-elements within the system.

Then, for about six minutes, I explained to him the idea of patches in

NetLogo, and showed him some simple examples – and then he had an

even more radical realization.

Benedict Would it be easier to just, instead of just creating all these recrystallized areas, with circles, would it be easier to just create them with the patches?

Then, after a 60-second explanation about the NetLogo patches, he de-

vised an entirely new algorithm.

Benedict I mean, just set them to different colors, like, ask patches [types the code] I don't even know if this will work. Hum. If you “ask patch at random xcor...”, ask them to set patch color blue […] So, if you want to increase the radius, you are going to set more patches adjacent to them to be larger… [pause] Are the patches aware of the radius around them? […] Hum, I'm asking the patches that are already blue, initially, I'm going to ask them, oh, that's going to be a problem, it is not going to be a problem in the first step, it is a going

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to be a problem for each successive step. So if I make the centers blue, and I make their radius green, then that will solve that.

Benedict’s algorithm was simple but effective. He would start with some

user-defined number of random seeds, and then make the seeds grow

radially while they still had unrecrystallized material (white patches)

around them:

to setup ask patches [set pcolor white] repeat n [ask patch random-xcor random-ycor [set pcolor random 140]] end to go set r 1 ask patches with [pcolor != white] [ask neighbors4 [if pcolor = white [set pcolor [pcolor] of myself]]] set total-volume n * (4 / 3 * pi * r ^ 3) set total-surfacearea n * (4 * pi * r ^ 2) do-plots end

to setup NetLogo procedures always start with “to.”

ask patches [set pcolor white] Ask all the patches to be set to the color white.

repeat n [ask patch random-xcor random-ycor [set pcolor random 140]] Repeats “n” times: picks a random patch and sets its color to a random color (colors are numbered from 0 to 140)

end

to go

set r 1 Sets the variable r (radius) to 1

ask patches with [pcolor != white] [ask neighbors4 [if pcolor = white [set pcolor [pcolor] of myself]]] Asks all the patches which are NOT white (i.e., since white is the uncrystallized materials, this corresponds to any crystallized material) to do the following: looks around yourself, if there is a white patch around you, “expand” yourself into that patch (setting that patch’s color to be your color).

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set total-volume n * (4 / 3 * pi * r ^ 3) Sets the variable total-volume to be the product of the number of particles and the volume of each based on their radius, using the

formula for spherical volume: 34

3n rp

æ ö÷ç ÷⋅ ç ÷ç ÷çè ø

set total-surfacearea n * (4 * pi * r ^ 2) Sets the variable total-surfacearea to be the product of the number of particles and the surface area of each based on their radius, using

the formula for surface area: ( )24n rp⋅

do-plots Updates the plots

end Every NetLogo procedure must end with the “end” keyword.

Benedict re-read his code and was mystified by the disappearance of the

radius:

Benedict I used to have code in there to set the radius, I don't know where it went. I must accidentally have erased it.

In fact, his previous model had a line of code to update the radius of the

particles, which was not necessary anymore:

set r r + (G * delta-t)

(Equivalent to ( )r r G t= + ⋅ D )

But it took him another five minutes to come to terms with the fact that

all of the code which used the radius variable was not necessary any-

more. In his new model, the growth of the particles was taking place

through this line of code,

ask patches with [pcolor != white] [ask neighbors4 [if pcolor = white [set pcolor [pcolor] of myself]]]

311

Which did not use a incremental “hardcoded” increase in radius as a

mechanism for growth, but was solely based on the neighborhood of

each nucleus.

Figure VIII-24 Benedict’s new patch-based

recrystallization model

Finally, Benedict was concerned with that would happen when two re-

crystallized grains would meet:

Benedict When they start impinging on each other, they’ll start flipping colors back and forth, one will set to this color, the other one will set to that color.

He decided to tweak the code and changed the rule for when two grains

meet, adding a rule which would randomly pick which grain would

“win” when they start impinging on each other. He ran the model and

was shocked at the results.

Figure VIII-25 Benedict’s first attempt at an

emergent algorithm

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Benedict WOW. That’s cool. I wasn’t exactly right. Like fractals. Fractals or grain boundaries with very high temperatures… Is this, like, some system in Materials Science, or is this just, like, ‘oh cool’?

Interviewer What do you think?

Benedict Well… other phases are randomly appearing in phases of one color which could never happen because that would raise the energy a lot. So that doesn’t make sense. But on the other hand, they are staying more or less in the original regions. It’s certainly not recrystallization, I know that much.

This constituted a pivotal moment in Benedict’s representational transi-

tion:

1. He created an equation-based model of recrystalization. However, the mathematical complexity required to complete the model was an obstacle (namely, calculating the overlaps among the growing crystals).

2. In search of a solution, he brainstorms: “if you had a grid…”

3. He soon realizes that the ‘grid’ itself could enact the model, i.e., the grid goes from being a mere measuring artifact in an equational model to the model itself.

4. Benedict still cannot understand what happened to the ‘radius’: “I must accidentally have erased it.”

5. He understands that the radius was not necessary anymore, and then starts to think about issues within the new representational infrastructure (“When they start impinging on each other…”)

6. After modifying the code and looking at the strange behavior on the computer screen, he states that they could represent “fractals or grain boundaries with very high temperatures.”

7. Finally, he asks: “Is this some system in material science?”, and then goes on to immediately identify two important elements of a plausible system: (a) it cannot increase the energy, (b) it should have some sort of organization. He hints at several important ideas in his final utterance: (i) movement of particles and energy are connected, (ii) the creation of a new crystal within a bigger crystal is energetically unfavorable, and (iii) spatial coherence is an indication of a systemic behavior.

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Benedict now sees a computer microworld generated by an accidental

variation of his own code as being a good candidate for a ‘system in ma-

terials science.’ Even though the variation in the code was very small, he

states with certainty that “it is not recrystallization,” suggesting that his

similarity triggers are not biased as much by the representation – subtle

variations in behavior can generate quite different phenomena. Thus,

this new, fractal-like behavior was not categorized as “almost recrystalli-

zation,” even if its code differs just a few characters from the actual re-

crystallization code.

From steps 1 to 7, Benedict transitioned from the traditional representa-

tions in engineering classrooms (equations, heuristics) to an agent-

based representation. As we track his transition, there is also a clear shift

in epistemological resources employed. In the beginning, “knowledge as

propagated stuff,” and authority-based explanations (Hammer & Elby,

2003) are more common. In the end, those resources are replaced al-

most entirely by knowledge as “fabricated stuff,” “free creation” or “di-

rect perception” – all resources much more related to inquiry, discovery,

and autonomy – the holy grail of modern engineering education.

I will not get into much detail about Benedict’s final recrystallization

model, but his NetLogo model will be analyzed together with the others

in a later section of this chapter.

After this first TA session, Benedict successfully completed his ABM

model and report on recrystallization. But for the purposes of this part of

the chapter, I would like to jump one year ahead to his return interview.

I was interested in finding out if his insights and representational shifts

would be forgotten, or if there would be longer term effects of his expe-

rience. That is the purpose of Scene Three.

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VIII.7.3. SCENE THREE: ONE YEAR LATER The return interviews took place exactly one year after their final inter-

view in the 2007 study. Only a subset of the students came for those in-

terviews (n=5), which lasted approximately 30 minutes. The interviews

followed the semi-clinical approach as in the previous year. I asked stu-

dents to describe their models from 2007, and then gave them two ma-

terials science phenomena for them to ‘think on their feet’ and verbalize

their initial ideas for a computer model. Those two phenomena were so-

lidification (to which they were exposed a year prior), and memory-

shape alloys (a new phenomena for most).

In this section, I will keep discussing Benedict’s data. My goal is to fur-

ther investigate the influence of representation on students’ ability to

explain a phenomenon that they know with different levels of familiarity.

The following transcripts are for his response when I asked him about

how he would create a model of solidification, i.e., a liquid metal inside a

container turning into solid due to a drop in temperature along the con-

tainer’s wall. Note that I use an adapted version of Dor Abrahamsos’s

“transcliption” (Fuson & Abrahamson, 2005), which puts text and

screenshots side by side. My trancliptions will focus particularly on what

students were drawing as they talked, and my analysis will focus on the

differences and affordances of agent-based representations and differen-

tial-based representations, since those were the two types of representa-

tions utilized by students in the responses.

In [a], Brickley starts his explanation drawing an empty square (the con-

tainer), and “assuming it was homogeneous.”

315

a I guess I would start by, assuming it was homogenous.

In this apparently harmless assumption, the first constraints of the diffe-

rential-based encoding are visible – macroscopic homogeneity and

symmetry are the typical starting points of simpler differential models,

due to the relative ease in building symmetrical/homogeneous analyti-

cal models.

b Well, I mean, you know that container walls will be the coolest part, so, and you know what temperature they would cool to. So you know that the solidification comes from walls, because that is where the cooling is coming from,

c so you will be able to determine the rate of solidification by the difference between temperature outside and temperature inside, [pause] let's call that Ti, [pause] so you will be able to determine the cooling rate, that way you determine the velocity of this solid phase coming in from the edges,

In [b], we continue to observe the symmetry constraint when Benedict

draws the four arrows pointing inward, each attached to one of the walls.

After stating that “the solidification comes from the walls,” he says, in

[c], that by knowing the temperature inside and outside the container,

one could determine the solidification rate.

d I mean, this will all be solid, but this was the direction that the edges would take. And all will be at the same temperature.

316

e [Benedict final drawing]

Finally, in [d], he finishes the explanation and draws the final state of the

system: another square with an “x” representing an all-solidified materi-

al.

Let us note, first, that Benedict studied this particular phenomenon

about a year before in class, and therefore I would hypothesize that he

did not remember details of the explanation, and was constructing an

explanation on-the-fly. His first attempt employed a classical differential

approach commonly seen in class – draw a simplified representation of

the phenomena and, gradually, extract the elements that would enable

the use of differential equations to model the problem – namely, for ex-

ample, gradients, infinitesimal slices, or continuous flows. His own re-

presentational choice exposed to him three initial manipulable elements:

317

Figure VIII-26 Benedict’s first attempt at

explaining the liquid to solid transformation

An empty rectangle.

The outside of the rectangle .

The inside of the rectangle.

With those three exposed representational elements, and assuming that

the inside and the outside were at different states (in this case, different

temperatures, from the problem’s statement), the three possible combi-

nations of events would be:

a. There would be a flux from the inside to the outside.

b. There would be a flux from the outside to the inside.

c. Both regions would be at equilibrium.

Benedict considered that, since the “container walls will be the coolest

part,” then “solidification comes from walls,” the flux would take place

from the outside to the inside (in this case, extraction of heat – note the

arrows in step b of the transcliption). His next modeling ‘act’ was to try

to build an equational relationship to describe not the phenomenon it-

self, but one aggregate aspect of it—its speed. His choice was to deter-

mine the cooling rate by creating two entities following his manipulable

elements: Tout for the external temperature, and Ti for the internal tem-

perature. Then, he states, “by the difference between temperature outside

318

and temperature inside, let's call that Ti, [pause] so you will be able to de-

termine the cooling rate”. Finally, his model ends when the system is at

equilibrium, once all the heat was extracted from the liquid. In other

words, once the rectangle was “filled” with solid, the system would stop.

He draws then a second rectangle to show that state, and an “x” on top

of it indicating that the “inside” would be at capacity.

Benedict’s solidification model is not incorrect – however, it does not

address the atomistic mechanism of solidification, but only its net effect.

My hypothesis is that Benedict’s explanation was not a reflection of his

knowledge about solidification, but a result of his initial representational

choice—drawing a rectangle—a type of choice extensively used in many

theoretical engineering courses. His ‘design’ decision left him with few

choices to move ahead, but to infer a flux and hypothesize about a flux

rate and an equilibrium state.

But an interesting turn of affairs took place when I prompted him to re-

member his NetLogo model from the previous year. His second expla-

nation, just seconds after the first, and only prompted by a 10-second in-

tervention (for a similar description, see Hammer & Elby, 2003) was

significantly different.

Interviewer And let's say you have that same grid you had when you were programming your model last year. You could have mobile particles too.

Benedict

a I mean I kind of simplified it by having only one wall, actually, I mean, temperature is here…[draws grid]

319

b I think it would be easiest if we had all of this set to be the solid, so they don't move.

c And then you have the liquid, you have a few of these floating around, and I guess you would set a fairly random velocity and direction for the liquid atoms, when the hit each other they could, kind of, they could have a term for sticking to each other and a term for transferring energy to each other

d and when they hit the solid,

e they have a term for sticking to the solid, so when it is stuck, it would just be there, and join the solid. Because the solid being at a lower temperature, so it would take energy from these.

So eventually, they would all end up sticking.

320

[Benedict’s final drawing, indicating the grid, the “solids” (shaded area), the liquids (blue circles), and one liquid attached to the solid]

The difference between the two attempts to explain the phenomenon

are revealing. Clearly, by asking Benedict to remember his NetLogo

model, he started off with a different representational stance. The im-

mediate consequence was that his new starting point was a rectangle di-

vided into a grid, or patches, and not any more an empty one. He added

a layer of ‘solid’, by shading one row of patches and making them im-

mobile. This time, he did not assume symmetry – the solid was located

adjacent to just one of the walls. His next step was to create the liquids,

and assign a “fairly random velocity and direction” for them. So far, his ini-

tial representational choice (the grid) led to a radically different path.

This time, solid and liquid were not represented as continuous invisible

entities, but as two categories of micro-entities pertaining to the grid.

One consequence of having two different entities is that interaction

rules need to be defined. Benedict addresses the issue by stating that

“for the liquid atoms, when they hit each other they could […] have a term

for sticking to each other and a term for transferring energy to each other

[…also] they [could] have a term for sticking to the solid, so when it is stuck,

it would just be there, and join the solid.”

One additional feature of this representational stance is its reversibility.

Let us now observe what happened when I asked Benedict about the

opposite phenomenon: liquefying the solid metal.

Interviewer And now let's say we changed our mind and create a solid to liquid, so we'll increase the temperature of this container, and make it all

321

turn to liquid, so, how would you, using the same ideas you just described.

Benedict

a Well…

b I guess, [pause] using the same similar idea up here, start off all of these and give each one a…

c so this is high temperature, this is low temperature,

d so for these ones on the edge, I guess I would give them a random kind of vibrational energy based on the temperature next to them,

e and then give them a set energy that they need to break off of this,.

f so as their temperature increases, they will have a greater chance of breaking off and heading off to the solution

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g As it goes eventually they all go into the solution.

h [Benedict’s final drawing, showing the liquid to solid and the solid to liquid models]

In this last transcript, we can observe one last important affordance of

the agent-based representation explored by Benedict, which I will call

asymmetrical reversibility. The idea is that, by reasoning backwards

(solid to liquid), he came up with a different algorithm, and not only a

simple copy of the previous one in the opposite direction. For example,

the mechanism for the liquids to stick to the solid (colliding) is funda-

mentally different than the algorithm for the solid to liquefy (vibrate and

detach). Conversely, in his equational explanation, the reversed version

of the algorithm was a simple restatement of the equations with a nega-

tive sign.

Below we have a summary of the comparison between the two represen-

tational stances, which I will use to analyze the transcription of other

students in the remainder of this section.

Table VIII-13 A summary of Benedict’s two

explanations First attempt Second attempt Differential approach Agent-based approachSymmetrical AsymmetricalContinuous Discrete

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Flux-driven Mechanism-drivenManipulable elements exposed:

An empty rectangle. The outside of the rec-

tangle. The inside of the rectan-

gle.

Manipulable elements exposed: A regular grid. Fixed squares. Mobile circles.

Possible interactions between elements:

Inside → outside flux. Outside → inside flux. Both regions at equili-

brium.

Possible interactions between elements:

Squares and circles could collide.

Circles and circles could collide.

Circles and walls could col-lide.

Symmetrical reversibility Asymmetrical reversibility Non-mechanistic similarity trig-ger

Mechanistic similarity trigger

VIII.7.4. FISHER Fisher built a interesting model of grain growth with dispersed particles,

and had a slightly below average grade (37.3, class average = 40.6). His

model was based on the grain growth model, so his contribution was an

add-on module rather than a model created from scratch.

Despite having dealt with local rules and agent based heuristics during

his model-building work, Fisher’s response in the post test was did not

use any agent-based heuristics, as we will observe in the following tran-

script, when he is trying :

Interviewer How would you create a model of a liquid-to-solid transformation?

Fisher

a Well, I guess I’ll just have a box with a [pause] and this area here will be liquid and then, I guess the solid particle will be in the middle.

324

b

And I guess as the particle expands, we could [pause] or as the solid solidifies, as the solid grows,.

Up to this point, using the same analytic framework employed in Bene-

dict’s case study, I hypothesize that Fisher’s first drawing (a box and a

circle) exposed the following representational elements:

A rectangle.

A shaded circle inside the rectangle.

The inside of the rectangle, i.e., the area between the shaded circle and the rectangle.

The outside of the rectangle.

With those four exposed representational elements, and assuming that

the container does not change its original shape and dimension, and that

all transformations are happening inside the container (i.e., no flux in

our out the rectangle), the three possible combinations of events would

be:

a. The shaded circle will grow (note his gesture in transcliption b).

b. The shaded circle will shrink.

c. The shaded circle will be at equilibrium.

Indeed, Fisher’s explanation cannot go much further than alternating

between those events. In what follows, after drawing the circle, he

immediately stops explaining the mechanism, and switches to a plot,

which he does not “know how it would look”.

325

Fisher

c

I guess I would have a graph or a plot showing the total surface energy, which would increase, and then the total energy within the [pause] so like [pause] I really don’t know how the plots would look but I’ll just guess.

d

So here, I guess, would be the total surface energy, and then, as the bulk material increases, then we would have something that is like this.

Fisher does not know how to connect the plot, the drawing, the beha-

vior suggested by his drawing, and his own memory of the theory seen in

class. It seems that he remembers the plot from the textbook (see Figure

VIII-27), which has three curves: one for the ‘bulk energy’ (negative),

one for the surface area energy (positive), and a sum of the two energies

(blue curve). The plots states that the bulk energy (i.e., the energy sys-

tem gains by transforming liquid [higher energy] into solid [lower ener-

gy]) will eventually overcome the surface energy increase (the energy

the system loses by creating more surface energy [as the solid increases

in size]). So he apparently understands or remembers this competition

between the two energies, but makes no mechanistic inference about it.

Figure VIII-27 Textbook picture showing the energy plots for solidification

326

He knows, however, that temperature will somehow influence the sys-

tem, i.e., lower temperatures will favor solidification, and higher temper-

ature would favor re-melting—so he decides to create a temperature

slider:

Fisher

e So that would be the energy of the solid, of the bulk solid, and I guess adjusting, I would probably have a slider or something for the temperature. So, then you could see, at higher temperatures, that the liquid would be favored and the energy of the bulk solid would actually be higher.

f

So, the smaller particle would be favored. So, you could see that from [pause] I guess the plots would look different. So at a higher temperature, it would probably be like, here is the surface energy, and then, the bulk would be something like that.

g So, just, I guess I would show just the relationship between those

Fisher’s explanations offer no mechanistic insight into solidification. He

remembers the overall effect of temperature, and knows that surface

energy and bulk energy are part of the process, but offers no causal con-

nections between those elements.

Figure VIII-28 Fisher’s attempt at explaining

the liquid-to-solid transforma-tion

327

His initial representation “trapped” him into a system where the only

manipulable element was the size of the solid sphere: it could grow or

shrink, and that would be defined by temperature (his only slider). Also,

his system’s reversibility is symmetrical, i.e., temperature simply makes

the sphere grow or shrink, by the same exact mechanism (which was not

even specified). A summary is on Table VIII-14.

Table VIII-14 A summary of Fisher’s explana-

tion Fisher’s solidification Differential approachSymmetricalContinuousFlux-drivenManipulable elements exposed:

A rectangle. A shaded circle inside the

rectangle. The inside of the rectan-

gle, i.e., the area between the shaded circle and the rectangle.

The outside of the rec-tangle.

Possible interactions between elements:

Shaded circle grows. Shaded circle shrinks. Shaded circle at equili-

brium. Symmetrical reversibilityNon-mechanistic

VIII.7.5. CHAPS Chaps built a recrystallization model which was graded at 40.1, almost

exactly the class’ average (40.7). His final grade in the course is very

similar to Fisher’s: 91.7 (vs. 91.1), and both students spent the same

number of hours creating their models (12h). In his post-interview,

asked about the exact same phenomenon (liquid-to-solid transforma-

tion), Chaps offered a very different explanation.

328

Interviewer How would you create a model of a liquid-to-solid transformation?

Chaps

a Well, you could probably [pause] one of your variables would probably… [thinks about the slider for a bit, and draws it]

b And then you would have your solid down here [pause] there.

c And you would [pause] there would be a probability of whenever a liquid atom hit the solid atom, or hit the solid, there would be a probability that it would stick and become solid.

d And there would also be a probability that at any given time, a solid atom would leave the solid and become part of the liquid.

329

e And those probabilities would be due to the temperature.

Figure VIII-29 Chaps’ drawings

Chaps’ explanation was very different from Fisher’s, despite all the simi-

larities between them (same grades in the course and in the modeling

activity, etc.). First, Chaps starts his drawing with a different set of ex-

posed representational elements:

A rectangle.

Several circles inside the rectangle.

The inside of the rectangle.

The outside of the rectangle.

With those four exposed representational elements, and assuming that

the container does not change its original shape and dimension, and that

all transformations are happening inside the container (i.e., no flux in

our out the rectangle), the two possible combinations of events would

be:

a. The circles could move (note the arrows and his gestures in tran-scliptions d and e).

b. The circles could collide with the containers’ wall.

330

c. The circles could stick together.

Indeed, Chaps’ explanation draws on those possible interactions. He

bases his description on a probabilistic event: “whenever a liquid atom hit

the solid atom,” and derives all related event (atoms detaching from the

solid) on that mechanism— every utterance in which he was describing

a mechanism has the word “probability”. In addition, in the end he even

relates the probability with temperature, a crucial concept in materials

science, chemistry, and physics (“those probabilities would be due to the

temperature.”).

Table VIII-15 A summary of Chaps’ explana-

tion Chaps’ solidification Agent-base approachAsymmetricalDiscrete Mechanism-drivenManipulable elements exposed:

A rectangle. Several circles inside the

rectangle. The inside of the rectan-

gle. The outside of the rec-

tangle. Possible interactions between elements:

The circles move. The circles collide with

the containers’ wall. The circles stick togeth-

er. Symmetrical reversibility Mechanistic

VIII.8. SUMMARY Some of the findings of this chapter are:

331

a. Students’ average programming ability, perhaps counter to stereo-type, is rather basic, and is mostly about MATLAB, which is an en-gineering language rather than a general purpose language such as C++ or Java. This suggests that (1) a programming assignment was not uncommon for students, but was localized in few specialized courses, (2) most of what students did with computers was around creating MATLAB programs to mimic differential equations, and (3) students’ performance in the modeling task was not explained by extraordinary programming ability.

b. The mean total hours on the project was 20.2, which averages about 5 hours per week—an amount which was shown to be compatible with the weekly number of hours dedicated for out-of-class work. Given students’ basic programming abilities, it seems that the as-signment was feasible within the context of the class.

c. Students’ feedback on the project was positive, even considering that (1) the assignment was proposed midway through the quarter, (2) it entailed a very uncommon type of activity (creating models from scratch), which was demanding, (3) the “NetLogo TA” was unfamiliar for most students (I did not belong to the department), (4) students obviously knew that they were part of a study.

d. On average, the peak of motivation happened when students got their first “beta” version to work, and that motivation declined to-ward the end, when students had to fine-tune and debug their mod-el, run experiments, and write an elaborate report.

e. The coding of students’ models showed that 18 of the 19 ABM models were successful in having (1) at least one type of agent with different properties at setup, (2) agents perform actions based on their own state, or their neighborhood’s state. (3) at least one graph-ical representation of the states of the main group of agents in the system, (4) at least one interface element conveying the states of the main group of agents in the system (normally, a plot).

f. The correlation analysis showed that some assumptions about good performers in modeling or programming assignments might not hold, namely, that good programmers generate better models. There was a weak correlation between programming ability and model evaluation.

g. The logfile analysis detected six prototypical modeling events (such as “stripping down an existing model,” “long plateaus of no coding activity”), and three personal coding styles (“copy and pas-ters,” “mixed-mode,” and “self-sufficients”). The empirical verifica-tion of these canonical coding strategies and coding profiles has im-

332

portant implications for design, in particular, building-core (BBC) constructionist environments, as I will discuss in the next chapter.

h. During the think-aloud explanations, there was a strong alignment between the students’ representations and the underlying structura-tion (agent-based or differential/equational). The manipulable elements exposed by students’ drawings did not seem to be only an auxiliary externalization, but mainly to shape the further develop-ment of student’s initial idea.

i. One of the initial assumptions was that students’ with a deep ABM experience would employ ABM in place of differential approaches. However, the data suggest that even after an intense modeling expe-rience, both approaches were present. In Benedict’s case that re-mained true even one year after the intervention. After his initial eq-uation-based reply to the solidification problem, it took a very sim-ple prompt to make him re-explain the problem using an agent-based approach. Similarly, Chaps and Fisher, even days after the modeling experience, had diverse approaches to explain solidifica-tion. In addition, the data suggest that they are orthogonal, i.e., stu-dents did not try to blend the two representations, but instead kept them very much distinct.

j. The agent-based explanations were in general more mechanistic, comprehensive, and reversible. The equational explanations were more superficial.

333

IX DISCUSSION 

334

IX.1. SUMMARY The larger-scale goal of this dissertation was to explore relations between

content, representation, and pedagogy, so as to understand the impact of

the nascent field of complexity sciences on the teaching and learning of

STEM content.

I conducted a series of studies of undergraduate students’ learning of

materials science. These studies consisted of both design research and

empirical evaluation. Over four years, I have iteratively designed a mod-

el-based curriculum for materials science – MaterialSim (Blikstein &

Wilensky, 2004) – a constructionist suite of computer models, support-

ing materials and learning activities designed within the approach of the

complexity sciences and agent-based modeling; and simultaneously

conducted an empirical investigation at a top-ranked materials science

department in a research university.

Specifically, I investigated:

a. The learning outcomes of students engaging in scientific inquiry through interacting with MaterialSim.

b. The effects of students programming their own models and interacting with pre-programmed models.

c. The characteristics, advantages, and trajectories of scientific content knowledge that is articulated in epistemic forms and representational infrastructures unique to complexity sciences.

d. The design principles for MaterialSim: what principles govern the de-sign of agent-based learning environments in general and for mate-rials science in particular?

Emerging from the dissertation is the following conjecture:

The epistemic forms of agent-based modeling can transform tradi-tionally intricate, specific materials science content, encoded as engi-neering laws and differential equations, into more learnable, malle-able, and generative principles and micro-rules, so as to enable stu-dents to deal with variant phenomena.

335

Before we hone on the rationale and explanation of this conjecture, I will summarize the studies and their main findings, with comments on the methodological contributions of each.

IX.2. SUMMARY AND FINDINGS IX.2.1. STUDY 1 Study 1 was comprised of two parts: one about current explanation and

representational strategies in a materials science classroom, and a set of

content-driven semi-clinical interviews with students. The main findings

were:

IX.2.1.1. Representational trajectories There was an overall pattern of representational trajectories throughout

the course: the prototypical explanation of a phenomenon was divided

into four explanatory events:

1. Textual explanationNormally a substitutional atom in a crystal oscillates about a given site and is surrounded by neighboring atoms on similar sites. […] Normally the movement of a substitutional atom is limited by its neighbors and the atom cannot move to another site. However, if an adjacent site is vacant it can happen that a particularly violent oscillation results in the atom jumping over on to the vacancy […] the probability that any atom will be able to jump into a vacant site depend on the probability that it can acquire sufficient vibrational energy.

The process starts with a textual ex-planation which is based on probabil-istic micro behavior of atoms,

2. Atomistic graphical representation

The second step is a graphical repre-sentation of the micro behavior, with minimal labe-ling.

3. Transitional graphical representation

336

The third step is a hybrid represen-tation, in which the graphical represen-tation is first ‘matched’ to a plot, and then to a diffe-rential expression (note a version of Fick’s law to the right of the curve).

4. Inscription

2

2

J Dx

Dt x

f

f f

¶=-

¶¶ ¶

=¶ ¶

Finally, after a series of deriva-tions, we arrive at the final equation for diffusion.

Such a pattern was found both in classroom transcriptions and text-

books. It suggests an underlying teaching rationale: micro-behaviors are

a proper introduction to most phenomena, but per se are not powerful

enough to predict phenomena—thus, conceptual, introductory explana-

tion and predictive mathematical apparatus are dissociated. Those mi-

cro-behaviors need to be transformed into manipulable representations,

which can ultimately predict behaviors. During several ‘mathematiza-

tion’ phases, the micro behavior is translated into representations of de-

creasing levels of adherence to the physical phenomena, and increasing

conventional mathematical symbolism. The differential nature of most

of these representations presupposes the subdivision of matter, forces,

337

fields, vectors, and fluxes into infinitesimal pieces—the initial graphical

representations are repeatedly fitted into a “calculus-friendly”, symme-

trical graphical shape.

Also, I analyzed diffusion as an instance in which the final “elegant” in-

scription (Fick’s Law) was obtained after a series of assumptions taken

as unproblematic (i.e., “there is an equal probability of the atom jump-

ing to every one of the six adjacent sites”).

This transition could pose difficulties for students, as the second part of

Study 1 suggested (see Table IX-1 for a summary of the differences be-

tween the representations found in the study), since instructors seemed

to ignore that representational shifts could have deep learning implica-

tions—the progression of the explanation, no matter how complex, was

regarded as “natural” and unavoidable. I also show that this representa-

tional scheme generates an overload of equations which have to be

speedily explained to students at the astonishing rate of one each 2.5

minutes.

Table IX-1 Comparison between discursive micro-behaviors and differential

formulations

“Discursive” micro-behaviors Differential formulation

Discrete Continuous

Conceptual Predictive

Textual/graphical Numerical/graphical

Prolix Concise

Free-form Symmetrical

As discussed in the Representation Comparison chapter, many of the

intrinsic characteristics of phenomena in materials science pose a prob-

lem for the differential formulation, namely:

338

Materials are composed by atoms which are discrete in nature.

Materials are composed by billions of atoms, so any useful aggregate description has to make use of averages.

Materials (and materials within materials) can be morphologically diverse and complex, and are rarely symmetrical and homogeneous.

IX.2.1.2. Fragmented knowledge Indeed, the data from the second part of this study suggested sizeable

difficulties in students’ understanding, partly, because of the difficulty in

harmonizing the intrinsic characteristics of phenomena in materials

science and the differential formulation, as stated in the three aforemen-

tioned bullets. Particularly, students’ responses were very dissimilar,

even for very basic concepts. For example, while a small minority of stu-

dents correctly viewed grains as orderly groups of atoms, the other ex-

planations barely resembled one another. The representational and

teaching strategies used in the classroom impacted students’ under-

standing in three ways. First, the focus on equational representations left

little time and resources for in-depth classroom discussions about the

micro-behaviors, and those behaviors were not given much considera-

tion as a language to make predictions. Second, even when students

claimed to know a topic, their explanations were oftentimes a verbal re-

production of differential inscriptions based on averages and aggrega-

tions, with no sense of causality. Third, the fragmentation of the content

into a myriad of loosely connected, phenomenon-specific, mathematical

artifacts made their reconnection difficult, as the data show – frequently,

equations or ideas from one content topic were used to explain another

topic due to superficial similarities and not common behaviors.

IX.2.2. STUDY 2 The purpose of Study 2 was to investigate the learning outcomes of stu-

dents interacting with and building models.

339

IX.2.2.1. Interaction with models In the first part of the study, the goal was to find out the cognitive im-

pact of foregrounding atomic micro-behaviors to students, through the

interaction with a pre-built NetLogo model (grain growth). Grain

growth has a logarithmic rate, i.e., its speed slows down as the pheno-

mena advances, which is obscure for many students. I showed how the

foregrounding of atomic micro behaviors enabled students to identify—

almost instantaneously—the mechanism for this non-linear growth, and

understand it as an emergent property of elementary local rules. Stu-

dents were able to infer the growth law and the grain growth algorithm

even without recurring to any equational manipulation or their class

notes. This was in stark contrast with Study 1, in which students had dif-

ficulties explaining even very basic ideas in the course (i.e., ‘what is a

grain?’). When visualizing the grains grow, students had in mind the al-

gorithm individuals atoms were following, and could infer aggregate be-

haviors from them (i.e., the rate of growth slows down because “as they

grow, it is increasingly hard to take away from them, or “either one can

happen, so it will take forever”.)

IX.2.2.2. Model building In the second part of the study, when students built their own models,

we observed that the agent-based representation was also useful to

extrapolate from the initial phenomenon (grain growth) to other phe-

nomena as well, by means of extracting, customizing, and combining the

atomic micro rules.

To further understand the cognitive model which the ABM perspective

might foster, let us consider again, for example, Bob’s explanation of

grain growth:

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Bob Well, grains grow through diffusion, through vacancy diffusion, and atomic diffusion, for one, it is all over the place, temperature increases, molecules move around faster […].

His statement reveals a one-level description of the phenomena, which

is compatible with my analysis of the current materials science structura-

tion. Ideas such as “vacancy diffusion” and “increase of temperature” are

connected to “grain growth” without a clear hierarchy, and with several

weak similarity triggers.

Figure IX-1 Bob's one-level explanation

During the work with MaterialSim, students developed a layer which

grouped some of the surface manifestations on the phenomena under

one unifying principle—in other words, these unifying ideas were deep

similarity triggers. Let us observe Liz’s statement:

Liz It is because, it wants to be more energetically stable, or have less energy in the crystal, so it will grow, just to form one big grain, because that’s the least energy configuration […]

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Figure IX-2 Liz's two-level structure

Liz identified one unifying principle, ‘lowering free energy’, from which

many of those external manifestations derive. The agent-based model-

ing environment offered a low-threshold tool to code and formalize al-

gorithmically this principle, enabling her to ‘mobilize’ this idea that was

previously just a vague idea. Finally, after the model building, students

were able to mobilize these generalizable principles, encoded as com-

puter code, to explain other phenomena which shared the same me-

chanism.

Figure IX-3 A two-level structure with

multiple phenomena

I showed how in less than 2.5 hours students could grasp the basics of

the NetLogo language, build, and test an agent-based model of reasona-

ble complexity. Through analyzing students’ artifacts and interviews, I

Grain Growth lower free energy

vacancy diffusion

atomic diffusion

temperature increases

molecules move faster

dislocation interaction

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identified the four main affordances of the agent-based representation

scheme more frequently used by students:

a. One-to-many generativity: a small number of algorithms and rules can be used to understand many phenomena. Examples: neighbor-hood-based local count, energy minimization, neighborhood- and radius-based restricted movement.

b. Formalization of intuitive understanding: students’ intuitive ideas about atomic behavior can be directly encoded into a formal computer language. Examples: the more misaligned, the harder to jump; an interface between different structures is less stable; melting and solidification are symmetrical.

c. Foregrounding of physical processes: the model resembles the actual phenomena both graphically and in terms of the rules em-bedded in the code. Examples: atoms vibrate and jump; atoms in a polymer chain move but keep the integrity of the chain; diffusion is just about atoms moving into vacancies; solidification is about atoms in the liquid hitting solid clusters.

d. Model blending: micro behaviors are easier to combine and super-pose than their ‘macro’, aggregate counterparts. Examples: combin-ing the grain growth and sophisticated micro-level geometries you get anisotropic grain growth; combining diffusion and spring-like repulsion algorithms you get dislocation motion.

IX.2.3. STUDY 3 The purpose of Study 3 was to provide a proof of existence of an agent-

based modeling activity in a real engineering classroom, develop new in-

struments to assess students’ artifacts, and conduct a more-depth analy-

sis of the cognitive and representational affordances of agent-based

modeling.

IX.2.3.1. Viabil ity analysis , feedback from students, and motivation plots

In this study, I investigated students’ familiarity with programming, their

views and feedback about the activity, and how much time they spent on

each part of the project.

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In terms of programming experience, the results were somewhat surpris-

ing. For 74% of the students, the longest program they had ever written

had between 51 and 200 lines of code, and 58% reported an “average”

familiarity with computers. For 74% (14 out of 19), MATLAB was their

first programming language. The data indicate that students’ average

programming ability, perhaps counter-intuitively, is rather basic, and is

mostly about MATLAB, which is an engineering language rather than a

general purpose language such as C++ or Java. This suggests the follow-

ing: (1) a programming assignment was not uncommon for students,

but was localized in few specialized courses, (2) most of what students

did with computers was around creating MATLAB programs to mimic

differential equations, and (3) students’ performance in the modeling

task was not explained by extraordinary programming ability.

I also assessed the number of hours that each task entailed. Consistently,

programming was the task that consumed most hours (24%), followed

by getting help from the NetLogo TA, and writing the final report. The

mean total hours on the project was 20.2, which averages about 5 hours

per week—an amount compatible with the normal course load for the

course, as the data showed. Even given students’ basic programming ab-

ilities, it seems that the assignment was feasible within the context of the

class, even considering that students had to learn a new programming

language.

Finally, students’ feedback on the project was positive, even considering

that (1) the assignment was proposed midway through the quarter, (2)

it entailed a very uncommon type of activity (creating models from

scratch), which was demanding, (3) the “NetLogo TA” was unfamiliar

for most students (I did not belong to the department), (4) students

obviously knew that they were part of a study, which could have been a

reason for some discomfort or even the feeling of being “used.” Despite

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all that, 61% considered NetLogo modeling a “good activity for the

course,” and just 17% disagreed (the other 22% were neutral). Students’

most common suggestions were for more support (particularly collec-

tive training sessions), and more time to complete the project. One only

student out of 19 suggested the elimination of the activity.

IX.2.3.2. Motivation plots The most important finding from the motivation plots was that, on av-

erage, the peak of motivation happened when students got their first

“beta” version to work, and that motivation declined toward the end,

when students had to fine-tune and debug their model, run experiments,

and write an elaborate report. There are three important implications of

such decrease in motivation:

Typically, due to a common misinterpretation of constructionist learning environments, designers oftentimes emphasize the work leading to getting a working prototype done. Further refinements, reports, or careful data comparisons are not as common.

It is during that second half of the project that many of the important analytical tasks take place (particularly, some very important for engineering students). Also, it is when motivation declines. It is crucial, thus, to design support and facilitation strategies in the “post-artifact” phase of the project. Those strategies are relatively less explored by constructionist researchers.

The process of building a model overlaps the programming work and the research work. As the motivation plots showed, the work leading to having a working prototype is very motivating—students feel positively challenged and find great pleasure in finally running their model. It is conceivable that this phase of the work can overshadow the research component (running experiments, connecting with theory, etc.), resulting in stronger models but without the needed scientific reflection. At some point, the model needs to become an “object to think with,” and not the only focus of the process. Therefore, one effective design decision was to have a “model deadline” and a “project deadline.”

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IX.2.3.3. Grading the models To assess how students were making use of the affordances of the Net-

Logo language, and also the quality and sophistication of the models, I

developed a specialized rubric with four dimensions: system definition,

rules, visualization, and interface/reporting. For each item within a di-

mensions, a weight was assigned based on the difficulty of implementa-

tion. In each of the four dimensions, a minimum threshold was defined

to consider students’ artifacts a “minimally working agent-based model.”

The coding of students’ models showed that 18 of the 19 ABM models

were successful in having (1) at least one type of agent with different

properties at setup, (2) agents perform actions based on their own state,

or their neighborhood’s state. (3) at least one graphical representation

of the states of the main group of agents in the system, (4) at least one

interface element conveying the states of the main group of agents in the

system (normally, a plot).

Given the constraints of the assignment, students did learn and compre-

hensively applied the important principles of agent-based modeling to

their projects. Even advanced features, such as the use of dynamically

reconnecting links, complex topologies, and multi-layered behaviors,

more often than not employed by expert modelers, were present in a

significant number of models.

The correlation analysis showed that some assumptions about good per-

formers in modeling or programming assignments might not hold,

namely, that good programmers generate better models. Not only was

there a weak correlation between programming ability and model evalu-

ation, but the author of the best model (Carlo, graded 60.5) had his

programming ability ranked in the lowest quartile. Similarly, the most

computer-savvy student (Benedict, averaging 4.6/5 in computer and

programming familiarity), had a model in the lowest quartile (grade

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28.9). In addition, of the 20 hours of the assignment, just about 25%

were dedicated to learning the language and programming, so I hypo-

thesize that the integral modeling performance is better predicted by a

combination of programming skills, disciplinary content, and “agentifi-

cation” skills (being able to imagine and transform into rules micro-

level, agent-based behaviors). The highest achievers in the class (per

their final grade) performed better at the assignment and reported hav-

ing spent more time writing the final report.

IX.2.3.4. A note to practit ioners The implementation of agent-based model-building in classrooms share

many of the early challenges of Logo implementations, but also different

issues. First, similarly to implementations of programming activities in

educational settings, three of the potential challenges are that (1) stu-

dents might not have any previous programming experience, (2) stu-

dents might not believe that programming is an approachable activity

that they can learn, and (3) training or retraining practitioners about

programming skills could be challenging.

In the particular case of NetLogo, since the activity involves building a

scientific model and not an animated story or multimedia presentation,

there is the additional challenge of modeling the scientific phenomenon

within an agent-based approach. Since this approach differs from tradi-

tional textbook representations, it is not straightforward to find litera-

ture to help students in their modeling endeavors.

All these challenges might seem overwhelming for practitioners in real

classrooms and their mounting demands, but after three years of class-

room observations, lab studies, and a full classroom implementation,

some strategies proved to be useful:

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Instead of focusing on retraining teachers who are already overcommitted, I focused on supporting the work through teaching assistants, who are likely to have programming experience. Consequently, they would only have to learn an agent-based modeling language and techniques for ‘agentifying’ phenomena. Granted, that is not a straightforward set of skills, but several engineering schools already offer graduate courses in computational methods (including agent-based modeling). Therefore it is not unrealistic to assume that many graduate students do have familiarity with agent-based languages and with the challenges of ‘agentification’ of scientific phenomena, but probably on utilize those skills of research. Focusing on teaching assistants, we offload from lecturers the burden of redesigning entire courses and learning new skills, conversely, they can add programming assignments to existing courses, probe students’ reactions, and gradually make changes to their courses.

The questions of ‘student motivation’ is significantly different at this level of education than, for example, at the middle-school level. I hypothesize that, after 15 years in the traditional educational system, students are not at all naïve about how they employ their time and effort. Conversely, they are extremely efficient and rational in allocating those resources. In the post-survey, students’ main complaint was not that ‘programming was hard,’ but that the assignment was not work enough points in the final grade. The assignment was worth 4% of the final grade (1/5 of the 20% allocated to homework), and students considered that it should be worth (13±8)%, almost three times more. The lesson here is that for undergraduate students, the myth of programming being and impossible task is just that—a myth. Given the right incentives, they will put effort in whichever task. However, I was initially interested in students being intrinsic motivated to do the assignment, and not only doing it ‘for the grade.’ I hypothesized that the fact that they were able to pick their own topic and build their own model would be a factor for intrinsic motivation. The results were mixed. In the post-survey, I asked about how important was the fact that they could choose their own topic to model. 44% of students stated that it was ‘important’ or ‘very important,’ and 56% chose ‘neutral’ or ‘not very important.’ This suggests, again, that at this level of education the issues regarding student motivation are complex – some students might not attribute much value to the possibility of pursuing their own topics of interest. Despite being perhaps

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disappointing for designers interested in ‘pure’ intrinsic motivation, the results suggest that a combination of intrinsic and extrinsic factors should be considered by practitioners. The correspondence between time-on-task and percentage in the grade should be carefully considered, and it should not be assumed that the ‘open-endedness’ of the activity will be a motivational factor for all students.

One-to-one sessions were very effective in advancing students’ projects, even if those sessions were short (between 30 and 60 minutes). As they progressed in the assignment, students got very efficient in identifying their own difficulties and asking the right questions, and avoided being stalled for too long in the project for not knowing a primitive or a programming technique. However, despite my initial hypothesis that students would appreciate more individual tutorials, the main suggestion for improvement (in the post-survey) was to have more ‘NetLogo classes,’ i.e., tutorials for the entire class, as opposed to just individual sessions.

It might be misleading for practitioners to consider that the main difficulty of this type of learning activity is the programming. In fact, an equally difficult task is to learn how to represent the phenomena using agents. This is an area in which short training programs or workshops for teaching assistants and/or practitioners would be extremely helpful. In these workshops, participants should not only create a model by themselves, but have contact with basic literature on the learning of ABM, and on the different representational affordances of ABM.

IX.2.3.5. Assessment A crucial element of alternative educational interventions is assess-

ment—an issue that becomes particularly difficult in the context of re-

structured content. Despite not being a focus of my design, we could ask

ourselves of the interaction with MaterialSim would generate perfor-

mance gains for students, as measured by traditional exams and quizzes.

Given that the traditional assessment instruments in engineering (and,

more generally, STEM disciplines) are focused on skills that are particu-

lar to a structuration, such as derivations and algebraic manipulations, I

would hypothesize that those gains might not be significant.

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First, as I have shown, how most quizzes and homework assignments fo-

cused overwhelmingly on “proof,” “derive,” and “plug and solve” types

of questions. Moreover, exams are done on paper during a 50-minute

period, and focus on recall of knowledge previously taught to students.

Therefore, to capture the learning goals presented throughout this re-

search, two important elements must be considered for fitting assess-

ment instruments. Since most of the work done by students was con-

ducted in a computer, and the restructured material sciences content is

more distant from aggregate equations, the assessment activities should

be analogous both in the media and in the encoding of knowledge.

Therefore, traditional pre-post designs might be ill suited for evaluating

this kind of research, because the some dimensions of learning might

not at all be captured by traditional content-oriented instruments. For

examples, asking about a phenomenon that was explained during class

might assess how well students recall the explanation—but since one of

the main learning goals of MaterialSim was to develop in students deep

knowledge of certain kernel models that could be used to understand

several other phenomena, that ‘recall’ instrument would be of little use.

Apart from the evaluation of the artifacts itself (the computer model

generated by students), I developed some other preliminary assessment

instruments to capture these extra dimensions. For example, in the post-

interview, I asked students to describe they hypothetical model about an

unknown material science phenomena. When appropriately refined, this

could be an assessment instrument which captures both students’ re-

called knowledge about particular phenomenon (as a basis for their ex-

planations), and their skill in making use of the affordances of the agent-

based structuration to generate explanations on their own.

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Also, as part of the activity, I asked students to hand in a report with a

description of the model, its limitations, ideas for extensions, and a

comparison between published data and model data. By examining this

document, we could also assess how well students understand the na-

ture of the modeling enterprise, detect and discuss the limitations of

their model, and envision improvements of the model—all skills that

speak directly to the real work of engineers and scientists.

Logfiles are another instrument for assessment which could help de-

signers examine more closely the programming aspect of the activities,

as we will discuss in the next section,

IX.2.3.6. Logfi le analysis The goal of the logfile analysis was to identify patterns in the model building process, which comprises two distinct (but intertwined) tasks: learn the NetLogo language itself, learn to “agentify” a given scientific phenomenon and program it using the language.

I was able to successfully collect 158 logfiles in total from 9 students.

Based on Luca’s in-depth case study and on the analysis of other five

students, I detected the following prototypical modeling events:

a. Stripping down an existing model as a starting point.

b. Starting from a ready-made model and adding one’s own proce-dures.

c. Long plateaus of no coding activity, during which students browse other models (or their own model) for useful code.

d. Long plateaus of no coding activity, during which students think of solutions without browsing other models.

e. Period of linear growth in the code size, during which students em-ploy a trial-and-error strategy to get the code right.

f. Sudden jumps in character count, when students import code from other models, or copy and paste code from within their working model.

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g. A final phase in which students fix the formatting of the code, inden-tation, variable names, etc.

Based on those strategies, and the previous programming knowledge of

students, the data suggest three personal coding styles:

1. “Copy and pasters”: more frequent use of a, b, c, f, and g.

2. Mixed-mode: a combination of c, d, e, and g.

3. “Self-sufficients”: more frequent use of d, e.

The empirical verification of these canonical coding strategies and cod-

ing profiles has important implications for design, in particular, build-

ing-core (BBC) constructionist environments:

1. Each coding strategy and profile might entail different support strategies. For example, students with more advanced programming skills (“Self-sufficients”) might require detailed and easy-to-find language documentation, whereas “copy and pasters” need more working examples with transportable code. This validates my initial design choice to offer exemplar models of increasing levels of sophistication to cater to various coding profiles. Transportable code is, thus, an important focus for the design of models libraries for beginners—the code examples need to be accurate but cannot contain code that is too specific or with many dependencies.

2. To design and allocate support resources, moments of greater difficulty in the modeling process should (and can) be exactly identified. The data indicate that those moments happens mid-way through the project, but it is feasible to design data-mining tools to optimize such detection, perhaps in real-time.

3. By better understanding each student’s coding style, we have an extra window into students cognition. Paired with other data sources (interviews, tests, surveys), the data could offer a rich portrait of the model-building process and how it influences students’ understanding of the scientific phenomena and the programming language.

IX.2.3.7. Case studies As shown in Study 2, model building was a crucial activity. Despite the

learnability properties of simpler agent-based explanations, full agent-

based algorithms need a technological infrastructure to “run”. Needed

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was a computational tool to capture students’ intuitions and ideas at the

correct level. The constructionist nature of students’ interaction with

the tool enabled them to build fluency, and perceive themselves as

scientists in their own right, transforming seemingly simple ideas and lo-

cal rules in powerful kernels for scientific modeling.

One of the initial assumptions was that after a deep ABM experience,

students would employ ABM in place of differential approaches. I im-

agined that, by identifying intuitive knowledge elements (atomic micro-

rules) and having students learn how to appropriately connect them,

they would constitute a fixed frame of mind to solve materials science

(as possibly other) problems. However, the data suggest that even after

an intense modeling experience, and despite the agent-based explana-

tions being in general more mechanistic and comprehensive, both ap-

proaches were present (which does not come as a total surprise, since

they were still getting the traditional instruction.) The ABM representa-

tion was much more present, in general, but in some cases the coexis-

tence of two different representational schemes survived even one year

after the intervention. One year later, after Benedict’s initial equation-

based reply to the solidification problem, it took a simple prompt to

make him re-explain the problem using an agent-based approach. Simi-

larly, Chaps and Fisher, just days after the modeling experience, had di-

verse approaches to explain solidification—agent-based and equation-

based. In addition, the data suggest that they are orthogonal, i.e., stu-

dents did not try to blend the two representations, but instead kept

them very much distinct in separate spaces.

Theorists have been debating for decades about several different archi-

tectures for human cognition and knowledge representation, from

knowledge-in-pieces theorists (diSessa, 1988; diSessa & Sherin, 1998)

to “unified-theorists” (e.g., Vosniadou, 1994). Recently, Hammer and

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collaborators have added to the debate the idea of multiple epistemolog-

ical coherences (Hammer & Elby, 2003; Rosenberg et al., 2006). Re-

cent studies (D. B. Clark, 2003) comparing such “unified” and “in-

pieces” approaches have shown that, indeed, students maintain multiple,

sometimes contradictory, ideas in their repertoires, and that context

plays a significant role in cueing these ideas. But how exactly does con-

text “cue” students into certain explanation paths?

My work seems to provide further evidence for the coexistence of con-

tradictory knowledge and manifold epistemological resources. Indeed,

students transitioned from authority-delivered knowledge to self-

generated theories, but some never completely abandoned their old

theories.

However, the “cueing” issue remains: in Benedict’s case, one could ar-

gue that the context was not very different: he was sitting on the same

exact chair trying to solve the same problem. So, what could have

prompted the use of one representation over another? What changed?

Why did he employ an agent-based explanation the second time

around? Why was a simple verbal cue enough for such radical a change?

I argue that the manipulable elements exposed by students’ drawings

seemed to not only be an auxiliary externalization, but mainly to shape

the further development of student’s initial idea. My verbal prompt

merely made him start conceptualizing the problem in an agent-based

fashion, and it was not before Benedict drew “moveable” circles that he

achieved at explaining the entire phenomena correctly—in other words,

his manipulable elements were not simply drawings, but “agents” on pa-

per, which he managed to “run” even without a computer. When his

drawing was just a rectangle with arrows (in the first explanation, equa-

tion-based), he could not go very far, since the representation was not

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“runnable”—at most, he could get back exactly the information that was

put into it. Not by coincidence, during the think-aloud explanations,

there was a strong alignment between the students’ representations, the

underlying structuration (agent-based or differential/equational), and

its effectiveness.

Another important construct in my analysis were similarity triggers,

which connect, or bridge two phenomena. For example, in both grain

growth and recrystallization there is “growth” of a geometrical shape. Al-

so, in both phenomena, there are “small shapes amongst much larger

shapes.” Before the model building, the most common outcome was for

students to use weak (and incorrect) similarity triggers to transition

from one phenomenon to another, normally based on non-mechanistic

aspects. Therefore, they could start the explanation of grain growth cor-

rectly (“some are going to grow”), but “growth” would connect them to

another phenomenon in which “growth” would also occur (in this case,

recrystallization), and they would complete the explanation mentioning

facts from this other phenomenon.

Figure IX-4 A student incorrectly “jumps”

from grain growth to recrystali-zation, sewing growth as a

similarity trigger.

After the model-building activities, the contrast was stark: students

would recognize those triggers at the level of behaviors, and not surface

Gra

in g

row

th "Some are definitely going to grow..."

Sim

ilari

ty t

rigg

er

Growth

Re

crys

taliz

atio

n "...like obviously the points that nucleate are going to grow first."

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characteristics, for example, these common behaviors could neighbor-

hood-based count, random walk, or energy minimization.

Below I summarize the studies, activities and questions in Table IX-2,

and, in Table IX-3 I list the methodological contributions of this disser-

tation.

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Table IX-2 Studies, activities, data, and

goals

Chapter Activity/data Question

Study 1 (1st part) Transcription of classes, textbooks, homework assign-ments, handouts.

What are the represen-tational practices in a materials science class-room?

Study 1 (2nd part) Content-driven inter-views with students.

How do students con-ceptualize the discipli-nary content? How do the representa-tional practices and current teaching styles influence students’ un-derstanding of it?

Study 2 (1st part) Students interacting with pre-built agent-based models.

What are the conse-quences of the exposure of micro-behaviors?

Study 2 (2nd part) Students building agent-based models.

What are the conse-quences of actively creating micro-behaviors and models?

Study 3 (1st part) Viability analysis and feedback from students, motivation plots.

Is ABM a viable as-signment in an Engi-neering classroom? How did student react?

Study 3 (2nd part) Grading the models. How were students using the affordances of the NetLogo language? Do better programmers perform better?

Study 3 (3rd part) Logfile analysis. Are there individual differences in coding styles? What are the prototypical moments in a programming project?

Study 3 (4th part) Case studies. How do previous knowledge, intuitions, and agent-based repre-sentation coexist?

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Table IX-3 Methodological contributions,

in bold, the original instruments developed for the dissertation.

Chapter Methodological con-tribution

Key terms or deliverables

Literature review

A rubric for categorizing model-based curricula.

A 12-dimension rubric

Rep. Comp.

A direct, side-by-side comparison of the same phenomenon represented in different encoding schemes.

Study 1 (1st part)

A methodology for eva-luating representations practices in classrooms.

A rubric to code quizzes and assignments.

“Equation counting” method (counting equations during classes)

Representational trajectories (e.g. how discrete phenomena get represented using conti-nuous mathematics).

Study 1 (2nd part)

A content-driven metho-dology for analyzing stu-dents’ utterances about scientific phenomena.

Identifying how similar the explanations of one phenome-non are across several students.

Study 2 (1st part)

Analysis of students’ ut-terances when observing a running model creating on-the-fly theories.

Study 2 (2nd part)

A procedure to analyze students’ models, and to evaluate their use of ABM affordances

Qualitative rubric with 4 affordances (one-to-many generativity, formalization of intuitive understanding, foregrounding of physical, model blending)

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Study 3 (1st part)

Analysis of viability, moti-vation, and feedback

Surveys about time-on-task Motivation plots Feedback surveys

Study 3 (2nd part)

Model complexity analysis Quantitative rubric with 90 items in 4 groups (setup, rules, interface, visualization).

Study 3 (3rd part)

Analysis of automatically-generated logfiles

Log filtering procedures. Code evolution analysis

tools (code size, compila-tion frequency, error fre-quency).

Study 3 (4th part)

Analysis tools for “think- aloud model-building.”

New constructs and analysis categories: similarity trig-gers, exposed representa-tional elements, and asymmetric reversibility.

“Trancliptions” redux. Long-term modeling tra-

jectories

IX.3. CONCLUSION The ubiquity and increasing need for computational science is posing a

serious challenge to extant knowledge encoding schemes in materials

science in particular, and in STEM education in general. Researchers

have already detected this trend – computer modeling in materials

science has more than doubled in the last 10 years (Thornton & Asta,

2005). However, students are still obliged to master hundreds of equa-

tions and isolated facts to get a firm grasp of the domain. Even if stu-

dents somehow were to connect those equations into a coherent corpus,

the mathematical machinery required to accomplish that would be high-

ly sophisticated. In addition, the many-to-one approach inherent to eq-

uational forms increasingly overloads the curriculum in a time when

curricula urgently need to be cleaned up.

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Based on Wilensky and Papert’s restructuration theory (Wilensky & Pa-

pert, 2006; Wilensky, Papert et al., 2005), I hypothesized that several

content topics in materials science could be re-encoded into agent-

based rules, and this new structuration would have better learnability

properties.

Throughout the three studies of this dissertation, I have (1) characte-

rized these two structurations, (2) investigated their origins, and dem-

onstrated their theoretical learnability differences, (3) empirically vali-

dated these differences, (4) shown that the activities necessary to en-

gage students in these new epistemic forms are viable in real classrooms,

and (5) empirically detected the coexistence and competition of these

multiple structurations in students’ cognition.

Based on these studies, I built the case that the con-

tent/representation/pedagogy fit is not arbitrary or general but, rather,

reflects the nature of the content. Specifically, the nature of materials

science—essentially a study of the behaviors of atoms and molecules

themselves—is intrinsically conducive to an agent-based approach. By

its turn, the epistemological infrastructure of agent-based modeling

strikes a chord with the constructionist principle of syntonicity. When

programming the behavior of a single atom within a material, students

oftentimes have to imagine themselves as an atom to fathom how they

would react to increased thermal vibration. Also, agent-based modeling

presupposes a deep knowledge of the system’s micro-rules, which can

only be properly learned through the construction of those rules – and

student-centered construction of artifacts is another of the pillars of

constructionism. Despite the learning gains of interaction with models,

the four powerful affordances of agent-based modeling (one-to-many,

model blending, etc.) were only fully employed when students had de-

veloped enough fluency as to have complete control over the behaviors

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generated by the agent rules. Such fluency cannot be achieved unless

students were to generate those same rules. If the “organic fit” hypothe-

sis is true, there could be a particularly important impact on teaching

and learning: by restructuring the content, educational designers would

be automatically influencing the pedagogies, i.e., you cannot possibly

teach agent-based modeling without its organically-fit pedagogy: con-

structionism.

Figure IX-5 The con-

tent/representation/pedagogy triangle

Work on several scientific domains present strong evidence that changes

in encoding have significant impact on learnability. Papert, Abelson,

diSessa and collaborators made differential geometry accessible to

young children by restructuring it with the Logo turtle (Abelson & diSes-

sa, 1981; Papert, 1980). diSessa’s restructurated Physics with the dyna-

turtle (diSessa, 1982) and Boxer (diSessa, 2000; diSessa et al., 1991).

Wilensky (1996, 1999a, 2003) restructurated biology, chemistry and

Contentmaterials science

Pedagogyconstructionism

RepresentationABM

361

social science with agent-based modeling, and brought previously in-

tractable disciplines to the reach of children. Anderson, Srolovitz and

collaborators, by restructuring materials science, were able to publish

five major papers in the top-ranked journal of their field in just 18

months (M. P. Anderson et al., 1984a; Srolovitz, 2007).

This dissertation is a contribution to making these miracles happen

every day, in every country, in every classroom, in every mind.

362

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