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Paper ID #13115
How Misconceptions Might be Repaired through Inquiry Based Activities
Ms. Gina Cristina Adam, University of California, Santa Barbara
Gina C. Adam is pursuing her Ph.D. in Electrical Engineering and a M.A. in Teaching and Learning atUniversity of California, Santa Barbara. Her main research interest is conceptual understanding in engi-neering education. Additionally, she helped as a graduate student researcher in two large scale engineeringeducation projects, one related to developing a taxonomy for the field supervised by Dr. Cynthia Finelliat University of Michigan and one on pioneers in engineering education supervised by Dr.Cynthia Atmanat University of Washington, Seattle.
Dr. Brian P. Self, California Polytechnic State University
Brian Self obtained his B.S. and M.S. degrees in Engineering Mechanics from Virginia Tech, and hisPh.D. in Bioengineering from the University of Utah. He worked in the Air Force Research Laboratoriesbefore teaching at the U.S. Air Force Academy for seven years. Brian has taught in the MechanicalEngineering Department at Cal Poly, San Luis Obispo since 2006. During the 2011-2012 academic yearhe participated in a professor exchange, teaching at the Munich University of Applied Sciences. Hisengineering education interests include collaborating on the Dynamics Concept Inventory, developingmodel-eliciting activities in mechanical engineering courses, inquiry-based learning in mechanics, anddesign projects to help promote adapted physical activities. Other professional interests include aviationphysiology and biomechanics.
Dr. James M Widmann, California Polytechnic State University
Jim Widmann is a professor of mechanical engineering at California Polytechnic State University, SanLuis Obispo. He received his Ph.D. in 1994 from Stanford University and has served as a FulbrightScholar at Kathmandu University it Nepal. At Cal Poly, he coordinates the departments industry spon-sored senior project class and teaches mechanics and design courses. He also conducts research in theareas of creative design, machine design, fluid power control, and engineering education.
Alexa Coburn, California Polytechnic State University, San Luis Obispo
Alexa is a third year Mechanical Engineering student from Huntington Beach, California. She attendsCal Poly, San Luis Obispo and plans on graduating in June 2016. Alexa recently had a Space Operationsinternship at Raytheon Space and Airborne Systems and plans to go back for a second internship thissummer. While attending school, Alexa is a part of an educational research team where she developshands-on learning activities that facilitate student understanding of dynamics concepts. Alexa is passion-ate about working with children and young adults, specifically young women to broaden their technicalunderstanding and encourage them to pursue education and careers in STEM fields.
Mr. Baheej Nabeel Saoud, California Polytechnic State University, San Luis Obispo
Baheej Saoud is an Aeronautical Engineering senior at Cal Poly San Luis Obispo and is set to graduate inJune 2015. He will be continuing on to graduate school in Manufacturing Engineering. Baheej has beencontributing to the Cal Poly Dynamics Research team since 2013.
c©American Society for Engineering Education, 2015
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How Misconceptions Might be Repaired
through Inquiry Based Activities
Gina C. Adam, Brian P. Self, James M. Widmann, Alexa Cobrun, Baheej N. Saoud
Introduction
Undergraduate dynamics is often cited as one of the most difficult courses that engineering
students must take because many of the topics are in direct conflict with their perception of the
world around them. Newton‟s laws of motion are fundamental to the study of dynamics and
students are particularly prone to having misconceptions drawn from their daily life interaction
with moving objects. An apple may fall from a tree to the ground faster than a leaf (although
they have the same acceleration in the absence of air resistance); two football players may
collide and the smaller player may get hurt more than the larger player (although an equal force
is exerted on both players)1.
These misconceptions can survive even after extensive direct instruction. Concept inventories are
specifically designed tests that target common misconceptions, so they serve as useful tools to
assess student learning and effectiveness of teaching practices. Performance on the Dynamics
Concept Inventory (DCI) at the end of a large size dynamics class taught by traditional methods
shows a student average of only 32.1%2. Such a low score shows that simply learning the correct
equations needed to solve a problem does not mean a student has mastered the conceptual
content of a topic 3, 4
.
Considerable effort has been spent trying to find instructional approaches that can repair these
deeply rooted misconceptions. In a study involving 6,000 students taking introductory physics,
Hake5 showed that instruction involving active learning and stressing conceptual understanding
resulted in an average conceptual gain equal to 0.48, almost double the average gain in
traditional lecture-based courses. There is a growing body of literature supporting active learning
in engineering education (see Prince6 for a review). A pilot study
7 found that active-learning
based courses resulted in an 8.5% larger normalized gain on the DCI than traditional instruction.
All the evidence confirming increased conceptual gains in classes utilizing active learning
methods have created excitement among educational researchers and teachers, but more
questions need to be answered regarding their practical implementation in classrooms. A long
on-going academic debate exists on how much the students should be involved and how much
instructional guidance is most effective. Matlen and Klahr8 explore the efficacy of low vs. mixed
instructional guidance in the context of teaching 3rd
grade children about the Control of Variables
Strategy for scientific experimentation. Four experimental conditions were used, namely high
followed by high instruction (H-H), high followed by low (H-L), low followed by high (L-H)
and low followed by low instruction (L-L). High instructional guidance included a mix of
inquiry questions and direct instruction (explanations and summary provided by the
experimenter), while low instructional guidance included only inquiry questions. Their results
showed that, in domains where learners have difficulty assessing the correctness of their
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solutions, inquiry activities are not sufficient to clarify concepts; therefore direct instruction is
needed for learning.
One type of active learning technique designed to increase conceptual understanding in
engineering is Inquiry-Based Learning Activities (IBLAs) 9-11
. IBLAs are based on a series of
Predict-Observe-Explain cycles that can incorporate direct instruction or teamwork as needed. In
an IBLA, individual students or teams of students are presented with a physical situation and
asked to predict what will happen. The students then investigate the situation by experimenting
with physical hardware that becomes the “authority”, thus forcing students to confront any
misconceptions (Figure 1).
Figure 1.The building blocks of an Inquiry Based Learning Activity (IBLA) are Predict-Observe-
Explain (P.O.E) series based on given scenarios. These P.O.E. series can be interspersed with
direct instruction and teamwork as desired by the instructor.
In previous studies, we have reported student performance on concept tests and their predictions
during the IBLAs 9-11
. This research, however, did not reveal how students approached solving
the problems, or what conceptual knowledge they used to attack the different scenarios. We
decided to use the qualitative technique of “think-aloud” to investigate how students‟ knowledge
is affected by the IBLA. For this study, students participated individually in either a purely
P.O.E-based IBLA or a P.O.E and direct instruction IBLA. We investigated how students‟
knowledge evolved during the IBLA and how P.O.E and direct instruction help students gain
conceptual understanding.
The goal of this study is to understand the process of repairing naïve misconceptions and of
acquiring desired scientifically approved models within the framework of an IBLA. The results
of this study help us understand how to design better IBLAs, particularly how to choose the
given scenarios for the P.O.E cycles and when to incorporate direct instruction.
Theoretical framework
The purpose of instruction is to help students acquire domain-specific knowledge and skills.
According to Shavelson, knowledge can be categorized as “knowing that” (declarative/factual
and conceptual knowledge), “knowing how” (procedural knowledge), schematic knowledge
(“knowing why”) and strategic knowledge (“knowing when, where and how”) 12
. Each type of
knowledge can be described in terms of its extent and its structure.
Students do not enter instruction with an empty mind. The naïve misconceptions (pre-instruction
“mental models”) that students bring to the classroom are typically based on everyday
experience and interfere with student‟s learning of the scientifically approved models.
Conceptual change refers to the shift in student‟s schematic knowledge from naïve models to
PredictionExperimental observation
Explanation and
re-evaluation
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desired scientifically approved models13, 14.
The knowledge shift due to instruction might not be
as dramatic and straight-forward as desired. Vosniadou & Brewer (1992)15
point out that students
can use both scientifically-sound propositions and their less-scientific prior propositions in the
same explanation of a phenomena. Helldén and Solomon (2004)16
found in their longitudinal
study that students tended to evoke the same, less-scientific explanations over time, despite being
exposed to contrary teaching. However, the students did use more scientifically-sound models
when prompted appropriately by the interviewer. Such accumulation of propositions might be
considered conceptual development rather than conceptual change13
. While conceptual change
focuses on developing a more scientifically approved schematic knowledge, the more gradual
conceptual development seen in practice can be considered more related to changes in the
declarative and procedural knowledge.
Studies have shown that experts have an extensive and highly interconnected declarative
knowledge organized according to broad scientific principles17
. Some questions require further
investigation. How are experts able to organize their declarative knowledge according to broad
scientifically accepted schematic knowledge? And how should the instruction be designed in
order to facilitate this process of knowledge organization in students‟ minds?
This study attempts to provide some insight into these questions by investigating how the extent
and the structure of the declarative knowledge changes as the students are exposed to an IBLA.
Literature review
A problem that is often used to demonstrate the application of Newton‟s 2nd
law to the motion of
a compound system is the Atwood machine. The system consists of two objects connected by a
string that passes over a pulley (Figure 2).
The Atwood machine can be a versatile problem to test students‟ conceptual understanding of
Newton‟s 2nd
law. Question 13 of the DCI is used to test for understanding of the relationship
between force, inertia and acceleration by comparing two versions of the Atwood machine. After
taking a course in dynamics, 44% - 64% of the students at different institutions responded
incorrectly to this question on a DCI post-test2. The primary incorrect proposition is that the
tension in a rope is always equal the weight suspended from it. McDermott, Shaffer and
Somers18
research on the Atwood machine also showed that many students had serious
difficulties with the acceleration, the internal and external forces, and the role of the string in the
Atwood machine. The students often failed to determine which force, which mass and which
acceleration should be associated with which system.
The conceptual knowledge (part of the declarative knowledge in Shavelson‟s framework)
necessary to understand Newton‟s 2nd
law relies on the concepts of acceleration, mass and force
(Figure 3). Also important is an understanding that the net force is the sum of all the different
forces (gravitational, tension, applied force, etc) acting on the object. There are links that
integrate all these concepts in a coherent framework. Newton‟s 2nd
law can be applied to an
individual object and extended to a system of interconnected objects (Figure 2, table).
A form of the procedural method explained in Figure 2 is traditionally presented to students as a
way of analyzing the Atwood machine and shows the connection to our conceptual propositions
used for coding. The procedural knowledge for completing this analysis often obscures the
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underlying concepts. The goal of the IBLA is to promote conceptual understanding rather than a
systematic mathematical solution to different problems. During our study, the students were
encouraged to discuss the problems conceptually and do as little math as possible.
Proposition
For one
object
(mass 2)
For the whole
system
D1. Mass is inversely proportional to acceleration
a ~ 1/m2 a ~1/ Mtotal
Mtotal = m1 + m2
D2. Net force is directly
proportional to acceleration
a ~ F2 a ~Fnet
D3. Net force is the sum of all forces acting on the object
F2 = T - G2
G2 = m2*g
Fnet= G1-G2
G1 = m1*g
G2 = m2*g
D4. Force and mass have a combined effect on acceleration
a = F2/m2 a = Fnet/Mtotal
Figure 2. Traditional Free Body Diagram (FBD) and mathematical explanation of Newton‟s 2nd
law in the Atwood machine
Figure 3. Concept map exemplifying the conceptual (declarative knowledge) involved in the
scientifically accepted framework of Newton‟s2nd
law.
Gravity
Tension
Applied force
gravitational field strength
(g)
Force
Mass
∑
Desired proposition D1(mass is inversely proportional to the acceleration)
Desired proposition D2(force is directly proportional to the acceleration)
Desired proposition D4(force and mass have a combined effect on acceleration)
Desired proposition D3(Net force is the sum of all forces acting on the object)
Acceleration
a
m2*ga
a2F2
m1*g
T
a1 F1
T
m2*g
m1*g
Page 26.858.5
Methods
Research goals
We investigated student‟s existing declarative knowledge of Newton‟s 2nd
law and how it
evolves as the student is exposed to different scenarios. Our study also tries to understand if the
inquiry-based modules can promote conceptual development and conceptual change. In this
exploratory study we used qualitative semi-structured interviewing with “think aloud” in order to
get a rich description of the student‟s understanding of pulley systems, and how this
understanding progressed during the inquiry-based learning activity.
The research goals of the study are to:
1) reveal the students „declarative knowledge of Newton‟s second law after they have been
exposed to traditional instruction during a course in dynamics.
2) determine how the declarative knowledge evolves as the student is exposed to different
scenarios in the IBLA.
3) examine the role of predict-observe-explain activities and the role of short direct
instruction in promoting conceptual development and conceptual change
Participants
The participants were either second or third year engineering students enrolled in an introductory
dynamics course. Students were in a variety of majors, predominantly mechanical engineering,
aerospace engineering, and civil engineering, and there were eight males and one female in the
study. At the time of the interview, the students have already been exposed to Newton‟s 2nd
law
in class. Participation was voluntary and unpaid, and informed consent was obtained before
conducting the think-aloud.
The Mass-Pulley IBLA
The students were assigned to individually participate in an IBLA that examined the relationship
between force, mass and acceleration in a classic Atwood machine. The IBLA used for this study
has been designed according to the principles of the variation theory30
. The theory can be applied
in lesson plans that take into consideration students‟ existing knowledge and guide the students
gradually to discern critical features of the object of learning. Several studies have demonstrated
the use of patterns of variation to improve student learning outcomes32, 33
.
The Mass-Pulley IBLA using the Atwood machine contains a sequence of four scenarios,
varying the total mass of the system, the mass difference between the weights and the structure
of the system (Figure 4 and Table 1). By using these different variations, we were able to gain a
better idea of student understanding of each desired proposition. For the first three scenarios in
the IBLA, the student was asked to (a) predict the correct answer and explain his/her reasoning,
(b) perform the hands-on experiment depicted in the Scenario, and (c) explain how the results of
the experiments compared with their original prediction. In order to emphasize conceptual
understanding, students were instructed to “think aloud” during the activities in order to make
their learning explicit and use as little mathematical tools as possible. Page 26.858.6
Figure 4. The four scenarios utilized for the IBLA (see Appendix A for the interview protocol)
Table 1. Pattern of variation used in designing the scenarios. The similarities and differences
refer to the system A and B in each Scenario
Similarities Difference Critical feature to be discerned
Scenario 1 Scenario 2
- Same type of system (2masses)
- Same mass difference between heavier and lighter block
Different total masses
Total mass of the system is inversely
proportional to acceleration when mass difference is the same
Scenario 3 - Same type of system (2masses) - Same total mass
Different mass
difference
Mass difference of the system is proportional to acceleration when total
mass is the same
Scenario 4 Same mass difference between heavier and lighter block
- Different type of system - Different
total masses
The relationship between mass difference, total mass and acceleration can be applied in the same way in different types of pulley systems.
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Data collection
The interviewing was done one-on-one, each student participating individually in a sequence of
instruction centered on the same IBLA. Three instructional sequences were investigated: (a)
IBLA only with predict-observe-explain (P.O.E) cycles, (b) IBLA with direct instruction after
Scenario 2 and (c) IBLA with direct instruction after Scenario 3 (Table 2, Figure 5). Three
students (A, B, C) were assigned per each instructional sequence (NoINT, INT2, INT3). Each of
the nine students was assigned a code for the sequence and the order in which they participated
(A, B, C). For example, INT2_B refers to student B (second one in the INT2 group) who had an
intervention after Scenario 2.
Table 2. Sequences of instruction. * P.O.E. stands for Predict-Observe-Explain
Sequence 1 Scenario 1
P.O.E
Scenario 2
P.O.E
Scenario 3
P.O.E
Scenario 4
P.
Sequence 2 Scenario 1
P.O.E
Scenario 2
P.O.E Direct instruction
Scenario 3
P.O.E
Scenario 4
P.
Sequence 3 Scenario 1
P.O.E
Scenario 2
P.O.E
Scenario 3
P.O.E Direct instruction
Scenario 4
P.
The interviewer who conducted all the nine interviews was a female research assistant. At the
beginning of the interview, the interviewer instructed the student to verbalize his/her thoughts as
he/she analyzed the different IBLA scenarios involving Atwood machines. The interviewer
provided the prompts during the IBLA, reminded the participant to continue verbalizing his/her
thought processes and conducted the direct instruction as required by the research design. The
direct instruction consisted of a succinct explanation of Newton‟s 2nd
law, ∑F = m*a. The
explanation included drawing on the whiteboard to help the student visualize the forces involved.
During the explanation, the interviewer checked for student understanding by asking questions
such as “What is the net force for each system?”, “What is the total mass of each system?”, “How
does the relationship between net force and total mass affect the acceleration?”.
Figure 5.Example of student involvement in the one-on-one IBLA
a) Student (left) experimenting with real pulley
systems (held by the interviewer – right)
during the one-on-one IBLA
b) The direct instruction part
of the one-on-one IBLA (student on the left,
interviewer on the right)
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Data coding
Video recordings of students‟ engagement were collected and the discourse was coded twice.
Four desired codes linked to the object of learning were predetermined before coding (see details
below). The first coding was exploratory and was used to extract trends and define other specific
codes of interest. The second used this coding scheme for the cognitive mapping12, 19
of the
interviews. These principles have been shown to provide a way to assess the structure of
declarative knowledge. A concept map is a graph in which the nodes represent concepts, the
lines represent relations, and the labels on the lines represent the nature of the relation between
concepts. The organization of the declarative knowledge can also give indications of the
schematic knowledge used by the students in their explanation.
In this study we use the following terms:
proposition (or concept link) = a pair of concepts and the labeled line connecting them;
mental model (or conception) = a set of interconnected propositions.
We extracted the concepts and propositions used by students indirectly from the IBLA
explanations. We limited our analysis to propositions because they already provide information
that includes the concepts and the link/relationship between them.
The selection of desired propositions was done keeping in mind the scientifically accepted
framework of Newton‟s 2nd
law. Four desired propositions linked to the object of learning were
predetermined before coding (see Figure 3).
D1. Total mass is inversely proportional to acceleration
D2. Net force is directly proportional to acceleration
D3. Net force is calculated from difference in existing forces (gravitational, external, etc)
D4. The acceleration is equal to the net force divided by total mass (F=m*a)
During the first round of coding, it became apparent that students sometimes utilize in their
explanations propositions that are naïve and based on daily life experiences, but true in limited
scenarios. We identified two such propositions that students used consistently and grouped them
under the label “weak propositions”. The students utilized either one or the other weak
proposition, but never both:
1. W1 - Single mass is proportional to the acceleration. Some students use the lighter block
in the system as the single mass (“counterweight”), while other students use the heavy
block (in their mind, the block responsible for the movement). The values selected for the
IBLA allow the students utilizing this weak proposition to make a correct prediction for
the scenarios 1, 2 and 3, but a wrong prediction for Scenario 4 (Table 1).
2. W2 - The ratio of the masses of the system (heavy mass/light mass) is directly
proportional to the acceleration. For the limited Scenario of a system of one pulley and
two masses, the ratio of masses in a pulley system does positively correlate with the
acceleration (see explanation and supporting equations in Widmann et al.20
). Because our
IBLA showed such systems in scenarios 1, 2 and 3, the students utilizing this method
Page 26.858.9
were likely to make a correct prediction. The ratio method cannot be used in Scenario 4,
since system A has only one mass pulled by an external force (Table 1).
Another type of proposition identified during coding was the incorrect proposition (naïve
propositions that were in contradiction with the scientific theory). All incorrect propositions
used were related to the inability to calculate the net force correctly. The difficulty was in
isolating the forces that contribute to the net force and then summing them vectorially. Some
students believed that different types of forces (gravitational, external, etc) of same magnitude
have different effects on the system.
We coded each student‟s IBLA as a coding map (Figure 6). The coding map provides an easy
visual way to investigate the evolution of student‟s declarative knowledge during a certain
sequence of instruction. The coding map graphically represents the matrix of propositions and
their respective confidence level for the entire sequence of instruction. The columns represent the
steps in the sequence of instruction, while the rows represent the propositions that students use to
solve that step. The specific codes were classified and color coded as desired propositions (blue),
weak propositions (purple) and incorrect propositions (orange) – see Figure 6.The area of the
bubble reflects the student‟s confidence in that particular code for that particular Scenario. This
confidence is based on the student self-declared confidence in their prediction and choice of
words during explanations. For example, words such as “I don’t know”, “I am trying to
remember from class”, “I have no idea why …” were used as an indication of low confidence.
Findings
In the Findings section, the coded data is grouped and analyzed using tables (see Tables 3-8).
This method was used as a means to analyze the data across students and to uncover potential
hidden patterns in students‟ handling of conceptual knowledge. The results are not meant to be
generalizable, but can be used as starting hypotheses for future larger scale research studies that
investigate conceptual understanding.
Research question 1 – What is the student’s declarative knowledge of Newton’s second law at
the beginning of the IBLA?
Table 3, column 1 shows that some students utilized only desired propositions, while some
utilized weak propositions, alone or together with desired propositions. The use of desired
propositions together with desired propositions is an indication that the students have
experienced conceptual development and no conceptual change.
Less than half of the students used only desired propositions. The majority, five out of nine
students, use done of the two weak propositions either together with desired propositions or by
itself. Three used the single mass weak proposition (W1) to explain their prediction for
Scenario 1.Two students used it in conjunction with desired propositions and one student used
just the single mass weak proposition. Two students used the ratio weak proposition (W2) to
explain heir prediction for Scenario 1. One student used just the ratio weak proposition. The
other student incorporated it together with desired propositions and an incorrect proposition.
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Figure 6.Coding map showing the evolution of a student‟s declarative knowledge during the sequence of instruction. The coding map is
a matrix of propositions. The rows are propositions utilized for a Scenario and the columns are the steps in the sequence of instruction.
Exemplified here is a coding map for student INT2_B participating in sequence 2 (direct instruction after Scenario 2). For Scenario 1
and Scenario 2, both Predict and Explain step, the student utilizes only one proposition to solve the problem, namely the ratio weak
proposition (numbered W2). His predictions are correct. After the direct instruction, in the Scenario 3 - Predict step, the student
utilizes the D2 net force proposition but also has an incorrect proposition (I1). After observing through experiment that his prediction
was wrong, the student uses D2 and D3 propositions with low confidence and reverts back to the W2 proposition in the
Scenario 3 - Explain step. In the last step (in the Scenario 3 – Explain), the student uses D3 and I3 propositions.
See the Appendix B for all the coding maps.
Sequence of instruction
Desired propositions
Incorrect
propositions
Weak proposition
Correct predictions Wrong predictions
Page 26.858.11
Table 3.Comparison between the number of students using different types of propositions at the
beginning of the IBLA (Scenario1 – Predict), the whole IBLA (all scenarios) and the end of the
IBLA (Scenario 4 – Predict).
Number of students
Explanation utilizing… Scenario 1.
Predict
Throughout
IBLA
(all scenarios)
Scenario 4.
Predict
1. Only desired propositions 4 2 7
2. Only weak propositions 2 0 0
W1 – Single mass 1 0 0
W2 - Ratio 1 0 0
3. Desired and weak propositions 2 5 1
W1 – Single mass 2 2 1
W2 - Ratio 0 3 0
4. Desired and weak and incorrect propositions 1 2 0
W1 – Single mass 0 1 0
W2 - Ratio 1 1 0
5. Desired and incorrect propositions 0 0 1
Research question 2 – How is the student’s declarative and schematic knowledge evolving as
the student is exposed to different scenarios in the IBLA?
As the IBLA progresses, the students‟ use of weak conceptions became more apparent. Two
students who used desired propositions in the prediction for Scenario 1 starting utilizing weak
propositions later in the IBLA (Table 3, row 1). Seven students utilized weak conceptions
throughout the IBLA, five in combination with desired conceptions and two in combination with
desired conceptions and with misconceptions. Students also seem to acquire incorrect
propositions along the way, probably due to misunderstandings of the data presented in the
intervention and as a way to explain their cognitive conflict. However, these incorrect
propositions were not persistent and didn‟t dominate the student‟s discourse.
Nevertheless, at the end of the IBLA, the students seem to have repaired their weak propositions
and started to utilize only desired propositions (Table 3, column 3). Seven students utilized only
desired propositions and one student utilized desired propositions and an incorrect proposition
(that gravitational forces determine a constant acceleration, while constant applied forces
determine an increasing acceleration). Only one student utilized the single mass proposition and
no students used the ratio proposition.
An analysis by scenarios shines some light on how student‟s declarative knowledge evolves over
the course of the IBLA. The high number of students exhibiting weak propositions during the
IBLA shows that these two weak propositions are widespread among students. It is important to
Page 26.858.12
notice that students either use the single mass proposition or the ratio proposition for the entire
IBLA, but never both simultaneously.
The two weak propositions were used by the students consistently as the IBLA progressed,
which seems to indicate that the students had naïve mental models based on these ideas (Tables
A and B). These propositions proved to be hard to change, especially because they were useful to
the students in certain limited scenarios. Table 4 shows that using these naïve mental models can
lead to correct intuitions in certain scenarios.
Table 4. Predictions (green = correct, red = wrong) using desired mental model (Newton‟s 2nd
law), ratio mental model and single mass mental model.
Scenario 1 Scenario 2 Scenario 3 Scenario 4
Scientific model
Correct Correct Correct Correct
Single mass model
Correct Correct Correct Wrong
Ratio model
Correct Correct Correct Not possible
The weak proposition regarding single mass appears to be repaired by the intervention in either
Scenario 2 or 3. Students INT2_Aand INT3_B had the weak proposition that the acceleration is
inversely proportional to the lighter mass and used it to explain Scenario 1 and Scenario 2.
INT2_A receives the standard intervention after Scenario 2 and understands that the total mass of
the system plays a role, not just the lighter mass. The student does not use the weak proposition
afterwards. INT3_B receives the standard intervention after Scenario 3. However, at the
beginning of Scenario 3 the interviewer asks the student to explain in more detail the role of the
mass. This question acts as a trigger for the student, who realizes that the total mass of the
system is inversely proportional to acceleration, not the lighter mass independently. The
intervention after Scenario 3 serves to strengthen this realization.
“Student: I feel like there is such a big discrepancy between these two masses that this
one will accelerate faster. At the same time F=ma, so mass here is bigger, therefore
acceleration will be smaller.
Interviewer: So mass of that block is bigger or mass of that system?
Student: Mass of the [pause] You’re right, mass of the [pause] Interesting [pause]. I
didn’t think about that.
Interviewer: I was just asking which mass you were talking about.
Student: I was talking about the 10oz one. But I didn’t even consider the fact that the
masses of the systems are the same.” (INT3_B, prediction for Scenario 3)
A closer examination across all students (Tables 5) shows that students who used the single mass
weak proposition (Table 5.1.) seem to not have the total mass proposition (Table 5.2). However,
they utilized the net force proposition (Table 5.3). The student with no instruction (NoINT_A)
did not repair the weak proposition and did not acquire the total mass propositions D1. Helped
by instruction, the other two students seem to replace the single mass weak proposition with the
total mass proposition (Table 5.1 and Table 5.2.).
Page 26.858.13
Tables 5.Students using W1 - Single mass proposition
* Low, Medium, High - student‟s confidence in the proposition at the time of explanation
** | marks the time of the direct instruction (after Scenario 2 or after Scenario 3) *** NoINTA – student A with no intervention; INT2_A – student A with intervention after Scenario 2
Student
5.1 - W1- Single mass proposition
Scenario 1. Scenario 2. Scenario 3. Scenario 4.
Predict Explain Predict Explain Predict Explain Predict
1 NoINT_A Low Medium High High High High High
3 INT2_A Low Medium Medium Medium
4 INT3_B Low Medium Medium Medium Low
Student
5.2 - D1 - Total mass influences acceleration
Scenario 1. Scenario 2. Scenario 3. Scenario 4.
Predict Explain Predict Explain Predict Explain Predict
1 NoINT_A
3 INT2_A High
4 INT3_B Medium High
Student
5.3 - D2- Net force influences acceleration
Scenario 1. Scenario 2. Scenario 3. Scenario 4.
Predict Explain Predict Explain Predict Explain Predict
1 NoINT_A High High High High High High High
3 INT2_A High High High High High High High
4 INT3_B Medium Medium High
Student
5.4 - D3 - Calculating Net force
Scenario 1. Scenario 2. Scenario 3. Scenario 4.
Predict Explain Predict Explain Predict Explain Predict
1 NoINT_A High High High High High High High
3 INT2_A High High High High
High High
4 INT3_B Low Medium Low Medium High
The student without intervention uses it in scenarios
3 and 4, while the students with intervention don’t.
Three students use the W1 proposition
to explain scenarios 1 or 2.
The students with intervention acquire D1 while
the student without intervention does not.
The students do not use D1, but….
…they seem to use D2 and D3
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Tables 6.Students using W2 - Ratio proposition
* Low, Medium, High - student‟s confidence in the proposition at the time of explanation
** | marks the time of the direct instruction (after Scenario 2 or after Scenario 3) *** NoINT_B – student B with no intervention; INT2_B – student B with intervention after Scenario 2
Student
W2 - Ratio proposition
Scenario 1. Scenario 2. Scenario 3. Scenario 4. Predict Explain Predict Explain Predict Explain Predict
1 NoINT_B Medium Medium
2 NoINT_C Low Medium High
3 INT2_B High High High High Low
4 INT3_A Low
Student
D1 – Total mass influences acceleration
Scenario 1. Scenario 2. Scenario 3. Scenario 4. Predict Explain Predict Explain Predict Explain Predict
1 NoINT_B Medium High High High High High
2 NoINT_C High High High High High High
3 INT2_B
4 INT3_A Low High High High High High
Student
D2 – Net force influences acceleration
Scenario 1. Scenario 2. Scenario 3. Scenario 4. Predict Explain Predict Explain Predict Explain Predict
1 NoINT_B High High
2 NoINT_C Low Medium
3 INT2_B High Low
4 INT3_A Medium High
Student
D3 – Calculating Net force
Scenario 1. Scenario 2. Scenario 3. Scenario 4. Predict Explain Predict Explain Predict Explain Predict
1 NoINT_B Low Low Low High High
2 NoINT_C Low Low Low Low Low
3 INT2_B Low High
4 INT3_A Medium
Four students use the ratio conception to explain
cases 1, 2, or 3.
No student utilizes the ratio
proposition to explain case 4.
Three students seem to master D1 total mass
conception, but not utilize the D2 net force.
conceptoon
In scenarios 3 and 4, students
start to acquire D2
Page 26.858.15
The ratio proposition is harder to repair, but Scenario 4 creates cognitive conflict. For example,
INT2_B uses the ratio proposition exclusively and with high confidence to explain Scenario 1
and Scenario 2. The student receives the standard intervention after Scenario 2, and attempts to
use the scientific model for making a prediction in Scenario 3. After making a wrong prediction,
the student realizes that his understanding of the new framework is poor and reverses back to his
ratio framework. The student questions the necessity of understanding a new framework since he
would have made the correct prediction using his ratio framework.
“Is it because these forces are different? I guess that would be easier for me to see it
right now in an equation than to see it conceptually by looking at it [pause] but if I would
have solved this the same way I did it previously, Scenario A would have been the fastest
one, just because of the ratios. To me that is easier to understand conceptually, than to
do the math.”(INT2_B, explanation after experiment for Scenario 3)
The ratio proposition can be used to correctly solve the scenarios 1, 2 and 3. Scenario 4 cannot
be solved using the ratio of heavy to light masses since there is only one mass. At that moment,
the students realize that their framework is limited and tries to explain the system behavior using
the desired propositions.
I am still kind of stuck in my old way [weight ratio approach], but I can’t really apply that
to a Scenario such as this [Scenario 4] which is where I would have gotten stuck.”
(INT2_B, at the end of the IBLA)
Students who used the ratio proposition (Table 6.1) seem to show the opposite behavior as the
students with single mass proposition. These students utilized total mass proposition (Table 6.2)
and not the net force proposition (Table 6.3.).Case 4 serves to create conceptual conflict so that
students realize the limitations of their ratio based approach and experience conceptual change.
Research question #3– What is the role of predict-observe-explain activities and the role of
short direct instruction in promoting conceptual development and conceptual change?
Impact of the Predict-Observe-Explain activities on conceptual development and change
The coded data show that students go through a process of conceptual development as they
acquire or strengthen desired propositions during the IBLA thanks to P.O.E cycles. INT3_A
strengthens his understanding of total mass after Scenario 1 (see Table 7.1 with dark green).
INT2_A, INT3_B and INT3_C strengthen their understanding of net force and how to calculate
the net force after Scenario 3 (see Table 7.2 with dark green).
Unfortunately, the road to conceptual understanding does not seem to be straightforward.
Undesirable strengthening of weak propositions can also happen during experimentation. This is
the Scenario for NoINT_A strengthening the single mass proposition after Scenario 1 (see Table
7.1 with light red) and for NoINT_B, INT2_A and INT3_A after Scenario 3 (see Table 7.2 with
light red). Moreover, undesirable weakening of desired propositions is also common (see Table
7.2 with light green). For example in Scenario 3, the students seem make the prediction mostly
based on the total mass being equal. When the experimental results contradict their prediction,
they realize that the net force plays a role in the system. They conclude that the acceleration must
be different because the net forces are different.
Page 26.858.16
* Low, Medium, High - student‟s confidence in the proposition at the time of explanation
Table 7.1 – Scenario 1
Confidence in the proposition
Observations
Predict Explain
Student
NoINT_A
Prediction Same Student uses D2 to predict with high
confidence that both accelerations will
be the same, since the net force
(determined as the mass difference) is
the same. The contradictory
experimental results make the student
gain confidence in the single mass
proposition. The student still mentions
net force in his Explain step
D1 - Total mass - -
D2 - Net force High High
D3 - Calculating Net
Force High High
D4 - Newton‟s 2nd
law - -
W1 - Single mass Low Med
Student
INT3_A
Prediction Same Student uses Net force proposition to
predict with medium confidence that
both accelerations will be the same,
since the net force (determined as the
mass difference) is the same. The
contradictory experimental results make
the student gain confidence in the total
mass proposition. The student doesn‟t
mention net force in his Explain step.
D1 - Total mass Low High
D2 - Net force Med -
D3 - Calculating Net
Force Med -
D4 - Newton‟s 2nd
law - -
W2 - Ratio - -
Desired acquisition/strengthening
Undesired acquisition/strengthening
* Low, Medium, High - student‟s confidence in the proposition at the time of explanation
Table 7.2 – Scenario 3 Predict Explain Observations
Student
NoINT_B
Prediction Same Student uses Total Mass proposition to
predict with high confidence that both
accelerations will be the same, since
their total mass is the same. In the
Explain step, he utilizes the ratio
proposition together with the net force
proposition to explain why the masses
are different.
D1 - Total mass High -
D2 - Net force Low High
D3 - Calculating Net
Force - High
D4 - Newton‟s 2nd
law - -
W2 - Ratio - Med
Student
INT2_A
Prediction Same Student uses Total Mass proposition to
predict with high confidence that both
accelerations will be the same, since
their total mass is the same. In the
Explain step, he utilizes the Net force
proposition to explain why the
accelerations are different.
D1 - Total mass High -
D2 - Net force High High
D3 - Calculating Net
Force - High
D4 - Newton‟s 2nd
law - -
W2 - Ratio - -
Page 26.858.17
Student
INT2_B
Prediction Same The student has the incorrect
proposition that the net force is
determined by the total weight of the
system. Student predicts with high
confidence that both accelerations will
be the same. In the Explain step, he
reverts to the ratio proposition.
D1 - Total mass
D2 - Net force High Low
D3 - Calculating Net
Force M1 Low
D4 - Newton‟s 2nd
law - -
W2 - Ratio - High
Student
INT3_A
Prediction Same
Student uses Total mass concept to
predict with high confidence that both
accelerations will be the same, since
their total mass is the same. In the
Explain step, he uses the ratio concept
to explain why the masses are different.
D1 - Total mass High -
D2 - Net force - -
D3 - Calculating Net
Force - -
D4 - Newton‟s 2nd
law - -
W2 - Ratio - Low
Student
INT3_B
Prediction Same After the instructor asks for
clarification on what mass he is
referring to, the student realizes that
total mass in determining the
acceleration. So he makes the
prediction with high confidence that the
accelerations are the same. In the
Explain step, he utilizes the Net force
concept to explain why the
accelerations are different.
D1 - Total mass High -
D2 - Net force - Med
D3 - Calculating Net
Force Low Med
D4 - Newton‟s 2nd
law Low -
W1 – Single Mass Low -
Student
INT3_C
Prediction Same Student uses Total Mass concept to
predict with high confidence that both
accelerations will be the same, since
their total mass is the same. In the
Explain step, he utilizes the net force
concept to explain why the masses are
different.
D1 - Total mass High High
D2 - Net force - High
D3 - Calculating Net
Force Low High
D4 - Newton‟s 2nd
law Low High
Desired acquisition/strengthening
Undesired weakening Undesired acquisition/strengthening
All students predicted Scenario 2 correctly since it is essentially the same as Scenario 1. For
Scenario 4, the students only did the Predict step, because no hardware was available for
experimentation. Nevertheless, Scenario 4 served as a promoter for conceptual change since it
challenged the students who utilized the ratio weak proposition.
Page 26.858.18
Impact of the direct instruction on conceptual development and change
The students acquire or strengthen desired propositions during the IBLA activity thanks to direct
instruction. For the direct instruction after Scenario 2, INT2_A strengthens the total mass
proposition while repairing the single mass proposition and INT2_B acquires the net force
proposition while challenging the ratio weak proposition (see Table 8.1). Unfortunately, these
students also acquire an incorrect proposition during the instruction. This proposition is short-
lived since the hands-on experiment presents contradictory evidence that the net force is
determined by the weight difference, not the weight sum. The problem is that the acquired
desired propositions are also short-lived since after making a wrong prediction, the student can
revert back to their previous strategies (for example INT2_A uses net force only and INT2_B
uses ratio).
For the direct instruction after Scenario 3 (see Table 8.2), INT3_A acquires two desired
propositions and weakens the ratio conception, while INT3_B acquires two desired propositions
and strengthens the other two desired propositions. Further scenarios would have been needed to
understand in-depth how students‟ knowledge changes.
This interplay between acquisition of desirable propositions, weakening of other desirable
propositions, while simultaneously strengthening some weak propositions poses problems when
designing IBLAs based on variation theory where multiple variables play a role in the system.
* Low, Medium, High - student‟s confidence in the proposition at the time of explanation
** | marks the direct instruction after Scenario 2 and before Scenario 3
Table 8.1.
Direct instruction
after Scenario 2
Scenario
2
Scenario
3
Scenario
3 Observations
Explain Predict Explain
Student
INT2_A
D1 - Total mass - High - Direct instruction helps
student understand that
total mass plays a role in
determining the
acceleration, not the single
mass. However, the student
gets confused and starts
utilizing total weight to
calculate net force instead
of the weight difference.
D2 - Net force High High High
D3 - Calculating Net
Force High - High
D4 - Newton‟s 2nd
law - - -
W1 - Single mass Medium - -
I1 - Total weight=>Net
force - High -
Student
INT2_B
D1 - Total mass - - - Direct instruction helps
student understand that net
force plays a role in
determining the
acceleration. However, the
student gets confused and
utilizes total weight to
calculate net force instead
of the weight difference.
D2 - Net force - High Low
D3 - Calculating Net
Force - - Low
D4 - Newton‟s 2nd
law - - -
W2 - Ratio High - High
I1 - Total weight=>Net
force - Medium -
Page 26.858.19
Student
INT2_C
D1 - Total mass High High High No conceptual acquisition,
since the student already
has a strong knowledge. D2 - Net force High High High
D3 - Calculating Net
Force High High High
D4 - Newton‟s 2nd
law High High High
W2 - Ratio - - -
I1 - Total weight=>Net
force - - -
Desired acquisition/strengthening
Desired weakening
Undesired acquisition/strengthening
* Low, Medium, High - student‟s confidence in the proposition at the time of explanation
** | marks the direct instruction after Scenario 3 and before Scenario4
Table 8.2.
Direct instruction
after Scenario 3
Scenario 3
Scenario 4
Observations
Explain Predict
Student
INT3_A
D1 - Total mass - High Student understands the limitation
of his approach based on ratio due
to Scenario 4. The Direct
instruction helps him acquire two
desired propositions.
D2 - Net force - High
D3 - Calculating Net Force - -
D4 - Newton‟s 2nd
law - -
W2 - Ratio Low -
Student
INT3_B
D1 - Total mass - High The Direct instruction helps the
student acquire the total mass
proposition and strengthen the net
force proposition. This allows the
student to get a big picture idea of
Newton‟s second law.
D2 - Net force Medium High
D3 - Calculating Net Force Medium High
D4 - Newton‟s 2nd
law - High
W1 - Single mass - -
Student
INT3_C
D1 - Total mass High High No conceptual acquisition, since
the student already gained the
concepts from previous wrong
prediction.
D2 - Net force High High
D3 - Calculating Net Force High High
D4 - Newton‟s 2nd
law High High
Desired acquisition/strengthening
Desired weakening
Undesired acquisition/strengthening
Page 26.858.20
Summary of findings:
RQ #1: A large number of students use desired propositions together with weak propositions.
This is an indication that the students have experienced conceptual development and minimal
conceptual change. Two weak propositions are widespread among students and are used
consistently throughout the IBLA, which seems to indicate that the students had naive mental
models based on these ideas.
RQ #2: Weak propositions and desired propositions seem to be connected. There are weak
propositions that seem more likely to show up when particular desired propositions are
lacking. As those weak propositions are weakened, desired propositions are acquired.
RQ #3:
o Hands-on experiments can promote acquisition of desired propositions. However,
weakening of other desired propositions and strengthening of weak propositions
can also happen simultaneously.
o Direct instruction can promote acquisition of desirable propositions. However,
students can also misunderstand the explanation and acquire incorrect
propositions. Moreover, the acquired desired propositions can be short-lived since
after making a wrong prediction, the student can revert back to their previous
strategies and ignore the knowledge just learned.
Implications
For instruction:
In order to facilitate the acquisition of a desired framework, the instruction should target the
naïve model that limits the student‟s understanding. The hands-on experiments should be
carefully designed using variation theory to challenge the weak propositions that underline the
student‟s naïve mental model, otherwise weakening of desired knowledge can happen when the
students make the wrong prediction. Direct instruction can be important to highlight the fact that
the system has multiple variables that are all interconnected and important, while hands-on
experiments allow students to test their understanding.
For research:
Different sequences of instruction with more in-depth explanations should be investigated in
order to understand the process of conceptual acquisition and strengthening of desired
propositions. Scenarios that change both net force and total mass should be added, and additional
scenarios that challenge the single mass and ratio weak conceptions should be explored.
Scenarios that include multiple pulleys can also be added as challenge towards the end of the
IBLA.
Limitations
A limitation of the current study is the small male-dominated sample. The results from this
exploratory qualitative study will be tested in future work on larger size and more diverse
samples. Another limitation was that assignment of students to one of the three sequences of
instruction was made at the time of the interview, which has the potential for bias. Potentially
problematic is also the fact that the intervention was not fully scripted, which introduced slight
changes from student to student.
Page 26.858.21
Conclusions
Students had three distinct mental models that they use regarding Newton‟s second law (one
scientific and two naïve models). Both conceptual development and conceptual change happened
during the IBLA. Conceptual development was typical, as the students acquired and strengthened
desired propositions, but they did not necessarily give up on their prior naïve propositions. Not
surprisingly, if students had a naïve understanding that was not contradicted by the results of the
experiment, they maintained it.
Conceptual change was evident when students were exposed to a Scenario that revealed the
limitation of their naïve mental model. Both conceptual development and conceptual change are
needed for students in order to have an extensive declarative knowledge organized according to
scientific model.
References
1. Georgette, J., B.P. Self, J. Widmann, K. Bohn, and E. Wang, Rolling, rolling, rolling: An inquiry-based
learning activity in dynamics, in Proceedings of the American Society for Engineering Education Pacific
Southwest Annual Conference. 2013: Riverside, CA.
2. Gray, G., F. Costanzo, D. Evans, P. Cornwell, B. Self, and J. Lane. The dynamics concept inventory assessment
test: A progress report and some results. In Proceedings of the American Society for Engineering Education
Annual Conference and Exposition. 2005.
3. Steif, P.S. and M. Hansen, Comparisons between performances in a statics concept inventory and course
examinations. International Journal of Engineering Education, 2006. 22(5): p. 1070-1076.
4. Goodwin, L., B. Self, and J. Widmann, Is There a Correlation Between Conceptual Understanding and
Procedural Knowledge in Introductory Dynamics? , in American Society for Engineering Education Pacific
Southwest Regional Conference. 2009: San Diego, CA.
5. Hake, R.R., Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics
test data for introductory physics courses. American Journal of Physics, 1998. 66(1): p. 64-74.
6. Prince, M., Does active learning work? A review of the research. Journal of Engineering Education, 2004.
93(3): p. 223-231.
7. Georgette, J., Active Learning using Model-Eliciting Activities and Inquiry-Based Learning Activities in
Dynamics, in Mechanical Engineering. 2013, California Polytechnic State University: San Luis Obispo, CA.
8. Matlen, B.J. and D. Klahr, Sequential effects of high and low instructional guidance on children's acquisition of
experimentation skills: Is it all in the timing? Instructional Science, 2013. 41(3): p. 621-634.
9. Prince, M., M. Vigeant, and K. Nottis. Inquiry-Based Activities to Address Critical Concepts in Chemical
Engineering. InProceedings of the Annual Conference of the American Society for Engineering Education.
2011.
10. Prince, M. and M. Vigeant, Using Inquiry-Based Activities to Promote Understanding of Critical Engineering
Concepts, in ASEE Annual Conference & Exposition. 2006.
11. Self, B.P., J. Widmann, M. Prince, and J. Georgette. Inquiry-based learning activities in dynamics.
InProceedings of the American Society for Engineering Education Annual Conference and Exposition. 2013.
12. Shavelson, R. J., Ruiz-Primo, M. A., & Wiley, E. W. (2005). Windows into the mind. Higher education, 49(4),
413-430.
Page 26.858.22
13. Yin, Y. (2005). The influence of formative assessments on student motivation, achievement, and conceptual
change.
14. Strike, K. A., & Posner, G. J. (1982). Conceptual change and science teaching.European Journal of Science
Education, 4(3), 231-240.
15. Vosniadou, S., & Brewer, W. F. (1992). Mental models of the earth: A study of conceptual change in
childhood. Cognitive psychology, 24(4), 535-585.
16. Helldén, G. F., & Solomon, J. (2004). The persistence of personal and social themes in context: Long‐and
short‐term studies of students' scientific ideas.Science Education, 88(6), 885-900.
17. Mitchell, A. A. (1986). The measurement of declarative knowledge. Advances in Consumer Research, 13, 454-
459.
18. McDermott, L.C., P.S. Shaffer, and M.D. Somers, RESEARCH AS A GUIDE FOR TEACHING
INTRODUCTORY MECHANICS - AN ILLUSTRATION IN THE CONTEXT OF THE ATWOOD MACHINE.
American Journal of Physics, 1994. 62(1): p. 46-55.
19. Clement, J. (1979). Mapping a student's causal conceptions from a problem solving protocol. Cognitive process
instruction, 133-146.
20. Widmann, J., B.P. Self, and M.J. Prince. Development and Assessment of an Inquiry-Based Learning Activity in
Dynamics: A Scenario Study in Identifying Sources and Repairing Student Incorrect propositions.
InProceedings of the American Society for Engineering Education Annual Conference and Exposition. 2014.
Page 26.858.23
Appendix A: Interview protocol for the pulley IBLA
**Notes to Interviewer:
Students must sign release form
Make sure the student is speaking loud enough.
Ask the student to talk aloud if they are quietly studying the drawings.
The student may run the experiment more than once.
If after trying to explain the student says “I don‟t know,” move to the next question.
If the student wants to do a sketch or even a quick free body diagram (FBD), that is
okay. What we don‟t want is for them to crank through a bunch of equations without
really thinking about it conceptually
The student should repeat the tests once or twice.
Bring a scale in Scenario the student wishes to weigh the sacks.
The student can write on the board right over the projection, so we can video this.
Introduction
I am going to present you with a number of conceptual scenarios in Dynamics and we want to
know what you are thinking as you solve them. Although it may not seem natural to you, we are
asking you to talk aloud while you are thinking. The more you say is the better. We are really
interested in the process of how students reason through different dynamics problems. If you
like, you can write on the blackboard as you think through the problems, but please keep
talking. We will start with a practice question so you can get the hang of things. At the end, we
will fully explain all the concepts after the videotaped session.
Practice This first problem is a practice problem. Please read the question out loud and then talk me
through what you are thinking as you solve the problem. (Prompts: Can you tell me more about
that? Could you speak louder? I can tell that you are thinking, could you explain what thoughts
you have?)
* After the practice, give feedback. I like how you… (2), I wish you would…(1)
Scenario 1
1. Looking at the picture of Scenario 1, which block will accelerate faster, block A or block
B? Or do they accelerate at the same rate, or not at all?
2. Why do you think that is the Scenario? (Prompt: Can you tell me more about that?)
**If they end up talking about ratios, make sure you pin them down on exactly what ratio
they are talking about.
3. Please report your confidence level for your prediction as a total guess, low, low-to-
moderate, moderate, moderate to high, or high.
4. Would you please perform the Scenario 1 experiment?
5. What did you observe when performing the experiment?
6. Please explain what is happening. (Prompt: Can you tell me more about that?)
Page 26.858.24
Scenario 2
1. Looking at the picture of Scenario 2, which block will accelerate faster, block A or block
B? Or do they accelerate at the same rate, or not at all?
2. Why do you think that is the Scenario? (Prompt: Can you tell me more about that?)
3. Please report your confidence level for your prediction as a total guess, low, low-to-
moderate, moderate, moderate to high, or high.
4. Would you please perform the Scenario 2 experiment?
5. What did you observe when performing the experiment?
6. Please explain what is happening. (Prompt: Can you tell me more about that?)
Scenario 3
1. Looking at the picture of Scenario 3, which block will accelerate faster, block A or block
B? Or do they accelerate at the same rate, or not at all?
2. Why do you think that is the Scenario? (Prompt: Can you tell me more about that?)
3. Please report your confidence level for your prediction as a total guess, low, low-to-
moderate, moderate, moderate to high, or high.
4. Would you please perform the Scenario 3 experiment?
5. What did you observe when performing the experiment?
6. Please explain what is happening. (Prompt: Can you tell me more about that?)
**Explanation after Scenario 3, before they go to Scenario 4. We will do two sets like
this, then decide what we want to do next.
Scenario 4
1. Looking at the picture of Scenario 4, which block will accelerate faster, block A or block
B? Or do they accelerate at the same rate, or not at all?
2. Why do you think that is the Scenario? (Prompt: Can you tell me more about that?)
3. Please report your confidence level for your prediction as a total guess, low, low-to-
moderate, moderate, moderate to high, or high.
Page 26.858.25
Note: 1 oz = 1/16 lbs
Confidence Scale
Total Guess Low Low-Moderate Moderate Moderate-High High
Page 26.858.26
Appendix B: Coding maps for the nine students assigned to three sequences of instruction
a. NoINT = IBLA only with predict-observe-explain (P.O.E) cycles;
b. INT2 = IBLA with direct instruction after Scenario 2;
c. INT3 = IBLA with direct instruction after Scenario 3.
Three students (A, B, C) were assigned per each instructional sequence (NoINT, INT2, INT3). Each of the nine students was assigned
a code for the sequence and the order in which they participated (A, B, C). For example, INT2_B refers to student B (second one in
the INT2 group) who had an intervention after Scenario 2.
Student NoINT_A
The student NoINT_A uses predominantly W1 single mass proposition to predict and explain all the scenarios. There is no direct
instruction and no Scenario to challenge this weak proposition, so the student does not experience any visible conceptual change.
Page 26.858.27
Student NoINT_B
In Scenario 1 – Predict, the student NoINT_B utilizes three out of four desired propositions (D1, D2 and D4), but with low
confidence. W2 ratio proposition and incorrect proposition I1 is also used. The experimental results confirm the student‟s prediction,
so more confidence is gained in the desired proposition D1 (area of the bubble increases). Scenario 2 is similar to Scenario 1 and the
student has no difficulty making the correct prediction. For Scenario 3, the student attempts to make a prediction using the same
propositions. The prediction is wrong; therefore the student is forced to seek additional explanations. The student realizes that the net
force plays a role in determining the acceleration, however has the tendency to introduce the ratio (W2) in the explanation as well.
Scenario 4 serves as a clarifying case, the student realizing that the ratio proposition (W2) has limited applicability.
Page 26.858.28
Student NoINT_C
In Scenario 1 – Predict, the student NoINT_C understands the role of total mass and uses confidently desired proposition D1. He also
has a vague idea of how to calculate the net force (D3), but does not know how to link net force to acceleration. The student makes
only correct predictions, but that is not indicator of robust scientific knowledge. In his explanations the student uses a mix of desired
propositions and the ratio weak proposition. Scenario 4 serves as a clarifying case, the student realizing that the ratio proposition (W2)
has limited applicability.
Page 26.858.29
Student INT2_A
In Scenario 1 – Predict, the student NoINT_C understands the role of net force and uses confidently desired propositions D2 and D3.
However, the weak proposition W1 single mass is the proposition that drives his predictions in Scenario 1 and Scenario 2. The direct
instruction after Scenario 2 helps the student understand that total mass and not single mass play a role in the whole system. However,
the student gets confused and starts utilizing total weight to calculate net force instead of the weight difference (I1). In Scenario 4, the
student utilizes the same desired propositions as used at the beginning of the IBLA, so no durable conceptual acquisition is visible.
Page 26.858.30
Student INT2_B
The student INT2_B participated in sequence #2 (direct instruction after Scenario 2). For Scenario 1 and Scenario 2, both Predict and
Explain step, the student utilizes only one propositionto solve the problem, namely the ratio weak proposition (numbered W2). His
predictions are correct. After the direct instruction, in the Scenario #3 - Predict step, the student utilizes the D2 net force proposition
but also has an incorrect proposition (I1). After observing through experiment that his prediction was wrong, the student uses D2 and
D3 propositions with low confidence and reverts back to the W2 proposition in the Scenario #3 - Explain step. In the last step (in the
Scenario #3 – Explain), the student uses D3 and I3 propositions.
Page 26.858.31
Student INT2_C
Student INT2_C utilizes proficiently the scientific framework in all the four scenarios. All the desired propositions are used with high
confidence.
Page 26.858.32
Student INT3_A
In Scenario 1 – Predict, the student INT3_A utilizes with medium confidence D2 and D3 related to net force and with low confidence
D1 related to total mass. By focusing on the Net force proposition, the student predicts that both accelerations will be the same, since
the net force (determined as the mass difference) is the same. The contradictory experimental results make the student gain confidence
in the total mass proposition (D1). The student doesn‟t mention net force in his Explain step. Scenario 2 is the similar to Scenario 1, so
the student has no difficulty in making the correct prediction. For Scenario 3, the student utilizes the same approach based on D1 and
makes a wrong prediction. In the Explain step, the student introduces the W2 ratio proposition with low confidence. The direct
instruction after Scenario 3 helps the student understand that the net force is important for determining the acceleration (D2).
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STUDENT INT3_B
The student INT3_B uses predominantly the W1 single mass weak proposition, alone (Scenario 1) or in a mix with desired
propositions (Scenario 2). In Scenario 3 – Predict,after the instructor asks for clarification on what mass he is referring to, the student
realizes that total mass in determining the acceleration. So he makes the prediction with high confidence that the accelerations are the
same. The experimental results prove his prediction wrong. In the Explain step, he utilizes the Net force concept to explain why the
accelerations are different. The Direct instruction helps the student acquire the total mass proposition and strengthen the net force
proposition. This allows the student to get a big picture idea of Newton‟s second law.
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Student INT3_C
For scenarios 1 and 2, the student INT3_C uses Total Mass concept to predict with high confidence that both accelerations will be the
same, since their total mass is the same. The student utilizes the same logic for the Scenario 3 and makes the wrong prediction that the
accelerations will be the same. In the Explain step, he utilizes the net force concept and Newton‟s 2nd
law framework to explain why
the masses are different. The direct instruction after Scenario 3 does not play a visible role in the conceptual acquisition, since the
student already gained the concepts from previous wrong prediction.
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