The Consultative Model – Day 1Context and Introduction

Ruben R. Puentedura, Ph.D.

TO POLY :ANGLE :STEP i. FORWARD :STEP 2. RIGHT :ANGLE 3. POLY :ANGLE ~STEP

END

P I CTURES

The figures show the action of this procedure with various inputs. It will be seen that in general the figure crosses itself.

POLY

On a more abstract mathematical level, the day comes when the child gets involved with figures that cross themselves and so need an extension of the theorem. For example, consider the following turtle procedure written recursively in LOGO:

POLY 275 156

STAR

POLY

348

ON MAKING A THEOREM FOR A CHILD

TO POLY :ANGLE :STEP i. FORWARD :STEP 2. RIGHT :ANGLE 3. POLY :ANGLE ~STEP

END

P I CTURES

The figures show the action of this procedure with various inputs. It will be seen that in general the figure crosses itself.

POLY

On a more abstract mathematical level, the day comes when the child gets involved with figures that cross themselves and so need an extension of the theorem. For example, consider the following turtle procedure written recursively in LOGO:

POLY 275 156

STAR

POLY

348

ZCDZCD

ZPDZPD

Alo

neW

ith M

KO

IconicEnactive Symbolic

+ +> > >

Pedagogy C

ontent

Technology

PK CK

TK

PCK

TPK TCK

TPCK

DS

MM

RP

UDL

WP

What's on

Your MacBook?

(podcasts)

Lenses

(webinars/podcasts)

TPCK/SAMR

(podcasts)

Other Podcasts

F2F Sessions

Pedagogy C

ontent

Technology

PK CK

TK

PCK

TPK TCK

TPCK

Substitution

Tech acts as a direct tool substitute, with no

functional change

Augmentation

Tech acts as a direct tool substitute, with

functional improvement

Modification

Tech allows for significant task redesign

Redefinition

Tech allows for the creation of new tasks,

previously inconceivable

Enhancement

Transformation

Internet Tools Office Tools

Media ToolsInformation Organization

Math & Science Tools

Utilities

DS

MM

RP

UDL

WP

What's on

Your MacBook?

(podcasts)

Lenses

(webinars/podcasts)

TPCK/SAMR

(podcasts)

Other Podcasts

F2F Sessions

Pedagogy C

ontent

Technology

PK CK

TK

PCK

TPK TCK

TPCK

Substitution

Tech acts as a direct tool substitute, with no

functional change

Augmentation

Tech acts as a direct tool substitute, with

functional improvement

Modification

Tech allows for significant task redesign

Redefinition

Tech allows for the creation of new tasks,

previously inconceivable

Enhancement

Transformation

Curricular Development

Assessment

Curricular Development and Assessment

• Curricular Development

• The Connected Approach to Learning• Connections between subject areas• Connections within subject areas

• Asking how we know what we know• Ways of knowing in the humanities, arts, sciences, and mathematics• Nonsense detection filters

• Integrating theoretical domains with applied practice• Micro theory into macro observation• Macro theories into micro observation

• Assessment

• Assessment for Learning

• Assessment of Learning

• Assessment of Technology in Learning

tides Bangor, Maine

Input interpretation:

tides Bangor, Maine

Result:

06:00 12:00 18:00 May 18 00:00

0

5

10

15

ocean

heig

ht�feet�

Monday, May 17, 2010

low tide8:26 am EDT�5 hr 23 min ago� �0.4 feet

high tide2:15 pm EDT�26 min from now� �13.6 feet

low tide8:41 pm EDT�6 hr 52 min from now� �0.7 feet

�computed using historical data, not taking into account weather, etc.

heights relative to all�time average lowest daily tide�

Generated by Wolfram|Alpha (www.wolframalpha.com) on May 17, 2010 from Champaign, IL.

© Wolfram Alpha LLC—A Wolfram Research Company1

Brief Lecture or Group Discussion(~10 minutes)

ConcepTest(~1-2 minutes)

Between 30-75% of students answer correctly

Fewer than 30% of students answer correctly

More than 75% ofstudents answer correctly

Peer Discussion:students try to convince each other

(~2-3 minutes)

!e instructorexplains remaining misconceptions

!e instructorrevisits and explains the concept

ConcepTest(~1-2 minutes)

Which of these scenarios does not describe an acceleration?

A. A car going round a circular racetrack at constant speed.

B. A car traveling on a straight racetrack at constant speed.

C.A stone falling from the top of a building.

D. A simple pendulum.

Which of these would best be described as the “Crossing of the First Threshold” in The Matrix?

A. Neo goes to the club.

B. Neo takes the red pill.

C.Neo meets the Oracle.

D. Neo returns to the Matrix to save Morpheus.

Higher Order Thinking SkillsCreate

EvaluateAnalyzeApply

UnderstandRemember

Lower Order Thinking Skills

Large Effect Size

Scores

Frequency

!4 !2 0 2 4

05

10

15

20

d=0.8

Scores

Large Effect SizeFr

eque

ncy

Three Additional Key Elements

• Triage Approach

• 80/20 Rule

• Shift from "school + homework" to "continuum of learning environments"

Resources – Part 1

• Vannevar Bush, “As We May Think”. The Atlantic Monthly. (July 1945) Online at:http://www.theatlantic.com/magazine/archive/1969/12/as-we-may-think/3881/

• Douglas C. Engelbart, A Research Center for Augmenting Human Intellect. (December 1968 live demo) Archived online at:http://sloan.stanford.edu/mousesite/1968Demo.html

• Alan Kay, “A Personal Computer for Children of All Ages”. Proceedings of the ACM National Conference. Boston (August 1972) Online at:http://www.mprove.de/diplom/gui/Kay72a.pdf

• Seymour Papert, “On Making a Theorem for a Child”. Proceedings of the ACM National Conference. Boston (August 1972) Online at:http://portal.acm.org/citation.cfm?id=569942

• Lev Vygotsky, Mind in Society: The Development of Higher Psychological Processes. Harvard University Press. (1978)

• Jerome Bruner, Toward a Theory of Instruction. Harvard University Press. (1966)• Garry Kasparov, “The Chess Master and the Computer”. The New York Review of Books.

(February 11, 2010) Online at:http://www.nybooks.com/articles/archives/2010/feb/11/the-chess-master-and-the-computer/

Resources – Part 2

• Benjamin S. Bloom, “The 2 Sigma Problem: The Search for Methods of Group Instruction as Effective as One-to-One Thinking”. Educational Researcher, Vol.13, No. 6, pp. 4-16. (June-July 1984) Online at:http://web.mit.edu/5.95/readings/bloom-two-sigma.pdf

• Alexis M. Berry and Sarah E. Wintle, “Using Laptops to Facilitate Middle School Science Learning: The Results of Hard Fun". CEPARE Research Brief. (February 2009) Online at:http://usm.maine.edu/cepare//pdf/Bristol_Final_Copy_cover.pdf

• TPCK - Technological Pedagogical Content Knowledge. (2008-2010) Online at:http://www.tpck.org/tpck/index.php?title=Main_Page

• AACTE (Eds.) The Handbook of Technological Pedagogical Content Knowledge for Educators. New York:Routledge, 2008.

• Ruben R. Puentedura, Transformation, Technology, and Education. (2006) Online at:http://hippasus.com/resources/tte/

• Ruben R. Puentedura, As We May Teach: Educational Technology, From Theory Into Practice. (2009) Online at:http://tinyurl.com/aswemayteach

• Ruben R. Puentedura, Rethinking Visualization: From Dynamic Illustration to Online Narrative. (2010) Online at:http://hippasus.com/resources/swarthmore2010/1_RethinkingVisualization.pdf

Resources – Part 3

• Alfred Barr, Cubism and Abstract Art. (1936) Online at:http://www.edwardtufte.com/bboard/q-and-a-fetch-msg?msg_id=0000yO

• Understanding Science. (2009-2010) Online at:http://undsci.berkeley.edu/

• Howard Rheingold, “Mindful Infotention: Dashboards, Radars, Filters”. City Brights: Howard Rheingold. (September 1, 2009) Online at:http://www.sfgate.com/cgi-bin/blogs/rheingold/detail?blogid=108&entry_id=46677

• Wolfram|Alpha: http://www.wolframalpha.com/• Justine Whitman, “Moon Motion and Tides”. Aerospaceweb.org Q&A. (19 February 2006).

Online at:http://www.aerospaceweb.org/question/astronomy/q0262.shtml

• “ConcepTests”. Starting Point – Teaching Intro-Level Geoscience. (2003-2010) Online at:http://serc.carleton.edu/introgeo/interactive/conctest.html

• Lorin W. Anderson and David R. Krathwohl (Eds.), A Taxonomy for Learning, Teaching, and Assessing: A Revision of Bloom’s Taxonomy of Educational Objectives, Complete Edition. Longman. (2000)

• Robert Coe, “It's the Effect Size, Stupid: What effect size is and why it is important”. Paper presented at the Annual Conference of the British Educational Research Association. (September 2002) Online at:http://www.leeds.ac.uk/educol/documents/00002182.htm

Hippasus

http://hippasus.com/rrpweblog/rubenrp@hippasus.com

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