Effective Integration of Dynamic Representations and Collaboration to Enhance Mathematics and Science Learning

Jeremy Roschelle, SRI International, California USA

KEYNOTE

Over the past 20 years, mathematics achievement of US 8th graders has been:

A. Improving?B. Declining?C.Staying the Same?

Pop QuizK

EYN

OTE

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Results from US National Assessment of Educational Progress (NAEP)

Average mathematics scale scores, grades 4 and 8: 1990–2003

At least a grade level of improvement since 1996

-- Judy Sowder

But most students still at the basic level. Unlikely to hit national goal by 2014 of all proficient.

Improving… but not fast enough.

Pop Quiz 2

Which factors predict high 8th grade scores?A. Use of computers

B. Use of graphing calculators

C. Solving problems from the textbook

More results from NAEP

Which factors correlate with high 8th grade scores?A. Use of computers

B. Use of graphing calculators

C. Solving problems from the textbook

Why?

•Computers used for drill & practice at the basic level or poorly integrated

•Graphing calculators used as representational tools for math at the proficient and advanced levels

This Talk: What is Effective Integration?

The Challenge of Effective Integration

Crossing the Chasm

Most educational technologies start with visionary promise but never achieve impact beyond a few exciting demonstration classrooms…

Keynote Overview

1. Graphing Calculatorsa success!

2. A mini-theory of effective integrationefficiency & innovation

3. Handheld Collaborationemerging with promise

Graphing Calculators

Integration?

50% of U.S. high school students have one…

… other countries use it too.

But is it effective?

What does research say?Positive correlations at scale

“Eighth-graders whose teachers reported that calculators were used almost every day scored highest. Weekly use was also associated with higher average scores than less frequent use. In addition, teachers who permitted unrestricted use of calculators and those who permitted calculator use on tests had eighth-graders with higher average scores than did teachers who did not indicate such use of calculators in their classrooms.” NCES, 2001

NAEP Scores with and without a calculator, by SES

0

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70

Lower SES Higher SES

Graphing Calculator

NA

EP P

erce

ntile

Sco

re

With Without

What does research say?Strong findings in experiments

• Gains across grade levels• Operations• Conceptual understanding• Problem Solving

40

50

60

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100

Elementary Middle HighPerc

entil

e of

Ave

rage

Stu

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afte

r Tre

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Operational Conceptual

Ellington’s metaanalysis of 54 experiments:

What does research say?Strong findings in experiments

In Algebra specifically…

Why? Socio-Cognitive Theory

• Cognitive load• GC frees resources for problem solving

• Dual coding theory• Graphical + Linguistic coding enhances learning

• Multiple representations• Effectively mediate social construction of meaning

How did graphing calculators cross the chasm?

Simple, inexpensive, robust technology

Built a huge teacher training network

Integration into National Standards

Incorporation in curricula

Required on assessments

Simple, Robust, Inexpensive Technology

•About $100•Batteries last 3 months•Don’t break•Relatively buzzword-free•Functionality is focused on mathematics content

Train the trainers network

• Teacher-led effort to integrate calculators in mathematics improvement

• For trainers, offers continual learning and improvement

• For teachers, offers localized supportBurt Waits & Frank Demana

T3 Operates in over 12 countries including Australia

Healthy Symbiosis BetweenTeachers and Technologists

Waits & Demana,Ohio State

Tom Ferrio,Texas Instruments

Building a Breakthrough Business ConceptMost “innovations” came from teachers; Texas Instruments

nurtured, listened, & evolved their product.

See Eric Von Hippel “Democratizing Innovation”

Integration into National Standards

Calculators and computers are reshaping the mathematical landscape, and school mathematics should reflect those changes. Students can learn more mathematics more deeply with the appropriate and responsible use of technology. They can make and test conjectures. They can work at higher levels of generalization or abstraction.

When Working mathematically, students … use technologies such as geometry software, graphics calculators and spreadsheets.

Incorporation in Curricula & Testing

Incorporated on key tests, such as Advanced Placement Calculus & Statistics

What does effective integration look like?

Starts with:1. A simple, inexpensive technology built on important

socio-cognitive principles2. Symbiotic relationship between teachers and

technologists allowing for “democratic innovation”Results in:

• Systemic support for “crossing the chasm”including teacher professional development, standards, curriculum & assessment integration

• Research results demonstrating effectiveness

Part Two: The cognitive revolution and technological revolutionaries

Douglas Englebart

Legendary Inspiration at

SRI

Herbert Simon

Nobel prize-winning leader of the cognitive

revolution

Englebart

In 1968, demonstrated• The mouse• Hypertext• Collaborative screen sharing• Graphical interface

http://sloan.stanford.edu/mousesite/1968Demo.html

Believed in Augmenting Human Intelligence:

Collaborative use of dynamic representations

Technology as a revolutionary cultural tool

Simon

Won the Nobel Prize for economic theory:

• Limited Rationality• People make good, not optimal decisions

A leader in the cognitive revolution

Representations matter to cognition

Domain specific knowledge

(in reaction to his work) social cognition

Englebart & Simon Together

Limited rationality + revolutionary tools…Simple Tools for Pedagogical Revolutionaries

Domain-specific + mediating collaboration…Domain-specific collaborative representations for learning

What Education Needs:Simple Tools for Revolutionaries

What Education Needs:Simple Tools for Revolutionaries

ImpracticalTheorist

RoutineExpert

What Education Needs:Simple Tools for Revolutionaries

AdaptiveExpert

(Hatano)

What Education Needs:Simple Tools for Revolutionaries

DigitizingLectures

VirtualRealities

What are the simple tools that teachers can grow with?

Keynote Overview

Graphing Calculatorsa success!

A mini-theory of effective integrationefficiency & innovation

Handheld Collaborationemerging with promise

Handheld Collaboration

Teachers already adopting handheld response systems. There is much more we can do!

Response Systems

Teacher presents questionStudents respond individually

Instant histogram results

How It Works

We identified consistent benefits in 26 studies

Benefits• Greater student engagement (16)• Increased understanding of complex subject matter (11)

• Increased interest and enjoyment of class (7)• Promotes discussion/interactivity (6) • Helps students gauge their own level of understanding (5)

• Teachers have better awareness of student difficulties (4)

Impressive results in physics

Why Start Here?

It’s Happening!• Teachers swarming conference booths.• Tremendous amount of re-invention and action research by practitioners ($15 million)

• Teacher support resources published; teacher support networks forming.

• Technology advancing rapidly (IR -> RF -> 802.11 -> Zigbee); graphing- or PDA-based.

Why Start Here?

It Fits•Fits what teachers do every day – work with full classrooms of children

•Affordable (around $1000 per classroom)•Addresses teachers’ “pain” – are my students engaged and paying attention?

Why Start Here?

Capabilities Advancing(series of examples)

1. Extends to Images

2. Extends to Text

3. Extends to mathematics

From simple contributionsof each student

(make a fn that goes throughthe point 6,4)

To full class discussionof a more complex concept

(characteristics of a familyof functions)

4. Extends to participatory simulations

Make your y value twice your x value…

Participation in Shared Artifact + Discussion & Reflection

Introducing… Group Scribbles

Hypercard : 1984 Mac ::Group Scribbles : Wireless Classroom

Post-It Note Metaphor

Leverages SmartBoard, Stylus-Based, Wireless Classroom

Allows classroom brainstorming

Where…?

Collaborative activities

Everyone participates…

Concluding Remarks

Simple, inexpensive, robust cognitive technology

Symbiotic innovation by teachers and technologists

Integration into National Standards

Incorporation in curricula

Required on assessments

How did Graphing Calculators cross the chasm?

Concluding Remarks

What are the simple tools that teachers can grow with?

Simple Tools for Pedagogical Revolutionaries

Concluding Remarks

HyperCard for the Wireless Classroom

Group Scribbles

With inspiration and help from:• Corey Brady, Louis Abrahamson, Bill Penuel, Larry

Gallagher, Charlie Patton, Lisa Brady-Gill, Krista Davis, Chris DiGiano, Patti Schank, Zaz Harris, Deborah Tatar, Raj Chaudshury and many more…

Jeremy.Roschelle@SRI.com

Thank you!