SimCalc: Democratizing Access to the Mathematics of Change

Jeremy Roschelle

DirectorCenter for Technology in LearningSRI International

9/1/2004 CHI FOO Presentation

Pop Quiz

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

A. Improving?

B. Declining?

C. Staying the Same?

9/1/2004 CHI FOO Presentation

Results from NAEP:Improving… but not fast enough

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.

9/1/2004 CHI FOO Presentation

What NAEP Tells Us

We need to accelerate improvement. Engage more students in “complex and

conceptually difficult” math not just the basics

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The Challenge

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“The economy is going down…”

GDP

Time

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Which plan to reduce the budget deficit to zero saves the taxpayers the most money?

Most calculus undergrads are perplexed!

years

Deficit spending per month

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“Democratizing access to the mathematics of change”

i.e., rate, accumulation, proportionality, slope

for kids who never make it to H.S. Calculus

WHY?“Change” is the central 21st century phenomena.

Every citizen needs accessto the mathematical fundamentalsof change!

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Pop Quiz 2

Which factors correlate with high 8th grade scores?

A. Use of computers

B. Use of graphing calculators

C. Solving problems from the textbook

9/1/2004 CHI FOO Presentation

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

9/1/2004 CHI FOO Presentation

Today, Two Main Points:1. Our Core Design Approach

Restructuring Knowing

2. Our Research Program on Scaling UpCheaper PlatformCoverage of CurriculumDiversity of Users

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Our Design Approach:Restructuring Knowing

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Our big representational move

Algebra

Graphs Tables

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Our big representational move

Algebra

Graphs Tables

Motion Phenomena

Learners

Technology

Curriculum

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Demo Recap

Learners Rep. Tech.

Math

•Motion•Graphs•Intervals•Counting

•Edit Graphs•Link Reps•Piecewise•Animation

•Historical roots in motion•Graphs before symbols•PW before Continuous

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Our Research Approach

Over 10 years, our research has been about scaling: From students to teachers to schools From expensive to cheaper devices From “calculus” to core middle school math Across demographic settings Across grade levels

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Our Research Approach

For today’s talk, only:

1. Diverse Students

2. Devices

3. Wide Variety of Teachers

4. Connecivity

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Diverse students

We have field tested primarily in disadvantaged settings in Newark, NJ; San Diego; Syracuse; Boston; Fall River, MA

But also Portola Valley, CA

7th, 8th, 9th, 11th, Freshman grade levels

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Diverse Teachers

Can a wide variety of teachers effectively use SimCalc given a limited amount of training?

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The Study

Randomized, Controlled Experiment 2-3 week Replacement Unit Outcome measure used both more “basic”

and more “conceptually difficult” items

Pilot in 2003-4 (23 teachers) Experiment in 2005-7 (140 teachers)

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The Study - Topic

Proportionality in 7th Grade Highlights more conceptually rich approach Beginnings of the pathway to Algebra &

Calculus Central 7th Grade Topic Texas had a strong course existing

that we could use as control

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Findings

Stronger Gains for SimCalc

M2 Items (18 Total)

M1 Items (9 Total)

Category

Control Treatment

Condition

1

2

3

4

5

6

Mea

n D

iffe

ren

ce f

rom

Pre

test

to

Po

stte

st

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Findings

Gains in

Every Quartile

M2 Items (Pre-Unit)

M2 Items (Post-Unit)

Category

Control Treatment

Condition

0.00

5.00

10.00

15.00

Sco

re o

n M

2 It

ems

(18

Tota

l)

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Findings

Wide Variation

Across Teachers

Control

Treatment

Condition

All Items Difference Scores

Teacher

-1

0

1

2

3

4

5

6

7

8

9

10

11

12

13

All

Dif

fere

nce

Sco

re

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Puzzle for future research

Why do teachers get stronger student gains?– Not “traditional” or “reform” style– Not length of time– Not our impression of the teachers

– Hypothesis: great teachers focus interaction on supporting students to do the conceptually challenging parts

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Diverse Devices

Calculators are ubiquitous, affordable

1:1 Access enables frequent, integral use

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Example : Match My Graph

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Did Students Learn?

Significant pre- to post-test gains on a test of mathematics of change concepts

– t(24)= 16.11; p < .001.

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Did Students Learn?

Students performed well on revised AP calculus exam questions. Example (results on next page):

s1

m/s

2 3 4 5

1

2

-1

3

6 7 8

A bug begins to crawl up a vertical wire at time s = 0. The velocity v of the bug at time s, 0 ≤ s ≤ 8, is given by the function whose graph is shown above.

1. At what value of s does the bug change direction?

(A) 2 (B) 4 (C) 6 (D) 7 (E) 8

2. What is the total distance the bug traveled from s = 0 to s = 8 ?

(A) 14 (B) 13 (C) 11 (D) 8 (E) 6

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Did Students Learn?

16%4%

67%

27%

88%

40%

0%

20%

40%

60%

80%

100%

% Correct Q1 % Correct Q2

NetCalc Pre-test

AP Students

NetCalc Post-test

NetCalc student performance compared to AP High School student performance(AP Results from The College Board, 1999).

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Connectivity

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The Response SystemTeacher presents question

Students respond individually

Instant histogram results

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1. Extends to Images

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2. Extends to Text

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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)

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4. Extends to participatory simulations

Make your y value twice your x value…

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About SRI International’s Center for Technology in Learning

We have 60 Learning Scientists and staff working on three intertwined lines of work:

Improving K-12 math & science teaching and learning (NSF)

Conducting large scale evaluations (Gates, Dept of Ed)

Consulting on product innovation (Texas Instruments, Intel, Palm)

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Computation

dynamic representation

Learning

cognition,epistemology

Conclusion

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Computation

dynamic representation

Learning

cognition,epistemology

discourse,participation

Conclusion

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Computation

dynamic representation

dynamiccoordination

Learning

cognition,epistemology

discourse,participation

Conclusion

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URLs

SRI’s Center for Technology in Learningctl.sri.com

IEEE Wireless & Mobile Technologies in Education in Japan in December.Google: “wmte 2005”

ICCE in Singapore in DecemberGoogle: “icce 2005 singapore”

MLearn conferenceGoogle: “Mlearn 2005”