SimCalc: Democratizing Access to the Mathematics of Change

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SimCalc Democratizing Access to the Mathematics
of Change

• Jeremy Roschelle

DirectorCenter for Technology in LearningSRI
International
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Pop Quiz

• Over the past 20 years, mathematics achievement
  of US 8th graders has been
• Improving?
• Declining?
• Staying the Same?

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Results from NAEPImproving but not fast enough
Average mathematics scale scores, grades 4 and 8
19902003
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.
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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
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Which plan to reduce the budget deficit to zero
saves the taxpayers the most money?
Deficit spending per month
years
Most calculus undergrads are perplexed!
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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?
• Use of computers
• Use of graphing calculators
• Solving problems from the textbook

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More results from NAEP

• Which factors correlate with high 8th grade
  scores?
• ? Use of computers
• ? Use of graphing calculators
• ? Solving problems from the textbook

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• Today, Two Main Points
• Our Core Design Approach
• Restructuring Knowing
• Our Research Program on Scaling Up
• Cheaper Platform
• Coverage of Curriculum
• Diversity of Users

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Our Design ApproachRestructuring Knowing
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Our big representational move
Algebra
Graphs
Tables
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Our big representational move
? Learners ? Technology ? Curriculum
Algebra
Motion Phenomena
Graphs
Tables
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DEMO
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Demo Recap
Rep. Tech.
Learners

• Edit Graphs
• Link Reps
• Piecewise
• Animation

• Motion
• Graphs
• Intervals
• Counting

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

Math
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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 todays talk, only
• Diverse Students
• Devices
• Wide Variety of Teachers
• 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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VIDEO
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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 existingthat we could
  use as control

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Findings

• Stronger Gains for SimCalc

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Findings

• Gains in
• Every Quartile

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Findings

• Wide Variation
• Across Teachers

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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
• 11 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 lt .001.

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Did Students Learn?

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

1. At what value of s does the bug change
direction? (A) 2 (B) 4 (C) 6 (D) 7 (E)
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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
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.
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Did Students Learn?
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 System
Students respond individually
Teacher presents question
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
Kaput Hegedus
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 family of functions)
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4. Extends to participatory simulations
Stroup and Wilensky
Make your y value twice your x value
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About SRI Internationals 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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Conclusion
cognition,epistemology
dynamic representation
Computation
Learning
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Conclusion
cognition,epistemology
dynamic representation
Computation
Learning
discourse,participation
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Conclusion
cognition,epistemology
dynamic representation
Computation
Learning
discourse,participation
dynamiccoordination
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URLs

• SRIs Center for Technology in Learningctl.sri.co
  m
• 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