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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
9/1/2004 CHI FOO Presentation
The Challenge
9/1/2004 CHI FOO Presentation
“The economy is going down…”
GDP
Time
9/1/2004 CHI FOO Presentation
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
9/1/2004 CHI FOO Presentation
“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!
9/1/2004 CHI FOO Presentation
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
9/1/2004 CHI FOO Presentation
Our Design Approach:Restructuring Knowing
9/1/2004 CHI FOO Presentation
Our big representational move
Algebra
Graphs Tables
9/1/2004 CHI FOO Presentation
Our big representational move
Algebra
Graphs Tables
Motion Phenomena
Learners
Technology
Curriculum
9/1/2004 CHI FOO Presentation
9/1/2004 CHI FOO Presentation
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
9/1/2004 CHI FOO Presentation
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
9/1/2004 CHI FOO Presentation
Our Research Approach
For today’s talk, only:
1. Diverse Students
2. Devices
3. Wide Variety of Teachers
4. Connecivity
9/1/2004 CHI FOO Presentation
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
9/1/2004 CHI FOO Presentation
9/1/2004 CHI FOO Presentation
Diverse Teachers
Can a wide variety of teachers effectively use SimCalc given a limited amount of training?
9/1/2004 CHI FOO Presentation
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)
9/1/2004 CHI FOO Presentation
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
9/1/2004 CHI FOO Presentation
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
9/1/2004 CHI FOO Presentation
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)
9/1/2004 CHI FOO Presentation
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
9/1/2004 CHI FOO Presentation
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
9/1/2004 CHI FOO Presentation
Diverse Devices
Calculators are ubiquitous, affordable
1:1 Access enables frequent, integral use
9/1/2004 CHI FOO Presentation
Example : Match My Graph
9/1/2004 CHI FOO Presentation
Did Students Learn?
Significant pre- to post-test gains on a test of mathematics of change concepts
– t(24)= 16.11; p < .001.
9/1/2004 CHI FOO Presentation
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
9/1/2004 CHI FOO Presentation
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).
9/1/2004 CHI FOO Presentation
Connectivity
9/1/2004 CHI FOO Presentation
The Response SystemTeacher presents question
Students respond individually
Instant histogram results
9/1/2004 CHI FOO Presentation
1. Extends to Images
9/1/2004 CHI FOO Presentation
2. Extends to Text
9/1/2004 CHI FOO Presentation
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)
9/1/2004 CHI FOO Presentation
4. Extends to participatory simulations
Make your y value twice your x value…
9/1/2004 CHI FOO Presentation
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)
9/1/2004 CHI FOO Presentation
Computation
dynamic representation
Learning
cognition,epistemology
Conclusion
9/1/2004 CHI FOO Presentation
Computation
dynamic representation
Learning
cognition,epistemology
discourse,participation
Conclusion
9/1/2004 CHI FOO Presentation
Computation
dynamic representation
dynamiccoordination
Learning
cognition,epistemology
discourse,participation
Conclusion
9/1/2004 CHI FOO Presentation
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”
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