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SimCalc: Democratizing Access to the Mathematics of Change

Explore the evolution of US 8th graders' math achievement in the past 20 years and the need to accelerate improvement. Discover how SimCalc aims to make complex mathematics more accessible to all learners, including underrepresented students. Dive into research findings, teacher effectiveness, and the impact of technology in math education.

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SimCalc: Democratizing Access to the Mathematics of Change

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  1. SimCalc: Democratizing Access to the Mathematics of Change Jeremy Roschelle DirectorCenter for Technology in LearningSRI International

  2. Pop Quiz Over the past 20 years, mathematics achievement of US 8th graders has been: • Improving? • Declining? • Staying the Same? CHI FOO Presentation

  3. 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. CHI FOO Presentation

  4. What NAEP Tells Us • We need to accelerate improvement. • Engage more students in “complex and conceptually difficult” math not just the basics CHI FOO Presentation

  5. The Challenge CHI FOO Presentation

  6. GDP Time “The economy is going down…” CHI FOO Presentation

  7. 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! CHI FOO Presentation

  8. “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! CHI FOO Presentation

  9. Pop Quiz 2 Which factors correlate with high 8th grade scores? • Use of computers • Use of graphing calculators • Solving problems from the textbook CHI FOO Presentation

  10. More results from NAEP Which factors correlate with high 8th grade scores? •  Use of computers •  Use of graphing calculators •  Solving problems from the textbook CHI FOO Presentation

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

  12. Our Design Approach:Restructuring Knowing CHI FOO Presentation

  13. Our big representational move Algebra Graphs Tables CHI FOO Presentation

  14. Our big representational move  Learners  Technology  Curriculum Algebra Motion Phenomena Graphs Tables CHI FOO Presentation

  15. DEMO CHI FOO Presentation

  16. 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 CHI FOO Presentation

  17. 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 CHI FOO Presentation

  18. Our Research Approach For today’s talk, only: • Diverse Students • Devices • Wide Variety of Teachers • Connecivity CHI FOO Presentation

  19. 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 CHI FOO Presentation

  20. VIDEO CHI FOO Presentation

  21. Diverse Teachers Can a wide variety of teachers effectively use SimCalc given a limited amount of training? CHI FOO Presentation

  22. 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) CHI FOO Presentation

  23. 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 CHI FOO Presentation

  24. Findings Stronger Gains for SimCalc CHI FOO Presentation

  25. Findings Gains in Every Quartile CHI FOO Presentation

  26. Findings Wide Variation Across Teachers CHI FOO Presentation

  27. 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 CHI FOO Presentation

  28. Calculators are ubiquitous, affordable 1:1 Access enables frequent, integral use Diverse Devices CHI FOO Presentation

  29. Example : Match My Graph CHI FOO Presentation

  30. Did Students Learn? • Significant pre- to post-test gains on a test of mathematics of change concepts • t(24)= 16.11; p < .001. CHI FOO Presentation

  31. 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) 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 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. CHI FOO Presentation

  32. Did Students Learn? NetCalc student performance compared to AP High School student performance (AP Results from The College Board, 1999). CHI FOO Presentation

  33. Connectivity CHI FOO Presentation

  34. The Response System Students respond individually Teacher presents question Instant histogram results CHI FOO Presentation

  35. 1. Extends to Images CHI FOO Presentation

  36. 2. Extends to Text CHI FOO Presentation

  37. Kaput & Hegedus 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 family • of functions) CHI FOO Presentation

  38. Stroup and Wilensky 4. Extends to participatory simulations Make your y value twice your x value… CHI FOO Presentation

  39. 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) CHI FOO Presentation

  40. Conclusion cognition,epistemology dynamic representation Learning Computation CHI FOO Presentation

  41. Conclusion cognition,epistemology dynamic representation Learning Computation discourse,participation CHI FOO Presentation

  42. Conclusion cognition,epistemology dynamic representation Learning Computation discourse,participation dynamiccoordination CHI FOO Presentation

  43. 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” CHI FOO Presentation

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