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Progress Towards an ACT-R/PM Model of Algebra Symbolization

Kevin A. Gluck. in collaboration with John R. Anderson Scott A. Douglass Michael D. Byrne. Progress Towards an ACT-R/PM Model of Algebra Symbolization. Funding for this project has been provided by the Air Force PALACE Knight Program and by NSF grant number CDA-9720359.

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Progress Towards an ACT-R/PM Model of Algebra Symbolization

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  1. Kevin A. Gluck in collaboration with John R. Anderson Scott A. Douglass Michael D. Byrne Progress Towards an ACT-R/PM Model of Algebra Symbolization Funding for this project has been provided by the Air Force PALACE Knight Program and by NSF grant number CDA-9720359. Sixth Annual ACT-R Workshop

  2. Goals Motivating the Project • Describe the types of instructional opportunities that are available given access to eye movement information. • Test for replication of the inductive support effect (Koedinger & Anderson, 1998). • Create ACT-R/PM (Byrne & Anderson, 1998) model of algebra symbolization. Sixth Annual ACT-R Workshop

  3. Domain: Algebra Word Problems Sixth Annual ACT-R Workshop

  4. Unit Unit Formula 1 2 1 2 Formula Inductive Support Manipulation Formula HIGH = Non-Ind. Supp. Formula LOW = Inductive Supp. Sixth Annual ACT-R Workshop

  5. The Inductive Support Effect Koedinger and Anderson (1998) reported: • Inductive Support students showed more pre-to-post improvement on symbolization. • Inductive Support students were faster at symbolizing during learning. Sixth Annual ACT-R Workshop

  6. New Study 18 students ranging from 6th to 9th grade Day 1 Pretest and Sample Problem Day 2 Sample and 4 Problems on Tracker Day 3 4 Problems on Tracker Day 4 4 Problems on Tracker Day 5 4 Problems on Tracker and Posttest Sixth Annual ACT-R Workshop

  7. New Data • No advantage for Inductive Support students on learning gain measures. BUT … During tutor use there is an advantage of inductive support on symbolization ... Accuracy and Latency Sixth Annual ACT-R Workshop

  8. New Data (Cont.) What if we look only at correct 1st attempts at symbolization? Will there still be a latency effect? What are students doing differently in these two groups? Sixth Annual ACT-R Workshop

  9. 1.3 16.6 1.3 3.1 Mean Fixations per Response(Correct 1st Attempts - No Inductive Support) Offscreen = 3.0 Fixations All other POR Regions average less than one fixation. Sixth Annual ACT-R Workshop

  10. Mean Fixations per Response(Correct 1st Attempts - Inductive Support) 3.0 2.4 Offscreen = 2.8 Fixations All other POR Regions average less than one fixation. Sixth Annual ACT-R Workshop

  11. ACT-R/PM Model-in-Progress Having only just recently completed the device interface, now reaching the point where the cognitive modeling can begin. • Relate modeling to other recent work in this area: • - Extending the work from EAPS 1 and 2 • (Koedinger & MacLaren, 1997) • - Composition effect and developmental model of symbolization by Heffernan & Koedinger (1997, 1998) Sixth Annual ACT-R Workshop

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