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Adventurous Problem Solving, applied in Electromagnetics Courses

Adventurous Problem Solving, applied in Electromagnetics Courses. F.F.M. de Mul, C. Martin i Batlle, I. de Bruijn, K. Rinzema University of Twente Department of Applied Physics Enschede, the Netherlands. CONECT. cooperation between Physics Departments of

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Adventurous Problem Solving, applied in Electromagnetics Courses

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  1. Adventurous Problem Solving,applied in Electromagnetics Courses F.F.M. de Mul, C. Martin i Batlle, I. de Bruijn, K. Rinzema University of Twente Department of Applied Physics Enschede, the Netherlands

  2. CONECT • cooperation between Physics Departments of • Universities of Twente / Delft / Amsterdam (VU) / Utrecht • objectives: • development of Physics CAI for exchange via Internet • 1997-2000/1 • UT-project: • “Integrating Mathematics in Physics Teaching”

  3. CONECT - UT • Project group: • C. Martin i Batlle Ph.D-student: research • K. Rinzema postdoc: development • I. de Bruijn didactic support • M.J. Peters magnetism • F.A. van Goor optics • F.F.M. de Mul E&M ; project leader

  4. Objectives • development of self-service education • to improve mathematical understanding and skills, • especially for use in E&M • using symbolic algebraic software • in the form of separate learning activities • all via Internet

  5. Pillars • “Integrating Mathematics in Physics” • “Adventurous Problem Solving” • Additional to normal teaching activities (classes, etc.)

  6. “Integrating Mathematics in Physics” • scalar and vectorial integrations • multidimensional integrations • using physical integration elements • Gauss, Stokes, Ampere – laws • underlying mathematics: • coordinate systems, vectors, -products, • grad, div, rot, • 3D-viewing

  7. Internet material developed for E&M: • Problems including Integration steps, • (with recording the student’s steps): • “Adventurous Problem Solving” • Exercises on Math applications in Physics • PPT-presentations of classroom problems • PPT-presentations about notoriously difficult subjects • Special Presentation: “Magnetism in orders of magnitude”

  8. Analysis Relations Approach Calculations Conclusions “Adventurous Problem Solving - 1” The Systematic Problem Solving Approach (SPA) “Ideal case”

  9. “Professional” “Student” Analysis Relations Approach Calculations Conclusions “Adventurous Problem Solving - 2” The Systematic Problem Solving Approach (SPA)

  10. “Adventurous Problem Solving - 3” Analysis Conclusions Relations Reflection Calculations Approach

  11. “Adventurous Problem Solving - 3” CAI- Problems:

  12. Example of: ”Adventurous Problem Solving” • Calculate magnetic field from a • a distributed current density j • Important steps: • analysis, symmetry, • integration, control Start Internet-connection

  13. Example of an APS General Menu

  14. Example of an APS Page

  15. Coupling with algebraic symbolic softwareused forexpressions and integrations • Intelligent control on student’s answers possible • More than one coordinate system • or solution strategy acceptable • Format of answers (expressions) flexible • Dimension analysis and control

  16. Registration during problem solving Name student, date/time, page, step, input by student, right/wrong scoring

  17. Analysis of student’s progress Analysis software (in Delphi): “APS_matrix” Start APS_matrix

  18. Evaluation • Interviews with students about • User Interface • Contents of the Internet course • “Adventurous Problem Solving” versus Systematic Problem Solving Approach • Results and Efficiency • Experiments to measure the Learning Effect • Various tests at various times during course

  19. User Interface • General satisfaction about • navigation • interaction • presentation of information • Less satisfaction about • Demands for use of precise notation implied • by algebraic software Contents • Satisfaction about • The type of problems in CAI • Feedback options • Help pages

  20. APS Satisfaction

  21. “Adventurous Problem Solving” versus Systematic Problem Solving Approach • Two conflicting opinions: • Pro APS (69%) • “you have to come up with your strategy yourself” • “better overview for figuring out the strategy” • Contra APS (29 %) • “messy” • “to learn the structure of problems you need a • structured and pre-described strategy”

  22. Results and Efficiency • CAI-problems using APS: • are complementary to the course • are tackled in a more elaborate way than on paper, • especially the Analysis stage • improve the Math skills with a factor proportional to • the time invested • but: are considered less effective for problem solving • than special “problem tutorials” and the study of worked-out problems

  23. Learning Effects (1) • Aim • Measuring learning effect of CAI in • “Integration Mathematics in Physics” • Method • Experimental and control group • Two tests (begin / end of course) • Open questions/problems • Various math subjects (diff./integr./coord./vectors) • Analysis of tests using co-variance formalism

  24. Learning Effects (2) • Results • The experimental group shows: • improvements in skills about: • coordinates, differential elements, integrals and dimensions • no difference with control group concerning vectors • no improvement in differential operators (grad/div/rot) • After the exam both groups have the same level

  25. Learning Effects (3) • Conclusions • CAI has profound effect, especially at beginning of the course • Important advantage • During the course, students are less hindered by insufficient math skills, and can concentrate on Physics

  26. Adventurous Problem Solving,applied in Electromagnetics Courses The end

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