Adventurous Problem Solving, applied in Electromagnetics Courses

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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
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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

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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 EM project leader

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Objectives

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

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Pillars

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

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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

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Internet material developed for EM

• Problems including Integration steps,
• (with recording the students 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

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Adventurous Problem Solving - 1
The Systematic Problem Solving Approach (SPA)
Ideal case
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Adventurous Problem Solving - 2
The Systematic Problem Solving Approach (SPA)
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Adventurous Problem Solving - 3
Analysis
Relations
Conclusions
Reflection
Approach
Calculations
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Adventurous Problem Solving - 3
CAI- Problems
E1 SPA Electric field of a long straight, homogeneously charged wire
E2 SPA Electric field of a segment of a homogeneously charged straight wire
E3   APS   Electric field in the point above an infinite, homogeneously charged plane (using strip or ring integration)
E4   APS   Electric field above, below and in a thick charged plane with charge density varying over thickness (using integration)
E5 APS The same, but with Gauss Law.
M1 APS Magnetic field of a uniform surface current flowing over an infinite strip with finite width.
M2 APS Magnetic field on the axis of a disk with finite radius and with non-uniform circular current density.
M3 APS Magnetic field of a long thick wire with non-uniform current density (with Amperes Law).
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Example of Adventurous Problem Solving

• Calculate magnetic field from a
• a distributed current density j
• Important steps
• analysis, symmetry,
• integration, control

Start Internet-connection
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Example of an APS General Menu
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Example of an APS Page
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Coupling with algebraic symbolic software used
for expressions and integrations

• Intelligent control on students answers possible
• More than one coordinate system
• or solution strategy acceptable
• Format of answers (expressions) flexible
• Dimension analysis and control

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Registration during problem solving
Name student, date/time, page, step, input by
student, right/wrong scoring
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Analysis of students progress
Analysis software (in Delphi) APS_matrix
Start APS_matrix
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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

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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

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APS Satisfaction
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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

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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

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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./vecto
  rs)
• Analysis of tests using co-variance formalism

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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

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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

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Adventurous Problem Solving,applied in
Electromagnetics Courses
The end