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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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• 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”

CONECT

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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

CONECT - UT

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• 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

Objectives

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1. “Integrating Mathematics in Physics”

2. “Adventurous Problem Solving”

3. Additional to normal teaching activities (classes, etc.)

Pillars

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“Integrating Mathematics in Physics”

• scalar and vectorial integrations

• multidimensional integrationsusing 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 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”

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“Adventurous Problem Solving - 1”

The Systematic Problem Solving Approach (SPA)

Analysis

Relations

Approach

Calculations

Conclusions

“Ideal case”

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“Adventurous Problem Solving - 2”

The Systematic Problem Solving Approach (SPA)

Analysis

Relations

Approach

Calculations

Conclusions

“Student” “Professional”

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“Adventurous Problem Solving - 3”

Analysis

Relations

ApproachCalculations

Conclusions

Reflection

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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 “Ampere’s Law”).

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Example of: ”Adventurous Problem Solving”

1. Calculate magnetic field from a a distributed current density j

2. 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

1. Intelligent control on student’s answers possible

2. More than one coordinate system

or solution strategy acceptable

3. Format of answers (expressions) flexible

4. Dimension analysis and control

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Registration during problem solvingName student, date/time, page, step, input by student, right/wrong scoring

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Analysis of student’s 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 InterfaceGeneral satisfaction about

• navigation • interaction• presentation of information

Less satisfaction about • Demands for use of precise notation implied

by algebraic software

Satisfaction about• The type of problems in CAI• Feedback options• Help pages

Contents

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APS Satisfaction

Statements

Num

ber

of

stu

dents

(%

)100

80

60

40

20

0

Certainly do

not agree

Do not agree

Neutral

Agree

Entirey

agree

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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./vectors)• 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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The end

Adventurous Problem Solving,applied in Electromagnetics Courses