Adventurous Problem Solving (APS)

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How to make university students solve physics problems requiring mathematical skills (especially integrations over charge and current distributions in 1, 2, and 3 dimensions (lines, surfaces, volumes).

Keywords: Electricity, Magnetism, charge elements, current elelements, Gauss' law, Biot Savart Law, Coulomb Law.

The files can be used freely, provided you promise to be so kind as to mention the name of the author and not to change the files without consulting the author.

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General objective:

  • Students frequently experience problems in mastering techniques for applying mathematical skills into physical problems. Notorious difficulties arise with integration problems of electrical charges or currents to electric and magnetic fields, or integration of those fields to energy patterns.
  • Accompanying mathematical courses mostly focus onto mathematical contexts, and the relation with physical applications remains vague.
  • This project offers students a framework to develop those skills by self-study.
  • The method, especially developed for this goal, is Adventurous Problem Solving. This method resembles adventurous games, in which the student has to find out how to proceed on his own.




Ways of reasoning:


·        Advisable (green arrow)

From “Analysis”, through:

“Look for applicable relations”,

“Construct a promising approach”,

“Do the calculations”,


“Conclusions about results in relation to expectations”.


·        Adventurous (blue arrows)

Frequent moments of reflection, alternated by excursions to activities, necessary for the process of solution.





Observed problem solving behaviour:


·        Professionals  (e.g. lecturers)

tend to follow a systematic approach from “Analysis” to “Conclusions”.


·        Students (especially when fresh)

hardly perform a thorough “Analysis”,

tend to stay avoid the “Approach”- middle stage and have troubles in reaching “Conclusions”.




Example of “ways of reasoning” ,

(direction clockwise)

·        dark gray: performed by a student

·        light gray: professional


(I)A  = (intro) analysis of physical situation,

KR    = explore key relations,

SP    = physics handling of key relations, to reach an accessible way to success,

WO = work out,

SP4 =  further calculations to numerical result,

C      = physical check of result,

E      = end result, conclusion.



The middle stages (“what relations do I need, and what can I do with them?”) get less attention.

This student was stuck in the introductory stages, and (later) in performing calculations in an almost random way (without a definite plan).