Adventurous Problem Solving (APS) 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. 

More
information: 

General
objective: 


Ways
of reasoning: ·
Advisable
(green arrow) From “Analysis”,
through: “Look for
applicable relations”, “Construct a
promising approach”, “Do the
calculations”, to: “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). 