Re: Go figure

["Daniel L. MacIsaac" <Dan.MacIsaac@Nau.Edu>]

> On Friday's quiz my 'liberal arts' bunch did VERY well predicting the
> relative brightness on one light bulb in parallel with two other bulbs in
> series.  However, (without calculator) they had mild difficulties with
> finding the total resistance of two 10 ohm resistors in series and _extreme_
> difficulties with the resistors in parallel (despite having worked with such
> combinations in lab the same week).
>
> Last year, my 'science majors' class would have had no trouble with the
> series and parallel but much more with the light bulbs.
>
> ?  Rick
A pair of related tales:
For nonmajors: 
My students also can conceptualize current flow and division
between branches accordind to resistances in the parallel case.  They
can orally convince me they follow this reasoning and can recapitulate
it even in new circumstances.

However, I have a disconcertingly large number of students who can't do
the algebra for this situation.  I routinely get 1/R1 +1/R2 = 2/(R1+R2)
kinds of responses or RT = 1/R1+1/R2 as a response.  I really believe
they understand a lot of the physicality of what is happening, but cannot
solve the algebra required.  They have passed algebra requirements but many
taking freshman physics for nonmajors are upper-division bio/premed people
who have not taken algebra for years. They have delayed the situation, and
are justly phobic and often highly and distressingly :^|  articulate due 
to their recent background course choices. 

For majors:
I had some majors tutoring my nonmajors last semester.  One problem was
calculating the work done moving an electron on various paths between 2
plates of an ideal parallel-plate capacitor.  I had worked on grav<>V 
comparisons a lot, and the majority of my students could explain what 
was going on to my satisfaction and why the work was path independant 
for this problem (starting on one plate ending on the other).  When they
asked a major for assistance, she set up a complex path integral and solved
it (frightening my nonmajors to death :^) and then thought it was
interesting she got the same solution as did the nonmajors using the 
endpoints.  So the majors had little conceptual understanding or appreciation
for the physicality of the problem, but could do the math like nobody's
business.

I believe there are two kinds of learning happening here, both are required.
I think I'd like to start mathematically screening my incoming students
with problems akin to those needed in intro physics for nonmajors (like
trig and algebra) and then apply screening results to advising.  Are there
studies published anywheres describing such an approach people could 
recommend?
 
Dan M

Dan MacIsaac, Assistant Professor of Physics and Astronomy, Northern AZ Univ
danmac@nau.edu  http://www.phy.nau.edu/~danmac/homepage.html