[Phys-L] Re: student mathematical capability

[Rick Tarara <rtarara@SAINTMARYS.EDU>]

----- Original Message -----
From: "John M Clement" <clement@HAL-PC.ORG>
> Basically math is taught as an abstract subject with very little
> physical connection.  I habitually hear from the math teachers "Why
> didn't they understand it after I told them?"  They never seem to get
> the connection between telling and not understanding.

Most definitely!  It seems that from elementary school on, far too many math
teacher religiously avoid the 'word problems' in their books.  Anecdote
time:  I recall that a bunch of us physics majors were taking a linear
algebra course as sophomores, and well into the course we asked the prof if
he could provide any practical examples of what we were doing (matrix
algebra at the time).  He really couldn't!

These problems are almost as bad with our calculus level students--who at
least are reasonably good at doing the algebra, but who struggle mightily
with setting up 'real world' problems and _really_ have trouble setting up
anything that requires the Calculus.  Oh, they can do integrals, they just
can't set up one for a given physical situation--at least not early in the
course.  We work very hard at that kind of thing.  We also use numerical
methods (spreadsheets) to approach more complex problems, trying to break
the physics down into simplified chunks that can be calculated in a straight
forward manner.  We just started this where we first try to calculate the
time and speed of a bowling ball dropped from 100km above the earth.  Step
1:  No air resistance but 'g' as a function of height.  Step 2:  Add in air
resistance, but with a constant 'b' factor, but playing with the 'v'
dependence.  Step 3: Use a linear dependency for the air density and
calculate 'b' as a function of height.  Later we collect data from dropping
a large, light ball and model it using the results obtained from the earlier
spreadsheets.

In the liberal arts courses, the problem is ALSO often the fact that we have
3rd and 4th year students who haven't seen or used geometry for 6 years nor
algebra for 3-4 years.  Of course, algebraic ratios are a mystery to almost
all students at all levels!  ;-(

Rick
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