[Phys-L] Re: student mathematical capability

[John M Clement <clement@HAL-PC.ORG>]

What is missing is the student understanding of math.  They come in
having memorized math manipulations, but have absolutely no idea of
what they are doing.  For example HS seniors have memorized the
formula for the circumference of a circle, but as soon as they have to
use it outside math class they no longer know it.  As them to
calculate the working done when a father pushes a merry go round in a
park with a given force for 2 revolutions.  The picture shows the
situation with the diameter specified in the picture.  Students will
often give the distance as twice the diameter for going around.  Then
some students will use the formula for the area of a circle.

I make them measure around the circle and estimate the distance.  They
usually come up with something like 3.25 times the diameter and only
after I say is there a math number like 3. something that might apply
will they remember Pi.

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.

When I point out that the students need to do measurement like
wrapping a string around a can and comparing the circumference to the
diameter I am always told there is no time to do that.  Well then
there is no time to get students to really understand.  The math
curriculum becomes useless and irrelevant.  Question:  why learn how
to solve difficult equations if you can not write a simple equation?
 After all any decent computer can solve any basic math equation, but
they can not yet write an equation from a description.

John M. Clement
Houston, TX


> > ... VAST majority of intro-level students ...
> > ... except for a gifted (or perverse) few ...
> > ... students for which the Pythagorean Theorem is 'heavy math'
>
> Hmmmm.  IMHO if physics students find the Pythagorean theorem to be
> a burden,
> this is a problem.  This problem cannot be solved by dumbing down
> the physics
> curriculum.  The advising system should be set up to ensure that
> such students
> take remedial math now, and not take physics until later.  If there
> is a
> breakdown in the advising system, the problematic students should be
> identified
> early in the year, so they can make a timely transfer out of physics
> into remedial
> math.
>
> ======================================
>
> As a secondary, less-useful line of inquiry, I am confused about how
> such a
> problem could possibly arise in the first place.
>
> 1) According to
>   http://www.saintmarys.edu/~admoff/General/
> incoming freshmen are required to have taken three full years of
> high school math.  Presumably the least-aggressive sequence of HS
> courses would be
>     -- Algebra I
>     -- Geometry
>     -- Algebra II / Trig
> and other more-aggressive sequences would only support my point
> (below)
> more strongly.
>
> 2) Also, according to
>   http://education.yahoo.com/college/facts/8462.html
> some 82% of incoming freshmen have SAT math scores over 500.
>
> 3) We are told that by the time the students get around to studying
> relativity in physics class, "the Pythagorean Theorem is 'heavy
> math'"
>
> I find it difficult to reconcile point (2) with point (3).  One
> might consider
> the hypothesis that primarily the least-math-capable students --
> i.e. the
> bottom 18% -- sign up for physics.  But that seems unlikely.
>
> I find it even more difficult to reconcile point (1) with point (3).
> A
> possible hypothesis is that students who could have handled the
> Pythagorean
> theorem on the day they arrived can no longer do so, because they
> have
> become less skillful during their time at college.
>
> I'm confused.  What am I missing?
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