[Phys-L] Re: student mathematical capability

[Rick Tarara <rtarara@SAINTMARYS.EDU>]

Well John, it is clear that you haven't taught any 'liberal arts' or high
school physics for a while (if ever), if you are not aware of the abysmal
state of math skills amongst college students (many but not all, of course).
For example, this week we are doing a free-fall experiment where we
ultimately want to graph the velocity versus time for a ball that has been
dropped from different heights (H).  That because the initial velocity of
the ball is zero and by using the kinematics equations that  H = 1/2(vi +
vf)t  to find that the instantaneous velocity just before hitting the ground
is 2H/t is mysterious to at least half my gen-ed class.  They 'get' H/t as a
velocity, but keep asking where does that '2' come from.  This same group
grabs the calculator to multiply by 10 and are mostly helpless when posed
with a problem such as 'a ball weighs 100 N on the surface of the earth, if
moved away from the surface by a distance equal to the radius of the earth,
how much would it weigh?'--even if you give them the Newtonian gravitational
force equation (no, not the 4space curvature equation ;-).

Rick



----- Original Message -----
From: "John Denker" <jsd@AV8N.COM>
To: <PHYS-L@LISTS.NAU.EDU>
Sent: Wednesday, September 14, 2005 11:05 AM
Subject: student mathematical capability


> Rick Tarara wrote in part:
>
> > ... 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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