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[Phys-L] Re: student mathematical capability



I'm still wondering about the testing, admissions, and advising angle.

Why does the college admissions office require the incoming freshmen
to have taken three years of high-school math, if the kids didn't
learn anything worth knowing in those three years? Why bother to ask
for a high-school transcript at all?

Why does anybody care about SAT math scores, if kids can get good scores
without understanding anything about math? Why should the kids take
the test? Why does the admissions office ask to see the scores?

Ditto for all the "standardized" statewide "proficiency" tests that
the Feds require. What's the point?

Ditto for the advising and course-selection process. What is the
point of trying to teach relativity to kids who cannot solve one
linear equation in one unknown? It seems like a misapplication of
resources. How hard would it be for the advisor to figure out that
the student cannot solve one linear equation in one unknown?
Nevermind a test, how about a questionnaire that asks, yes or no,
do you think you can work a story problem that involves one linear
equation in one unknown? Those who answer 'no' should take a remedial
math course; they can take physics some other time.

There is a small trade school in Pasadena that mails its own
"placement exam" to each incoming freshman over the summer. It's
a closed-book limited-time honor-system test, and forms the basis
for decisions about which courses the student should take. (This
exam does not even remotely resemble an SAT.)

It is worth thinking about the math-phobic and story-problem-phobic
teachers Peter S. and Michael E. described. I'll bet the state
solemnly certified them as "highly qualified".

Maybe I'm old-fashioned, but I don't like being swindled. If a
student gets a good grade in the course but can't do the work, it's
a swindle. If the student gets a good grade on this-and-that
standardized test but can't do the work, it's a swindle. If the
teachers are certified as "highly qualified" but aren't highly
qualified, it's a swindle.

================

Returning to the testing angle: I'm not a big expert on designing
tests. But anybody with even infinitesimal expertise and/or teaching
experience can see the problem with the SAT -- a blind person could
see it instantly -- it tests the ability to do 60 easy problems.
It hardly even attempts to test the ability to do not-quite-easy
problems. The "new SAT" changes this only marginally if at all.
There is a fundamental structural problem because all the questions
are worth one point apiece; students who encounter a "hard" (i.e.
not super-easy) question are well advised to just skip it. Even
if they're gunning for an 800 (which most of them aren't) they
should skip it and come back to it at the end if there's time.
You don't need to be a test-designing genius to realize that if
some of the questions are five times harder than others, they ought
to be worth 5x more points. (This is only /one/ of the things you
need to do ... assuming you don't want to encourage breadth without
depth.)

The guys at collegeboard.com claim to be experts in test design,
and they've been doing this for decades, yet apparently they haven't
figured this out ... what a crock!

I've only see a few of the statewide tests. They seem even lamer
than the SAT ... with the exception of the NY Regents tests, which
seem better (but not as good as they used to be).

As I've said before, teaching to the test may or may not be a bad
thing, depending on the test. I unabashedly teach to the test (with
a few add-ons) when training private pilots and commercial pilots,
because I think it is a good test. In contrast, for high-school
math and science, we need better tests. Muuuch better tests. Now.
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