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Math Considerations

Publication Date: 2007-12-11

Norm's remarks were posted on EDDRA, Dec. 11, 2007. He gave me permission to post them here. They are certainly worth reading.

I'm Norm Matloff, a computer science professor at the University of
California, Davis. Math has been and is a big part of my life. All my degrees were in
math. After my doctorate, I became a math professor, later a statistics
professor, both professions that are clearly mathematical. Later still
I moved to computer science, a field which is putatively mathematical.
And I definitely believe in the "cultural" value of math; more on this
below. So, I don't have to be sold on the subject.

Yet those who say that most jobs that seem to be "mathematical" in
actuality rarely use math are correct. Most engineers, for instance,
never use calculus in their work--quite contrary to what most people
would expect for such a basic freshman subject in engineering curricula.
And I would say that fewer than 1% of computer science graduates ever do
any kind of formal math in their entire careers.

This is even true in research. There are over 30 faculty in my
department. At most six or seven of them use college-level math in
their research; most never use it, and in fact would plead ignorance if
you asked them to work a calculus problem, much less something like,
say, group theory.

A poster argued, though, that there is a "cultural" value to math.
People use it, albeit informally and at a nonadvanced level, in their
work, and even in their daily lives. I fully agree with that, and would
add that math can make one a sharper, more logical and more insightful
thinker, even in such things as political arguments.

HOWEVER: Unfortunately, I disagree with the implicit claim that the
more math a student takes, the more "cultural" benefit he or she
derives. The key word in the last sentence of the preceding paragraph
is "can." After three decades in academia, I've come to the conclusion
(which I did much earlier, of course) that the vast majority of students
derive little if any such "cultural" benefit. As the saying goes, "You
can lead a horse to water but you can't make him drink." As a much
less-known saying (known mainly to me and the one who stated it) puts
it, there is "the phenomenon of high [test] scores, low ability."
("China's New Engineering Obstacle," by Chen Lixin, an engineering
professor in China, Prism, pub. by the American Society for Engineering
Education, September 1999.)

A central factor underlying this is the obsession with test scores. I
do believe that standardized tests have value, but that all-too-familiar
problem of "teaching to the test" is very, very real.

Let's again use calculus as our example. Most of the better students in
high school nowadays do take calculus there, as an Advanced Placement
(AP) course. AP is death to careful, thoughtful inquiry. There is a
rush to cover the entire material by May, when the national AP exams are
given, thus no time to stop and ask, "What does this really mean?" And
since the AP exam is given in a multiple choice format, there are very
few test problems that probe the "What does this really mean?" issues.
And in turn, since these are not on the national AP exam, the teachers
have no incentive to cover them, and the students have no incentive to
think about them.

It's a bit better in some university calculus courses, but since those
courses tend to be large--easily 500 or more in big universities--the
exams are again multiple choice, so we still have the same problem.

I just read today that Congress wants to spend $43 billion (yes, billion
not million) in the next few years on improving math and science
education at the K-12 level. I believe that money would be much better
spent in numerous other areas.

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