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Math Considerations

Posted: 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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