In a nice conversation about writing for education, Adam Gidwitz (the author of A Tale Dark and Grimm) pointed me to The Mathematician's Lament. The book makes (much more clearly than I) a point I have been making informally for years: If you want students to know and love math, you definitely should not teach it in school! (Same for literature.) The mathematics requirements in school empty the subject of its meaning and point, and are useless to boot. How many non-scientists use the quadratic formula, ever? Discovering the formula would be fun, using it is a drag (and exceedingly rare).
ps. Maybe the point of math education is not to have them enjoy or love or even like it.
ReplyDeletepps. You could consider banning math from school; then it might become as exciting as smoking in the bathroom!
I think the point about mathematics being taught in a more practical way is an excellent one.
ReplyDeleteMy first "applied" mathematics/numerical methods course was a real eye-opener. The professor emphasized the equivalence between "exact" analytic solutions (i.e. the integral tables, trigonometric identities, and other tricks we spend years learning in school) and "approximate" numerical solutions (techniques for solving problems that make good intuitive sense and can be easily implemented with computers).
I think it would be a tremendous improvement if secondary school curricula focused more on the latter. I, for one, found problem solving in that way to be more engaging, hands-on, and closer to what scientists and engineers do in the real world.
I have mixed feelings about the math education ideas expressed in The Mathematician's Lament (essay version http://www.maa.org/devlin/devlin_03_08.html ). My experience tutoring, TAing and teaching suggests that the vast majority of students care even less about pure mathematics than they do about Algebra I. The students who are mathematically inclined and generally enjoy or are at least minimally annoyed by problem sets are happy to delve into the theory behind the mechanism and get a deeper understanding. That many mathematically-inclined students join math clubs in which more pure or at least creative math is taught (the common counter to "kids don't like math") does not apply to the median student who would rather play soccer.
ReplyDeleteWhen one thinks about what the average person knows (or needs to know) about math, the 12 years and 2000 hours of math education that a typical American goes through seems woefully inefficient. Perhaps we should be teaching people +-*/ and the area of a rectangle and shoving them out the door as David suggests. Realistically, I think this is what 95% of what most people use.
However, if we applied this level of pragmatism to other fields, we would have a population that could read road sides, only vaguely understood how their votes related to the government and only knew presidents Washington, Lincoln, FDR, Bush and Obama.
I think a deeper (longer, more painful...) education is necessary to insure a broader understanding of the world even if the person does not apply what they learned in a concrete way. Also, we need to make people work on a subject for at least a few years to insure that the future engineers realize that they are good at math, the future writers realize that they are good at writing, etc.
So what math do we teach for twelve years? I think repetitive calculation is not the root of the problem, but rather the flower. Learning to think creatively requires real feedback and that one be able to set ones own pace and path. But how is a teacher supposed to teach 30 people of varying abilities simultaneously? Explain interesting proofs that only 6 students get? Work on a students individual project for 2 minutes a day?
Certainly, some group activities and project-based learning could help the situation. And it's a shame that we don't pay teachers competitively, insuring that most mathematically inclined individuals will forever say "screw it, I'd rather go into investment banking." But I think the root of the problem is that we have an overly efficient education system based on the mass production model that can't allow for creativity or individuality. I think fixing this basically requires a massive increase in education spending and the idea that we have to evaluate students subjectively and individually and not only with objective tests.
I guess i mis-spoke I didn't mean to suggest that we only teach useful math; I was suggesting that we not teach math if the effect of that teaching is to cause students to hate it.
ReplyDeletehttp://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html
ReplyDeleteThis reminds me of what you are talking about. The teacher is allowing students to "discover" mathematics themselves by solving real word problems. The other short talk is this one.
http://www.ted.com/talks/arthur_benjamin_s_formula_for_changing_math_education.html
His idea also reflects what I think you are getting at that forcing math that very few students will actually use is not productive. Very few people have to do an integral after high school, but everyone takes chances.