Written: Oct. 13, 2012
I have recently read in the Oct. 2012 issue of the Notices of the American Society (pp. 1205-1206), an opinion, by the president of the American Mathematical Society, Eric Friedlander, and seven other mathematics machers, protesting one of the recommendations of the report "Engage to Excel" by President Obama's Council of Advisors on Science and Technology. The recommendation was to employ scientists who use mathematics extensively in their work, as opposed to professional mathematicians, to teach math to students who are going to use math extensively in their work, but are not going to be mathematicians.
Of course they make up many "good" reasons why it is so important that mathematics should be only taught by card-carrying members of the American Mathematical Society, and/or the Math Association of America, or at worst, members of the Society for Industrial and Applied Mathematics. Because only mathematicians can competently convey the concepts of math.
Do you want to know the real reason for their outcry? They are worried about their own narrow special interest. The Math lobby, like the Tobacco lobby and many other lobbies, make up good reasons why their narrow special interests are "good" for everyone. Once in a while they happen to be right, and, by sheer coincidence, the special interests are consistent with the general interest, but neither in the Tobacco case, nor in this case of having professional mathematicians monopolize math education, are they right.
Don't get me wrong. Quite a few professional mathematicians do a good job educating future scientists and engineers (myself included), but most mathematicians are so high up in their platonic abstract Pi-In-The-Sky world that they do a poor job teaching the basic low-level math needed by future scientists and engineers. And Even those few who can relate to the future scientists and engineers, and teach them useful knowledge, are bound by a very obsolete, and mostly useless, curriculum, that teaches them useless things that computers can do so much better.
For example, this semester I am teaching
Second Semester Calculus.
To my horror, I have to teach them how to integrate using only pencil-and-paper: Integration by
Parts, Trig substitution, Partial Fractions. I keep telling them that in the real world,
in the unlikely event that they would need to integrate the function 1/(x^3-6*x^2+11*x-6) from
x=4 to x=6, they would go to Maple (or, any other Computer Algebra System) and type
and that for most integrals, not even Maple knows how to do it exactly, and one would need numerical integration, also built-in.
The reason that the Calculus Reform movement failed so miserably is that the "reformers" were still professional mathematicians, brain-washed with traditional mathematics. Hello, the computer is here! Traditional mathematics was developed without a computer. For many questions even basic algebra is not necessary. If two apples and three oranges cost seven dollars and five apples and two oranges cost 12 dollars then one can easily find the prices of these fruits by the good-old guess-and-check, i.e. by exhaustive search, write a simple double do-loop and get the answer before typing in the two equations with two unknowns.
So instead of teaching them intricate trig substitution, I would teach them (were I free to make up my own curriculum) how to solve problems using Maple (or, yet better, the free and open-source system called SAGE).
If you really care about a deep conceptual understanding, then why stop with mathematicians? Let philosophers teach math! Now they reall care about the deep meaning, e.g. of the number three, that the average member of the Amer. Math. Soc. takes for granted.
So President Obama, my advise to you is to listen to the wise recommendations of the above-mentioned committee and not to the professional math lobby, who just makes up many "good" reasons why mathematicians are indispensable, but their true motivation is to increase, or at least maintain, the number of professional mathematicians, so that they can badly teach calculus six hours a week, and spend the rest of their time publishing yet another theorem that only six people (at most!) in the world can understand, or care about.