Thursday, September 8, 2011

How to (what?) Our Math Education?!!?

Having concern for the state of mathematics education here in America is such a common thing among the population that there are probably almost as many ideas for a solution as there are people with concern. And while the issue is unsettled, it is great to have voices loud enough to keep the discussion lively and vogue. A recent (August 25) addition to the discussion is the New York Times Op-Ed piece
How to Fix Our Math Education
by Sol Garfunkel and David Mumford. I guess it is a hit piece on the No Child Left Behind initiative, but more it is an indictment on the standard idea of teaching math for math's sake at the elementary and secondary level. Their view seems to be that since mathematics was developed in tandem with science and applications, it should be taught that way. Bringing in the deep conceptual beauty of mathematical relationships in a class focusing on engineering or finance would better serve the students' educational needs rather than teaching the pure elements of, say, algebra in their own right.

I will let you read the article and form your own conclusion. My take? Little can be farther from the truth! The applications of mathematics are many, varied and beautiful. But the essence of mathematics is the study and development of pure rational thought. It is precisely the abstract nature of pure mathematics that should be taught to young students in our schools. And it should be taught as an art at every level, with applications only to serve as neat ways to display its innate beauty. The lack of a cohesive story about abstract mathematical relationships and patterns in our math class sequences is what fails our educational systems today. And not the fact that we do not apply math correctly. This is just my opinion.

I found the letters in rebuttal to this article of most interest to me: Read here for some of them:
Math = The Practical and the Beautiful
One real money quote that gives away my take on this whole business? From the Computer Scientist Jonathan David Farley's letter at the end:
You do not study mathematics because it helps you build a bridge. You study mathematics because it is the poetry of the universe. Its beauty transcends mere things.
Pure candy, that quote is!!


Jake said...

And poems aren't just sets of words that rhyme. Sure, rhyming is part of it, but we don't read Shakespeare for the rhymes. If all that high school students are taught is cookie-cutter equations and the shapes they can make (which is what this "applied math" curriculum seems to reduce to), then how will they fare baking a math cheesecake? To solve real-world problems - which are never cookie-cutter compliant - requires understanding. Otherwise, how will students solve the problems (not just in math) no one has ever seen before? Sure, if I had just learned physics, and not paid attention to the finer mathematical details, I would still know how to solve lots of physics problems. But throw in some of those details, and that's the difference between "I wonder why the potential of an infinite line charge is logarithmic" and "Hey! It's the fundamental solution to Laplace's equation with n=2."

Richard Brown said...

Well said, Jake. Certainly, our educational system in mathematics needs a thorough review and reformation, in my mind. Not that that will happen. But really, if designed from the ground up, the process of self-discovery of mathematical concepts, the importance of talking about mathematics as a way of learning mathematics, the rigorous development of the formal relationships among mathematical ideas through inquiry and initially through intuitive reasoning would not be things only brought in when one reaches the senior level in university.

Math is not really about solving problems. It is about understanding structure. Once the underlying structure of any complicated thing is well-enough understood, knowing how to say something conclusive about it becomes the consequence. It matters not at all if the thing one is studying involves numbers or not.