Should We Teach Math?
Matthew Martin
8/16/2012 03:56:00 PM
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Apparently there has been a debate raging on whether we ought to require math for graduation in high schools and college. Andrew Hacker went on the attack against math requirements, while the self-described reformed math-phobe Jennifer Ouellette defends.
Here's my take: I'm a firm believer in what they used to call the three R's--reading, 'riting, and 'rithmatic (yes, I hate the slogan too, but that was all the rage not too long ago). That's because, in the modern era of internet, online journals, ebooks, and--ahem--academic blogging, there's really only three skills you can't teach yourself without some help. They are reading, writing, and foundational mathematics. Once you have mastered those three crafts, you can pick up a book and learn anything you want to, regardless of whether you can afford private tutors or college tuition.
Now some people struggle with certain subjects more than others. Charlemagne, who became an avid reader after teaching himself to read latin but for some reason always struggled with writing, comes to mind. That's just life--some people will breeze by in a subject and others have to put in some more effort. But while society now insists that everyone be proficient in reading and writing, we have become content about letting people slack off in math, telling them that they're just not a "math person." This ought to be alarming since, in today's economy, defining yourself as a "non-math person" automatically prohibits you from getting any of the top-paying jobs.
Not everyone needs to study differential topology. I've come to accept that. But everyone should be required to learn enough so that if they want, they could get the right set of text books (probably starting with some pre-reqs first) and eventually teach themselves topology. This means that every high schooler needs a fundamental understanding of the concepts in calculus, and some basic knowledge of proof techniques, not to mention the algebra needed to put any type of math to practical use.
That said, there are serious problems with how we teach math at both the k-12 and collegiate levels. No, that "new math" crap they keep trying to reintroduce isn't helping, and "old math" isn't the problem. The problem is that math teachers assign problems, and expect students to divine the answers to them purely on the basis of the class notes they scribbled down from the chalkboard. A far more useful exercise than having student's copy tedious definitions and explanations from the board would be to simply have them go through fully worked out example problems. I don't mean teachers should give an example problem here and there, or that they should provide answers for students to check their work. I mean that the best way to learn how to do math problems is simply to read through, step-by-step, how someone has solved math problems. Math is a language, and we ought to teach it the way we teach everyone their native language--by inundating them with examples to emulate. It is true that we don't want students to skate by merely memorizing a solution rather than understanding how to get to it, but no amount of theorems, definitions, explanations, or intuitions will match the level of understanding gained from having seen a relevant example done before.
The other big problem with how we structure math education is that we segregate certain areas of math into separate classes and call them "algebra" and "calculus" when in reality they are not self-contained topics. I will confess that nothing in algebra ever made sense to me until I took calculus and learned concepts like limits and convergence. We should start introducing calculus concepts much earlier than we do, and doing so will not only make calculus easier, but also a lot of the math courses that traditionally come before calculus.