Teaching Math

April 1, 2008

Most people assume that mathematicians know how to teach math, but how much expertise do the practitioners of a discipline have in the teaching and learning of that discipline? Certainly they have gone farther in their study of mathematics than the rest of us, but does that experience qualify them as experts on how the rest of us learn, or the best way to get us to learn?

I ask this out of genuine curiosity and concern. The mathematics teaching community has become highly polarized in recent decades over the “right” way to teach math (as if there could be just one “right” way). Each camp angrily challenges the ideas put forward by the other camp. And bystanders are forced to deal with an uncomfortable truth: if one camp of mathematicians is right, then the other camp, i.e., a large number of mathematicians, are necessarily wrong.

If you think I exaggerate, consider this quote from a recent interview in Science (21 March 2008, p. 1605), “Larry Faulkner has successfully steered the National Mathematics Advisory Panel through some of the roughest waters in education” (my emphasis). Getting mathematicians to agree on how and when algebra should be taught is apparently a very, very tough job.

If you would like to read the report they produced, go here. Here are a few highlights of Science magazine’s interview with Larry Faulkner:

  • “The 19-member panel was supposed to rely on sound science …, but only a relative handful of the 16,000 studies it examined turned out to be useful. The vast majority, says Faulkner, were of insufficient quality, too narrow in scope, or lacked conclusive findings. The literature is especially thin on how to train teachers and how good teachers help students learn.”
  • Q (Science): Why do so many students have trouble with fractions? A (Larry Faulkner): Fractions have been downplayed. There’s been a tendency in recent decades to regard fractions to be operationally less important than numbers because you can express everything in decimals or in spreadsheets. But it’s important to have an instinctual sense of what a third of a pie is, or what 20% of something is, to understand the ratio of numbers involved and what happens as you manipulate it.”
  • Q: How could schools lose sight of that? A: Well, they did.”
  • Q: What’s the panel’s view on calculators? A: We feel strongly that they should not get in the way of acquiring automaticity [memorization of basic facts]. But the larger issue is the effectiveness of pedagogical software. At this stage, there’s no evidence of substantial benefit or damage, but we wouldn’t rule out products that could show a benefit. If a product could be demonstrated to be effective on a sizable scale under various conditions, the panel would be interested.”
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