This article from The Toronto Star exemplifies the ever-pervasive group-think about why the traditional method of teaching math won’t work.
From the article:
“Many parents want to get rid of “discovery math,” broadly defined as “doing it weird.” If only that loopy Liberal government would teach math the way we learned it when we were kids, the theory goes, there’d be no problem. Sure, great, except for one thing. Very few parents I’ve met can perform more than the most rudimentary arithmetic for themselves. If you all learned math so well, why do you inch toward Junior’s algebra homework with a cross and a bulb of garlic?”
First of all, not all parents are like that. Second of all, there are some aspects of math that parents haven’t done in a while, so they are rusty. Unless you use something often, you forget how things are done. I myself have to brush up on percentages if I haven’t worked with them for a while. Same with calculus, linear algebra and other topics. It doesn’t stand as proof that the traditional method failed. Also what does he mean by “very few parents I’ve met”?
He goes on:
“This summer I made my stepson spend some time on Khan Academy, an educational website, to brush up his math before he enters Grade 8. He was briefly baffled by questions that asked, say, 6 1/4 – 3 3/4. One way to do it is to convert both sides to improper fractions. But it’s easier if you simply recognize that 6 1/4 is the same as 5 5/4. You can do the differences in your head in about two seconds. The question is, how do you produce the kind of students who will make that insightful leap?”
Khan Academy is very traditional–a detail this author conveniently ignores. And recognizing that 6 1/4 is the same as 5 5/4 comes after being instructed in the procedure (which Khan provides) and practicing with it. It doesn’t come intuitively for most people. So that “insightful leap” as he puts it, is more like procedural fluency giving way to doing it in your head–as he likely learned it years ago.
He goes on:
“All I know for sure is that you don’t do it by teaching a bunch of rules students will learn by rote — the beloved “old-fashioned way.” That may work for basic math facts….But very quickly, math becomes so complex you can’t have a rule for everything. Khan Academy teaches and tests 111 different skills at the fifth-grade level alone. You’d go crazy learning a rule for each skill. You must be able to intuit a useful method for each situation.”
And many of these skills grow from basic traditional instruction in procedures which give way to transfer. He ends on this note:
“Second, support students by giving them more practice time. The only way to learn how numbers work together is by tackling incrementally more difficult questions, lots of them, over time. Kids need to practice insight just as their parents practiced times tables.”
If what he means by practicing insight is practicing procedure which in many cases leads to understanding, well then: I guess he and I are saying the same thing: Traditionally taught math works well.