At the first open house of the school year, I had the misfortune to listen to my kid’s teachers talk about the much-maligned multiple methods in math. The topic is controversial with American parents, but judging by what I’ve see so far (my oldest is a third grader) I find multiple methods old school. When I was growing up it was known simply as math, and now half of my class is in the US on H1B visas. The problem with implementation of this teaching strategy is not with the approach itself but with the teachers, and, I suspect, Department Of Education bureaucrats, who have only faintest grasp of the idea and cannot adequately explain it to parents what it is.
“There is more than one way!” gushed our third grade teacher. “Students can memorize that 9+3=12 or they can draw the number line which will help them visualize it.” Then she dropped the name of some DOE honcho who appeared in some video explaining how there is more then one way in math, and, similarly, there is more than one way in humanities. I’m paraphrasing the teacher here, and no, I didn’t catch the name of that DOE character and I didn’t see the video.
Our teacher was excited about the plan to have the class write an essay arguing whether or not it’s OK to wear two different socks. Sure, it’s OK to wear two different socks and such behavior is not a crime, and kids will have fun developing wacky arguments both pro and con. Yet one can write a well-argued essay proposing to eat Irish babies, which, of course, doesn’t mean that we can take such a proposal seriously. There will be wrong answers in humanities, especially once we get out of the realm of tastes. I hope the teacher doesn’t believe that “more than one way” means “anything goes”, but she didn’t make the distinction.
Her metaphor for math was off, too. Yes, multiple methods enables students to experience math in different ways. But it doesn’t mean that, as she says, there is more than one way, as much as it means, as my math teachers used to say, that all roads lead to Rome. My math teachers weren’t touchy-feely Californians. One was a hard-nosed blue-stocking and another rode his T-34 all the way yo Berlin. But they, my math teachers, were romantic about their discipline.
Yes, 9+3 is 10+2, but 10+2 is no more no less than a convenient shortcut or a way to check oneself. At the end it’s about 9+3. There is a beauty in math, I was taught, in learning that all methods will produce the same result, that everything checks out. This is quite different from developing an argument about a favorite book where well-argued answers will wary. Hosiery decadence is a different matter entirely.
All roads might lead to Rome, but, although the Romans built very good infrastructure, not all roads are created equal. As students learn more math they will find that there ways to prove a theorem that will do, and then there are elegant solutions. Again, beauty (and joy) in math. For now knowing that we don’t write checks in X’s and 0’s is sufficient. Arabic numerals are still tops.
It’s only natural that after decades of centrally-imposed failed experiments in math education American parents are suspicious of the currently promoted multiple methods. It doesn’t help when teachers mention multiple methods in one breath with new math without reassuring the parents that the two are not the same. That’s what ours did, anyways. And then she invited us to come talk to her if we have any questions. If she has questions — as she should — she is welcome to make an appointment with me.