A version of this review appeared in the January-February 2008 issue of the VaHomeschooler's newsletter. I thought it was worth keeping, especially in light of the recent news on Shanghai schoolchildren.----------
Most of us, I suspect, are less than confident when it comes to math and wonder if we've got what it takes to teach it. But I imagine Liping Ma was a little anxious, too, when, as an eighth-grader from Shanghai, she was sent to be "reeducated" by illiterate peasants in a rural Chinese village -- and quickly found herself teaching elementary school instead.
Ma's unexpected detour turned out to be a fruitful one, starting her on a path that led her to the United States to study teaching itself -- and, in particular, what it takes to be a good math teacher. Three decades after her Cultural Revolution experiences, Ma created a sensation (in math and education reform circles, anyhow) with her research on math teachers in the U.S. and China. Ma concluded, unsurprisingly, that Americans are weak in math because our elementary school teachers don't really know the subject themselves.
But Ma's book, Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States, ISBN 0-8058-290803, is far more than just a critique of math instruction in U.S. schools. It also paints a vivid picture of what really good math instruction looks like -- and it contains some hints about how homeschoolers could become pretty good math teachers, whatever their educational backgrounds.
Why on earth do I think homeschoolers (and especially those of us who rarely think of ourselves as "teachers") should read a doctoral-dissertation-turned-book comparing elementary school math teachers in the United States and China? Before I try to answer that question, here's a question for you:
Imagine you are teaching division with fractions. To make this meaningful for kids, something that many teachers try to do is relate mathematics to other things. Sometimes they try to come up with real-world situations or story-problems to show the application of some particular piece of content. What would you say would be a good story or model for 1 and3/4 divided by 1/2?
If you find this difficult, you've got plenty of company. Less than half the U.S. teachers in Ma's study could get the correct answer, much mess provide a real-world example. The Chinese teachers all got the math right, and 90% of them came up with a conceptually-correct illustration.
Ma's study is filled with a number of equally horrifying examples, but that's not the meat of her work. She goes on to examine the teachers who can handle the material -- the Chinese group -- and tries to discover what they're doing right.
Most of the Chinese teachers have what Ma refers to as a "profound understanding of fundamental mathematics." But it doesn't seem to be a result of formal education. In fact, most Chinese elementary teachers leave school at ninth grade, followed by two or three years of normal school, whereas U.S. teachers typically have at least a bachelor's degree.
Ma asserts that Chinese teachers become good teachers by teaching and by doing math. U.S. teachers are at a disadvantage here, because they are assume to emerge from the U.S. educational system knowing how and what they will teach and not needing to study any further.
Consider a third group: homeschoolers. Granted, most of us will never gain the deep, broad foundation in mathematics that Ma found in veteran Chinese teachers. On the other hand, most of us start off no worse than the average public school teacher in this country -- and we're in a better position to learn on the job. Most homeschoolers, in my experience, aren't afraid to admit they have holes in their education, and that they learn alongside their children. Also, we don't need to develop an arsenal of teaching techniques for a wide range of kids -- we just need to figure out what our own kids need.
In China, teachers devote a considerable amount of time outside the classroom studying the curriculum themselves, both to make sure they understand the material and to think about how students will approach it. This reminds me of the way many homeschooling parents approach a math curriculum, trying to view it through the eyes of the kids who will use it. (For instance, I quickly figured out that any materials containing cute and colorful visual distractions would only frustrate my child.)
Given the amount of time homeschoolers spend debating the merits of various math curricula, this leads to the obvious question: is the Chinese math curriculum superior to what's available in this country? Perhaps, but Ma doesn't focus on curriculum. The Chinese classroom looks very "traditional," and teachers there stick closely to the curriculum, but Ma says they also transcend it -- the curriculum is a framework for a great deal of discussion. This may be the most valuable message of Ma's book: they believe elementary mathematics is worthy of respect.
In this country, elementary mathematics is generally seen as a rather dull preliminary to more exciting areas, leading to a "take your medicine" approach to math -- learn the procedures, check the box, and move on as fast as possible to something more interesting. But elementary math, as a body of knowledge, is more than just memorizing math facts and learning algorithms. "Know how, and also know why," say the Chinese. Underlying the more obviously practical aspects of elementary mathematics is a connected, unified whole that is an "intellectually demanding, challenging, and exciting field -- a foundation on which much can be built," Ma writes.
What Ma suggests we need to do is slow down and appreciate math -- play with different approaches, seek out connections between concepts and the logic behind the procedures, and not accept "because that's how you do it" as the final answer. Are we, as parents who probably got a mediocre math education ourselves, really up to this? I think we are. Eventually, many of us expect our children to go beyond us in math. Perhaps we can give them some good tools to take with them, like the Chinese teachers Ma studied. She quotes one whose sixth-graders have just won a math contest:
"They did it! They solved problems that they have never learned before. They solved problems that even I myself don't know how to do! I am proud of them. But I am also proud of myself, because I am convinced that it is me who fostered their ability to explore new problems on their own -- the capacity to surpass their teacher!"
