I’m writing on Christmas Eve day, and I’m sure by the time you read this we are long into 2012 and possibly past it. But this moment is so important for math instruction in our 40+ states that have adopted Common Core standards; we are also on the eve of significant ramping up of Common Core implementation.
I’m looking forward to the Standards for Mathematical Practice. I have a lot to say about these eight mandates, which are repeated on each page of the Common Core content standards in each grade. They appear as a floating reminder that math instruction is not (only) about memorization and regurgitation, but about deep understanding, proof and argumentation, focused exploration and interpretation.
I’m convinced that the Standards for Mathematical Practice are doomed to fail in most schools.
Why? Because it seems that most teachers and principals don’t understand a simple fact: to teach elementary school math well, you have to know elementary school math really well. And most people (be they teachers, principals or otherwise) simply don’t understand much elementary school math.
I don’t know what teacher preparation programs are doing out there when it comes to math instruction, but from my experience in hiring teachers and my stint as an adjunct in one program, my guess is that if there is a math course in most of them it consists of something like, “Here’s the Harcourt Brace textbook. Here’s the Saxon textbook. Here’s the Scott Foresman textbook. Here are some tricks for teaching long division.”
One of the beautiful babies in the bathwater of teacher preparation is the program I went through at Bank Street College. At Bank Street, where theories of learning were developed by watching and learning from children rather than from following a bureaucrat’s mandate, my math mentor taught me that children need to struggle with mathematical concepts, and teachers need to guide them through that struggle with strategic questioning that builds understanding, always with the next math concept in mind. Children also should know why they are learning math concepts and facts, and have an authentic contextual basis for their study.
Linda Metnetsky said, “When the teacher gives the answer, all math thinking stops.”
And of course, the easiest thing to do is to give the answer, and demand that the kids memorize it. After all, that’s what Scott Foresman tells you to do. Teaching math progressively is far from the fluffy, no-facts, fuzzy math of popular culture. If done correctly, it’s a far more rigorous and intellectually demanding exercise than traditional math instruction on the part of the teacher.
Common Core. Lack of math knowledge among teachers. No concern in graduate programs for this problem. What are we to do?
As always, in times of crisis, I turn to books for advice. (Real books, written by authors, not textbooks written by committees, that is.) I’m not talking about how-to books, manuals of how to teach mathematics. I’ll take plenty of time to explore those in a future post, including books by Marilyn Burns and Cathy Fosnot among others. I’m talking about books that inspire or make clear the importance of loving and learning more about math.
Luckily there are a few friendly books out there that do a good job of either laying bare the crisis of math deficits or of explicating just why it’s so beneficial to understand math.
I’m going to describe a few of these books here, but I’d love to hear some reader comments recommending more. And please, don’t say, “The McGraw Hill series has some great looking times tables in it.”
Innumeracy by John Allen Paulos: Paulos wrote this tract around 25 years ago but its message is still relevant. While there is tremendous shame associated with illiteracy, society still finds it acceptable to be innumerate. And the consequences for that portion of our society that can’t read a stock table or tell an increasing rate of oil production in a foreign power from a drop in GDP from one quarter to the next extend far beyond the realm of whether 2 + 2 is always equal to 4.
How Mathematics Happened: The First 50,000 Years by Peter Rudman: Rudman is not quite a feminist, and you have to avert your eyes at some of the turns of phrase, but he brilliantly catalogues the timeline of the use of mathematical concepts beginning with our hunter gatherer days. Two powerful ideas I took away from this book are that (a) the development of mathematical knowledge in our concept mirrors the development of these concepts in individual children (that’s self-similar like a fractal, although he doesn’t use those words; you will if you love math as much as I do) and (b) there really is a reason why we should explore our base-10 system and other bases with children as we study math. I hadn’t understood it before, but after reading this book every time I look at a clock I think about it.
Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter: As I’m kind of slogging through it right now (because it’s dense, not because it isn’t interesting), this tome is not nearly as accessible a read as the two books above. It didn’t win the Pulitzer Prize for nothin’—the author calls it a “metaphorical fugue” inspired by Lewis Carroll, and that’s pretty much what it is, tracing the history of mathematical thinking about patterns and puzzles, their relation to paradoxes, music and computers. Imagine Willy Wonka wrote an autobiography but his obsession was puzzles, not chocolate.
What do you think about the math thinking behind math teaching? Any great books to recommend?