Not to put too fine a point on it, I think we've blown it in the math education business. We have many superb teachers, and the subject itself is nothing short of spectacular, but somehow we fail to reach most of the students we teach.
I'm not the only one who thinks that, of course. It's quite a common perception. But what surprises me is that so little is done to put things right. Actually we discuss the problem a lot and I have been part of innumerable such discussions (Dialogue, Small napkins). But now, after all this, I've come to feel that we've focused too much on how to teach and not enough on what to teach. We talk about big classes and small, and investigations and drill, and group work and lectures, and formulas and manipulatives... and all these have their place but ultimately they simply generate heat--and the clouds of war (math war) roll in.
We need now to focus on the what, the material that we put before our students. I believe that if we can get that right, the rest will follow; but if we can't, the math-ed problem will always be with us.
What do I mean by this? Suppose your task is to teach an introductory calculus course. What should you teach? Well that's a silly question--I teach calculus! What's calculus? Here, you say patiently, taking a calculus text-book down from the shelf and opening it to the table of contents, We start with this, and then we do this, and then... So my point is that maybe there's a much better way.
Over the years I've written lots of stuff about this, slowly trying to converge on something that's at least right for me. For example, here's a paper which explores the metaphor of math teacher as artist. A recent paper that I am quite pleased with argues that we should be teaching the mathematics of mathematicians. Lest you think that’s a tall order, I have three things to say. First, yes it is––good investigative problems are hard to find. Second, I am impressed by how much “real math” can be engineered to work well at the high school level. And third, I believe our kids are capable of so much more.
My current work centres around the creation of problems and activities for grades 9 to 12. With the help of my graduate students, I take these into the classroom, and post them on my Math9-12 website. My work is funded in part by the KNAER Mathematical Knowledge Network (MKN), an initiative of the Ontario Ministry, and in part by SSHRC. I am always looking for new sources of funding.
Publications and Lectures