What I Can Do, and What I Can't

I can teach mathematics.

I can't fix a broken child.

I've immersed myself in elementary Euclidean geometry over the past four years. I know its contours well. I know the form in which it first appeared. I know the developments that it underwent it its long history. I know the history of its pedagogy, and I have deeply held opinions about how it should and should not be taught today.

Moreover, I've watched students quite carefully as they struggle through the course. I know the sorts of mistakes they are likely to make, I know the sorts of misconceptions they are likely to harbor. I know what I need to say to correct these. Moreover, I know just how students should be led from idea to idea. I know how to build up the body of geometrical theorems so that it's structure will be pellucid. (Don't think that I claim I'm exceptional in this regard. I know how to do it because I've seen others do it and do it well. Almost all that I know I've shamelessly lifted from minds much better than my own. Alas, but this is the fate of those who progress only because they are led.)

If you're bright and motivated and you put yourself under my authority, then when we're done you will know elementary Euclidean geometry.

But still, many of my students don't know much about geometry when they're finished with my course. (I teach about 250 students in a year. Of these, at most 100 are competent by the end.) Why not? What happened with them? Bright though they might have been, motivated they were not. I can't fix that!

Instruction isn't to blame. Neither is curriculum.I do love what I teach, and I know that I make that love plain. (Students marvel at it. Students quite regularly tease me about it. Here's the proof.) I know that my explanations are clear. I know that my assignments are of the right sort - they review the basics but always end with questions that really do challenge.

Classroom disruption isn't to blame. I'm lucky. I have little problem with it. Others do. (One of the dirty little secrets of education here in the U.S. is just how many of our students are little better than feral. What do you do with a student who stands in the hallway and shouts "Motherfucker" again and again. I chewed him out and then wrote him up. Will that make any real difference in his life? Probably not.)

But if none of these things are to blame, what is? What's the source of the problem? I must say that my ideas are inchoate. At times I simply blame the parents. At others I blame the wider culture. But the fact cannot be denied. Many of our students don't care a bit about their education, and I can't fix that.