“Oh, I get it,” the students say, and I tell them that that's great, and that it is not enough. I tell them that learning math is a lot like learning to play a musical instrument or like learning to dance or to play a sport. Having once successfully played through a piece of music, or having once correctly executed a move, is all very well as a starting point - and only practice and repetition with feedback will ensure that they perform reliably and smoothly. “Getting it” goes only so far, and learning involves something more and other than that.
This is what I tell my students, so I do “get” that insight is not enough, that learning requires changing behaviors and habits, and yet it seems I have not learned this lesson at a behavioral level myself. And so it was that one of the most useful experiences of the Math conference at Asilomar yesterday was cutting the last class to stare at the ocean and think about what I had wanted to do and not do this semester, and about what is actually happening in my classroom. It’s been an unexpectedly difficult semester for private reasons (conditions at school would have predicted the best teaching year ever), with limited occasion for reflection on my work, and the Math conference provided a chance to take stock and regroup.
I “get” that assigning a large number of practice problems has little or no advantage over assigning fewer problems and is likely to even be counterproductive, I see that assigning homework problems that a large number of students won’t be able to do correctly on their own is silly, I know that having the students do more work than I have time to check is a waste of their time as well as mine, and I believe that there is much value in spending some minutes of class time every now and again on activities whose purpose is building relations rather than practicing math skills. Yet, judging from what I’m doing it would seem I disagreed with all of the above. Somehow, all kinds of resolutions made late last year got lost in the flurry of starting up again this year, and I’ve found myself teaching in ways I had made definite decisions not to.
So, what to do? Since it’s not a matter of “getting it,” not a matter of knowledge or conviction about what to do, I’m thinking about what kinds of feedback mechanisms to set up toward changing my behaviors. I could write down what I want to do and keep rewriting it daily to remind myself. I could talk to colleagues about what I want to do and ask them to do random five minute observations and let me know what things are looking like – and I am fortunate enough to have several fantastic colleagues who would be willing to do this. I could tell the students that there’s a cap of a certain number of homework problems and ask them to remind me if I forget my own policy. I’m sure they’d be delighted to oblige.
On another note, it’s been nice to rediscover the online math ed community recently after having neglected these readings for lengthy periods at a time this fall. New ideas and debate are like food and sleep in that they’re easily given lower priority during hectic times, and yet these things are all necessary for teaching and learning well in the long run. Glad for all of you who are still around and writing...