This past week, I stumbled across this essay by Paul Lockhart , delineating the various and extensive problems that he sees with regard to math education, and education more generally. It resonated with me for a few reasons, not the least of which being the fact that my own high school Geometry experience was very much like what he described in the essay (though in my case, it was exacerbated by a particularly difficult interpersonal relationship with the teacher).
It’s a great example (among the pile of examples that I’ve collected) of teacher’s striving to teach something very different from the subjective experiences of students. Generally speaking, I have found that the teachers who are doing the work that I feel is most interesting are all trying to get at something a bit larger than having their students commit a body of knowledge to mind. Mostly, it seems like these folks are trying to teach a way of thinking. Certainly, that’s what I’m trying to do in my own work, and I think it’s what someone like Paul Lockhart is doing in his own work. And of course, it’s completely contrary to what the various attempts to push education toward increased “accountability” and standardization are seeking to accomplish. For whatever they might claim about their goals, it seems rather obvious that mandating the ways in which students should learn to think is a very different aim than teaching them how to think.