Eigenmumbles

I learn mathematics not through my eyes, but through my fingers. I sympathize with students who would prefer not to listen to me lecture. If I were in their shoes, I would probably find it more productive to work problems most of the time. I try to incorporate in-class problem-solving into my classes for precisely that reason. But there is not enough time in lecture to really dig into a problem, getting lost on side tracks and running around in circles while only gradually closing in on the answer. To me, the value of homework lies in that process of getting lost often enough so that your fingers can work past the algebraic thickets without distracting the rest of you from your high-level task. It’s hard to design homework problems that force students into the algebraic thickets while providing both enough tools for them to make their way through and enough connections to “the real world” so that nobody complains that the homework is pointless. But we try, and we keep trying.