My post(s) about requiring students to do math in pencil seems to have generated some interest. Joanne Jacobs picked it up here. Cold Spring Shops picked it up here.
This is a good time, I think, to point out my old post about the use of graphing calculators. I was, in many ways, a strong believer in old fashioned teaching methods. Math in pencil, first principles, lined paper, show your work. The thing is, though, that I never believed in memorizing formulas (and, let me tell you, my kids loved me for it). So, upon further reflection, it's not really a matter of being old-fashioned, but a matter of promoting thoroughness. This is especially true in the case of students who would refuse to show their work. Having once been that sort of student, I understood their utter frustration with my docking points for lack of work. The idea, however, was to promote thoroughness in their thinking. Mind you, I'm not saying mathematical intuition should be discouraged. But, for most people, there will come a point when the math is far too complicated to simply intuit. And at that point, you need a more organized method of thinking about math, even if you choose to do it in your head. It is a teacher's responsibility to train that sort of organization at a young age, when it can be trained. In my opinion, the best way of doing that is to enforce showing one's work.
In related news, I completely see the logic in how spelling and penmanship can improve a student's writing. I also taught by using "fill-in" handouts--my method of enforced notetaking. There is something to be said for the effect of writing on learning.
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