*Investigations in Numbers, Data and Space*,

*Everyday Math*,

*Connections*, etc.) and the controversy around them, I always think of Mrs. Gravely, because these programs are actually trying to replicate what Mrs. Gravely did on a good day. For instance, she handed me a shoebox for my first assignment. In it was a disk puzzle and a set of questions to be answered about the puzzle. There were no instructions, and each kid got a different shoebox. I spent all evening trying to figure out the answers to those questions. I described to the class how I had worked them out. Other kids had done it differently, and we discussed the pros and cons of each method. None of us was judged as "incorrect" for the method he/she had chosen. I had never before engaged with a math question at that level of interest. She had gotten us into

*mathematical thinking*, which is more creative and quite different than much of what goes in the land of "don't ask why; just invert and multiply." I felt like I belonged in a math class; it was OK to be there and I was doing what the other students were doing. I began to read ahead in the math book, especially the side bars about Pythagorus and Archimedes. What I had seen as an uncomfortable hour of marginal benefit, where the teacher made hieroglyphics on the board and spoke in a foreign language to native speakers, had become interesting, even relevant. As any modern expert can tell you, in K-12 schools, mathematics is basically a psychological game; it's all about engendering a sense of belonging in that disaffected group, so they start to put forth effort again. The top scorers can survive traditional teaching, but the low scorers are where the opportunities are for the teacher to go from good to great. Mrs. Gravely was the embodiment of the truth that most "modern" methods are not new.