For most of my elementary school career I was in the advanced group in math, which meant that I worked with a small group of classmates on advanced subjects. In the younger grades we usually received separate instruction from an assistant teacher. This changed from fifth grade on, when our small grade was divided into girls’ and boys’ classes. My group now consisted of me and one other friend. She and I were sent to the back of the classroom with the textbook for the following grade and expected to work on our own. If we needed help we had to wait, a lot. We finally hit upon the tactic of referring to the teacher’s answer book: we would look up the solution to the problem that had stumped us and then try to figure it out by reasoning backwards. At home in the evenings we would confer with parents or my friend’s older brother. I am not sure if our families quite understood how poorly we were being instructed.
In seventh grade our math teacher started us off by assigning us an enormous number of review problems covering what we had done the previous year. This bored us out of our minds and then annoyed us – why were we doing so many problems that were redundant rather than learning something new? You have to imagine the seventh grade version of this sentiment, coming from smart but sometimes sassy students. To our great good fortune this teacher had to take a leave of absence in order to have an operation. Not to worry – she was fine and everything turned out alright. But at the time her leave-taking brought relief to us, although at first we did not know what to expect. The school’s business manager, a former teacher, took over the class for the needed weeks. She paid attention to the two of us and noticed our lack. So she started teaching us algebra. When our regular teacher came back, the business manager continued to teach us and our counterparts – the smart math students – both in our grade and the grade above, boys and girls. At the end of the year all of us took the ninth grade algebra regents and did very well. It was a tremendous amount of additional work for this woman to take on and I remain grateful to her for doing so. She became one of my most powerful role models as a teacher, but not just for rescuing us or for putting in the extra time. She also shared with us some of her reflections on her teaching; this may have simply been who she was, or she may have felt more able to do so because our set-up was non-traditional. She told us that if she gave a test and her students did not do well her first reaction was not to fault her students but to critique her own teaching, to wonder where she had failed and how she might amend her current students’ understanding and do better in the future. It was mind-blowing for a teacher to share these thoughts with a student in such a traditional school.
In eighth grade we were not so lucky. We were given a free period for math, during which we were expected to sit in the library and amuse ourselves. We gave up our lunch period three times a week, bringing our trays upstairs to the classroom, where the new math teacher, a well-meaning but slightly awkward young man new to the profession, tried to teach us algebra two and geometry. We never got very far. I do remember one lovely interview with our new principal, who got up and demonstrated by walking the process of halving infinity ad infinitum or at least until one reached the wall and could go no farther. The joy he showed in explaining and sharing his knowledge won me over for good, but he had too much on his plate to teach us regularly.
My friend and I went to the same high school and both continued in advanced math classes. By twelfth grade, when I took AP Calculus, I found my interest had waned considerably as the material grew harder and my preference for the humanities grew. I think that my friend’s interest fell off sooner than mine, but we were never in math class together. Years later when I took a class in teaching math at Bank Street I interviewed my former study partner and was amazed to learn that she was rather anxious or even phobic about math. We met over dinner and she shared how tallying up bills and tip and such made her nervous. I am not sure what part of our experiences caused or helped this fear to grow, but it was touchingly sad. Bank Street wisely makes most of their students take this math course, knowing that my friend’s reactions are all too typical. In class we sat and solved problems, working with manipulatives and other tools, including M and Ms - no, not for counting but for exercises in probability and statistics. I still remember one fellow student exclaiming that she finally really understood fractions, how they worked as relationships. Leaving aside questions of gender, which are pertinent and much studied and discussed elsewhere, I wonder as ever about the ways in which our learning is shaped by experience, for good and ill. That includes the messages that teachers and schools give, whether intentional or not. That math is daunting and complicated.