Did you ever write a "mathography" or have your students write one? They're basically autobiographical accounts of your experiences with and feelings about math. I've assigned them and have written a few, and this post, "
MAA Calculus Study: Women Are Different," made me dig up some parts.
The MAA calculus study looked at women and men who took calculus at the beginning of college as part of the coursework for their intended majors, and found that "any indication that they may not be up to the task is much more influential for [women] than for men.... Only 4% of the men earning an A or B were dropping calculus because they did not understand calculus well enough to continue its study, but this was true of almost a fifth of the women earning an A or B. Even more notably, not a single man earning an A or B felt that this grade was not good enough to continue the study of calculus, but this was true of 7% of the women who were switching out of the calculus sequence. [...] Strenta et al (1994) [...] found [...w]omen were much more likely to question their ability to handle the course work, and women were much more likely to feel depressed about their academic progress. They also found that women were more likely than men to leave science because they found it too competitive".
I'm 49, so my college experience is a little dated, but these words are definitely a blast from my past. I spent much of my childhood loving math and thinking I might become a mathematician, was widely considered a "math brain" by other students and by teachers, scored extremely high (a 640) on the Math SAT in 7th grade as part of screening for what was then called the Study of Mathematically Precocious Youth, got a 790 on the Math SAT as a junior, placed out of Calculus I by taking AP Calculus in high school, was a National Merit Scholar, got into Harvard, Yale, and Princeton [note: it was a LOT easier then], and chose Swarthmore College, where I double-majored in chemistry and math and won the senior math prize for my math paper.
I've never strung all those facts together into a brag like that before, so why am I doing it now? Because when I read it over as if I were a woman I didn't know, it seems ridiculous, astounding, even horrifying, that I WAS GOING TO QUIT MATH -- right after loving first semester Calculus II in college and getting an A in it -- BECAUSE I DIDN'T THINK I COULD CUT IT. In fact, I didn't take any math second semester freshman year. I only went back to math classwork because my chemistry major demanded it, and then I double-majored (with great trepidation and sure I'd be kicked out as a phony at any time) because my college boyfriend talked me into it.
Now, some of this near-math-dropout status is down to me being a hot mess. My confidence in everything was low, my academic performance in college was streaky, and my work habits were inconsistent. But the rest... well, if you're still with me, read on for an example of how much difference math experiences in school can make, whether they are positive or negative. Look especially for experiences that contributed to the fixed mindset I had at the time about math -- a belief that people were simply either good at math or they weren't -- which made me vulnerable to feeling helpless, tuning out, and quitting when the going got rough.
*****************************************************************
At school, math was a mixed experience for me. I’ve had years when I had nothing but praise for my math smarts, and years when I was told I wasn’t cut out for “higher math”. When I started elementary school as a first grader, I liked how predictable math was. My family had undergone a lot of upheaval: I had lived in at least seven places in three different states, my parents had gotten divorced and my mother had remarried, and she and my stepfather had started new jobs. My family was young and fairly poor at a private school where most kids’ families were rich and settled and had elegant houses and clothes and even maids. I was scared of the strict teacher and the other kids, but once I understood how to do math worksheets and get the “right answer,” I felt like I had something reliable to count on and succeed at. I liked math and worked hard at it, and my teachers had me do a lot of advanced elementary school math independently with a book in the corner. I liked concentrating on my own most of the time, although sometimes it was lonely, and it was frustrating when I got stuck.
In my sixth grade year, my family moved again and I went to a larger, public, grades 1-6 school. My teacher made a big deal to the class about how I tested at 12th grade level in math (whatever that meant!). I was immediately labeled a “Brain,” in a partly friendly but still annoying way. I am not sure why he told the rest of the class about my math testing results, but I have a vague hunch that it was to demonstrate to everyone that girls could be good at math (something that was not exactly a truth universally acknowledged in 1976).
I am 49 now, and I think a lot of my students’ parents were also raised in this time, when teachers were trying to send messages that girls could succeed in math, but unintentionally made most students feel like there were “brains” who were good at math and could do it, and then there was everybody else, who… maybe couldn’t. It makes me sad when students tell me their parents tell them they can’t do math, and I became a math teacher partly because it bothered me that my clever, hardworking adult friends sometimes felt that way too. I’ve read and heard that in other countries, people take it more for granted that anyone can put in effort and succeed at math.
For seventh and eighth grade, after my parents’ second marriage broke up, I moved with my father back to Baltimore and the private school. Again, math was a safe and fun place for me amidst family stress and turmoil. My teacher, Mr. N-------, loved math and was really excited to work with kids who were good at it. He stretched our boundaries: he had us programming in 1978, using cassette tapes for data storage! He was very energetic and strangely charismatic, and a lot of us really wanted to do well in his class and were quite competitive with each other. I did the best, but it was an oddly uneasy role because the other best students were all male.
In eleventh and twelfth grade, I met my math nemesis. Mr. F------, a philosophical soul of around 60, was known as a hard and eccentric teacher. I had had his wife for fourth grade and adored her. I figured I would love Mr. F------. And for a few months, for first-year calculus, I think I did. But things started to go downhill then. We noticed he would lecture only to the boys (and the boys and girls in the class gradually sat separately, unlike in our other classes). He would tell little anecdotes about one female student from a few years back who actually did really well in his class, sounding surprised. The not too subtle message was that having a girl do well in his class was a freak occurrence, possible but not likely. We all (boys and girls) picked up on this stuff, but we didn’t take it too seriously. Where was the harm? After all, he was fair… wasn’t he? The girls started to do worse in his class. But wasn’t that normal? Already there were fewer girls than boys in first-year calculus.
By twelfth grade, Mr. F------ laid it on really thick about how THE CALCULUS was HIGHER MATH, and not everyone was cut out for it. People might have done really well at algebra or geometry, but that didn’t mean they were the ones who would do best at higher math. We all figured some of this was aimed at me. I had entered with a whiz-kid reputation, and he was letting me know it didn’t mean anything. And sure enough, by this second year with him, my performance started to fall off. His handwritten quizzes made me panic, though I still did well on printed, standardized test questions. When I got increasingly lost and my grade dropped very low, I went in to ask him for help. He listened to me with a patronizing smile, then said, "You know, you're a very pretty girl." [Yes, I am COMPLETELY sure that's what he said. And yes, I was infuriated, and I told adults and other students about it. But it was a different time and nothing happened because we all thought he "meant well".] After seeing my complete shock at that response, he said not to worry, but just that he thought I didn't seem to know that. He made it clear that he thought girls should focus on their social lives and not fret about math too much. I asked again for help on catching up and he said dismissively, "Just do the homework." I left, fuming, and of course checked out completely. Although I did fine on the AP Calculus exam, I scraped by with a C- for the class for the year, along with a vow to never take “higher math” again.
However, I decided to major in college in chemistry, which required me to take second semester calculus. I had a sweet, smart, older gentleman as a professor: “Fast Eddie” Skeath, a former track star and a super-fast blackboard-writer. Then a miracle occurred: it was fun again. I got it again. I felt safe again. I did well again. In the end, I tentatively took more math and ended up double-majoring in math and chemistry. I did have a fairly erratic math major career, though. Sometimes I’d do really well in very hard classes, and I even won an award for a senior geometry paper, but that same semester it was a big disappointment to me that I did quite badly in the only post-elementary-school class I had in math with a female teacher, and never really did know why. I think I was just sometimes rather unfocused, and perhaps still too easily discouraged if I hit a rough spot. Overall, though, I had a great time in math, though I thought of chemistry as my “main” major because I was told it was more employable.
I have never regretted my choice of college majors. They were hard at times, because more than in other subjects, there are assessments in chemistry or math where you just flat out have the wrong answer, and it doesn’t feel great. But learning how to work past that and succeed at problems you used to do wrong is a great feeling, and gives you confidence in how you use math or science to solve real-world problems. Because fewer Americans major in these subjects even though there are more jobs related to them, I’ve always been able to use one or both of my majors to find interesting work, especially as a teacher (now) and a chemistry software company grant writer and customer support manager (earlier). I hope that any of my students leave my classes with those college and career paths open to them if they choose to take them, but regardless of their career paths, I hope all students get some of the same pleasure out of math I have, and leave my class feeling successful and knowledgable.
