Thursday, January 12, 2017

Mathematical Autobiography

For Tracy Zager's amazing new book (book, FaceBook, forum, Twitter), she's asking for mathematical biographies. I used to ask my preservice teachers to do that, but haven't in a while. Thinking that I'm going to again for this read... so I should, too. I'm not sure what lessons there are to glean from it, but we don't get to choose our story!

My home was centered on art and literature. Father a lawyer, mother an artist, both avid readers. (When we had to clear out their house there were at least 20,000 paperbacks in the attic. Crazy.) So I always loved art, reading and writing more than math. Science I loved, though, and my parents were generous with books and museums for it. Math, I was good at, but it was boring. And more so each year. I was a competitive little jerk in elementary, though. In third grade I poked a pencil through my finger when I was peeved at missing an answer on a timed test. That was pretty much the end of the competitiveness.

Math got more and more boring as it went on into middle school, because there was so much repetition. I didn't understand why we did the same ideas every year. The details were barely different, but the same ideas over and over. And the lessons day to day involved so much repetition. I was lucky to have the kind of brain that this stuff just stuck. Although that made homework feel like hitting your head against a wall. But then we had an experimental self-paced program in 7th grade and I got to do 2 years of math in one. Only had to take assessments, so practice didn't have to be repetitive.

Bad news was in 8th grade my folks switched me to a small Catholic school. (In preparation for going to a Catholic high school; my father was in the first graduating class and my grandmother helped found it. Not optional.) The math was entirely repeat, so after a month they arranged for me to take algebra at the nearby junior high. I got the book and the assignments, and tried to catch up on my own. Without reading the text. Are you kidding? I was amazed at how long the homework was taking. I was good at guess and check, but that was so slow. The first day the teacher was doing the problems that people had put on the board. The first problem she wrote the equation, and subtracted something from both sides...

... and the heavens parted. I still remember that feeling 40 years later.

I enjoyed the math a little bit more after that. The ideas had gotten more interesting. But the homework was still terrible and classes excruciating. There was no AP at my small high school, and I got to go to the community college for calculus. Best thing about that was time with my friend Mark who was in the same boat. Class was uninspiring and I got an uninspired A-. Plagued by falling asleep in class most every day. (A problem that continued through all my schooling and still today in some meetings, church services and watching tv. It was me, not the teacher. I apologized but...)

My guidance counselor hated me for some reason, and never filed the forms for transfer credit that he was supposed to do. (More troubling was the request for scholarship info he never filled. He was the yearbook advisor and tried to convince my parents that I was failing that. Weird little monk he was.) But that was my big break. Michigan State placed me in honors calc, and I got to meet John Hocking. He was a real mathematician and shared topology with us. He convinced several of us to switch to or to add a math major. Because there was all this math we just had to know. Bill Sledd, John McCarthy and why can't I remember the name of my awesome tensor calculus prof? Awesome profs, and choosing math teaching over physics lab assistant for a job sent me off to grad school in math. (After a year doing art in Spain... story for another day.) I was going to still do cosmology or super string theory, but just come at it from the math side.

In grad school at Penn, my future advisor was our analysis prof, Nigel Higson. Awesome mathematician, barely older than us, fun and inspiring. When he got hired away by Penn State, he let me follow. When I was considering quitting to go get secondary certification, he encouraged me to finish - "you're so close, and you never know what it could lead to." Right as always, Nigel. Nigel's enthusiasm and curiosity for math are still inspiring me. But it was also then I saw the next level. His view of what was true and how things worked were beyond me. I could do Ph.D. mathematics, but I didn't have the drive and/or capacity for results that birthed fields of mathematics or got published in Annals. But to get to the point where I could see that... I'll always be grateful. Invited to dinners with Field medal winners who were also charming company? That was only going to happen at Nigel's house. Not to mention getting to hang around the effervescent Paul Baum.

My last years at Penn State were also when I got introduced to math ed, by my friend Sue Feeley, who was a math ed Ph.D. student. Putting Polya into someone's hands is a dangerous gateway book, Sue! I was trying to reform a math for elementary education class, and started to find out what I should be doing to teach. Blew my mind. Teaching went from something I liked a lot to my first love. And teacher's mathematics along with it.

Yotta, yotta, yotta, 20 years later, badaboom badabing, here I am. Loving math, math art, math games, math history and loving the teaching of it.


  1. Going through all the tedium of elementary, middle, high to get to the really good stuff! So glad you're on the case, John!

    And that you're a fellow fall-asleep-anywhere person!

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