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.

Hocking

John Hocking
From a newspaper article 1981 before a trip to China,
the year before we met.

I attended the memorial of John 'Gib' Hocking this summer, with three of my undergraduate classmates from Michigan State. Ed Aboufadel, Terry George, and Jim Koss.  By accident, my community college calc credit wasn't accepted at MSU, and it was one of the most fortunate accidents of my life.  I enrolled in honors math, met people who are my friends to this day, and completely changed my career trajectory.  He convinced me to continue on in math, and Ed is the one responsible for me winding up at GVSU.

To say Gib had a fascinating life doesn't do it justice. He went from working at Ford to the University of Michigan, served in army intelligence post-World War II, became an excellent fencer, sailor and race car driver... as well as a respected mathematician. His and Judy's home was famous for its hospitality and at the memorial many testified to the wonders of what they called Three and a Half. He bought the race car in England while on a Fulbright with the proceeds from his calculus text. (Bought by the publisher so it wouldn't compete with their top seller, said the author.)  After retiring from MSU, he worked with a grandson repairing sailboat engines, designed the first new mechanical navigation device in a century, learned how to design heating and cooling systems (and designed them), and became an expert wood worker with the third nicest workshop in the world.  (My guess is he knew the probability of meeting 3 people with nicer ones at the same time was effectively nil.)  The Topology text he wrote with his advisor Gail Young (cf. the math genealogy) was the standard for years and is still respected though old-fashioned. (Dover edition still available!) As a retiree he rewrote large section of a sailing navigation text that had stood for 100 years to simplify and clarify the mathematics.


Ed and I chatted about him this week.  Ed recounts how that first semester led him to decide to be a math major. "I want to be a math professor, like that guy." Renaissance man, well-rounded. A mathematician but not just a mathematician. Excellent teacher, Ed tells how he learned a lot about teaching just from being his student. Dr. Hocking really looked at his students and saw what was going on with them. Always made eye contact, and strove to have a sense of where we were.  Further, he reached out to us, mentored us. Recommendations, advice, ... personalized our experience at Michigan State which can be rare with 40,000 students. He was a man who was very obviously intelligent but incredibly approachable. 

4 spartans in Ann Arbor

We had him for five quarters in a row, and we had no idea how rare that was.  He introduced us to topology, like the Alexander horned sphere, Möbius band, and Klein bottle. Shared what problems he was thinking about.  Ed notes how he really gave the flavor of what was in store for him as a math student.  He taught about the field of mathematics as opposed to just the topic of the day. Always used lots of applications, sailing examples.  Ed says he somewhat recently was using the idea of bearings as examples while teaching trigonometry.  I'm very grateful to Ed for both inviting him to speak at GVSU a few years ago for our seminar, and for finding out about and organizing our trip to the memorial.

I became a math major because by the time I finished all the stuff that Dr. Hocking had convinced me I needed to take, I was one class away from the degree.  The appeal of teaching - based on his teaching - led me to pick the math TA position over the physics lab assistant position.  He really formed us into a community.  The four of us from the memorial (plus Amy Crammin Shao) were my first experience in a real study group, though we worked with many people from the class over the years. He had the whole class out to his house for Christmas.  At the memorial, Bill Sledd, one of his colleagues from MSU (and another influential teacher from my past) remarked on how that group of students sent a remarkable number of people on to grad school.

Manipulative from Gib's GVSU seminar

Gib had tricks he'd pull out in the classroom, like a fancy move for drawing an extra large perfect circle, or writing behind his back while facing us. But mostly he was just tremendously authentic, sharing important stories from his life and his genuine thinking about his problems of the moment. We felt like we got to know him.  A favorite pet memory of mine is the whole class chipping together to get him a Rubik's cube (expensive in the early 80s) for Christmas.  He opens it, turns it this way an that, then says, "Oh," and solves it the first time in a minute.  What a lightning quick, fascinating playful mind he had.  Several people remarked at the memorial how much he loved games and I love to think what he might have done with games in the classroom.

Same sparkle at 90.

So raise a glass and toast to the teacher who inspired you most. Here's to Gib!

Special Thanks: Wendell Hocking, who shared the pictures of Gib for this post. And to the whole Hocking family for letting us share in the memorial.

Appendix: The American Mathematical Society shared the following notice on their "In Memory Of..."
John G. Hocking (1920-2011)
Hocking, a member of the faculty at Michigan State University from 1951 to 1987, died March 23 at the age of 90. He received his PhD from the University of Michigan in 1953 under the direction of Gail S. Young. Hocking and Young wrote a text, Topology, that was widely used. Hocking was an AMS member since 1951. Post script: the AMS has finally posted a longer notice, written by Gib's student Som Naimpally.

Ken Robinson

So I showed the Ken Robinson video to my class on the first day and it was quite interesting. The video started with medium engagement, but by the end everyone was tuned in. The story about the choreographer (Gillian Lynne) seemed to really connect.



The first connections were to elements of their own stories, and were interesting. Then one of the students brought up a connection with how Robinson describes us as being educated out of creativity. Her sister is interested in being a soloist, and it took ears of retraining or untraining to get her out of what she had been taught to do as a choral member. I'd never heard of that before, but it connected exactly to the point I wanted to make.

They have been educated - and successfully so, as college calc students - in school mathematics, which has almost nothing to do with mathematics as practiced by mathematicians. (Which really needs a descriptor. Real mathematics isn't going to interest anyone. Creative mathematics? Cool vs. school or cruel mathematics?) Instead of being able to repeat what someone shows you, it should be about solving problems that you don't know how to solve. In which situations mathematicians excel, because they are entirely willing to be wrong, and even glad to be wrong if they learn from it. They're willing to, as my friend Dave says (quoting his favorite Australian, Brian Cambourne) to "Give it a go!"

As long ago as 1982, my calc instructor, John Hocking, worked mightily to convince us to have no fear. To be wrong 100 times if it teaches you something. That math was exploratory, and creative. He shared his topological research with us... which was amazing and fun. He's the reason I added the math major in the first place. Often he put it as "blank pages are just waiting to be filled."

Now can I help my calc students to do the same?