Welcome to Recipes for Pi!
I’d like to introduce myself to writing about teaching math by giving some history about me and math while explaining part of why I’m starting to write this. This blog was in part born out of a mixture of enthusiasm and anger about the ways that the world learns and shares math, triggered and brought to a head by an event in my own math education. For me, writing is the best way to process my feelings about and reactions to events. I was motivated to share my writing, and to begin a blog, when one of my students asked me about the event in question. So, read on and enjoy!
I was recently reminded of how much I dislike math class – and how I learn math best.
Last semester, I registered to take a graduate-level math class. I hadn’t taken a math class since college, and had begun to miss being on the learning – rather than teaching and learning-for-teaching end – of the classroom. I figured that taking the class would be difficult – both because it was a graduate-level class and because I’d be taking it while teaching – but was motivated to face the challenge because, well, I like doing math.
Before about 5 ½ years ago, I hated math. That’s surprising to those who’ve gotten to know me best in the past 5 ½ years, but the fact that I love math now is a total shocker to those who know me from before. Throughout elementary, middle, and high school, I was one of those students who often baffle math teachers most – the extremely conscientious kid who does all of the homework, stays after class to ask questions, and aces tests, but is convinced she’s terrible at math. I always felt as though while I could eventually do anything with enough memorization, I never really understood what was going on. If you’d asked me then what it meant to do math, I would have said, “Math is learning complicated, nonsensical procedures and algorithms, and using them again and again and again until you can do it with your eyes closed (or at least without your notes).”
But when I got to college, something changed. Here’s what I think happened:
- I stopped solving problems by memorizing everything the teacher said to do, because the problems weren’t like that. Most of the problems weren’t like the examples – you had to build your own methods from the tools you were given, not copy a procedure.
- I stopped worrying about the answer and started paying attention to the process, because the problems weren’t about the “answers.” The problems we were doing were proofs – and when you’re doing a proof, you already have the answer. Math wasn’t working the machine properly, but building the machine you needed.
- I started working with other people. My classmates and I figured out how to do the problems together, and the professors came to our informal homework meetings to talk to us, too. Math was social, cooperative, a conversation among people – students and teacher – learning together.
As I started really thinking about math and bringing my tastes to my mathematical work, I began to see how many ways there are to interact with math. I also began to see how very beautiful the work of finding, simplifying, proving, and changing patterns can be.
And when I began teaching math at Saint Ann’s, I grew to love math even more. I had to really think about interesting things to do with math, and do them – mostly for the first time, because these were precisely the activities I avoided in elementary and high school. My peers’ love of doing math was infectious, and their patience with and appreciation of my pace of thinking were blessings. I got to try to build classes where, whether by conscious or sub-conscious effort on my part, my students learned math the way I learn math best – by talking with each other, figuring things out for themselves, and certainly not just listening to the teacher.
I probably thought that taking a graduate math class was a good idea because the images of math class I had in my head were of math classes at Haverford and the classes I try to run. And the feelings I had after one week in this math class were probably so very negative for those reasons as well.
After about a half an hour into doing the homework assignment, I could feel my old math anxiety returning. Here was math class at its near-worst for me – math as competition, math as listening to a professor spout information, math as a race to accumulate facts. I was working alone. My professor quoted from a textbook for two hours and did nothing to create an environment in which a bunch of people really interested in math (himself included) could work and learn together. There were a TON of problems for homework, because we’d covered an entire chapter – itself covering all of introductory group theory – in two hours.
And I began to feel math anxiety all over again.
This made me angry. Math anxiety?? Me?? I like math! I know that, in working on math with others, I can contribute ideas, ways of thinking, and ways of structuring thoughts that are valuable. I also know that I can solve and find the resources to help me solve problems that I come across and find interesting.
There are many, many ways to learn and participate in math (and any subject of study, for that matter). One of those ways is listening to a professor in lecture and working through chapters-worth of math problems every week – and maybe that accelerated, private, listening-based way of learning is great for some people. But it certainly isn’t good for me. I can learn more modern algebra by working through a good book on my own, at my own pace, by sharing interesting problems with friends and peers, and, most importantly, teaching it.
So, I dropped the class. And I know, better than I did before, how I learn math and how I want to teach it.