My Thoughts: I love doing this "you ask ME a question" thing on quizzes because it lets me see what my students are wondering about. I try to encourage them to narrow their focus on material related to our course, and I sometimes give minimal to zero credit if a question is too far afield or not well-formed. (Sometimes, I tell the student to come talk to me in person and then give them credit retroactively.) But, I don't exercise this policy too stringently because I like to see what they'll ask. Sometimes, it's about me! I think this is because they can see my enthusiasm for math both in and out of the classroom. In the context below (a math course for almost entirely History, English, and Communications majors), this may in fact (unfortunately) be the first time they've encountered a teacher who really enjoys the course and wants the students to enjoy it, too. So, I let them ask things about me and my life. I know that there are some Education majors in the class, too, so I hope that I can sometimes inspire future teachers, even if they won't be teaching mathematics.
Context: "Math of Everyday Life" (quantitative reasoning course for non-STEM majors).
Question: I'm curious as to what led you to become a math professor. Was that always a goal for you?
My Answer: As a kid, I was “good at math” but, looking back, I realized I was just quick with numbers and liked following rules and formulas. Over a long period of time, I have come to realize that this is not at all what math is all about, it’s just a very small part of it.
I studied math and physics in college because I liked understanding how the world works and liked the idea that we can prove things (using logic in math, or using experiments in physics). I realized that I didn’t really like doing the lab work required for physics and that I was only interested in it because of the mathematical theory involved. So, I went off to grad school to get a PhD in math, with a focus on applying mathematical methods to physics. (Specifically, I studied partial differential equations, the Finite Element Method, and the Navier-Stokes equation. Those are things you can google.)
That didn’t go all that well. I took a lot of advanced courses in math and did alright, but I started feeling jaded. I didn’t feel an impetus to do research. I realized that I liked learning as much as I could because I was fascinated by the knowledge and wanted to let everybody else in on the wonderful secret that math is beautiful. I wasn’t really interested in taking that gained knowledge and applying it to my own research problems or writing papers or anything like that. I just wanted to talk about math with other people and help them learn.
So, I got really into teaching. At my school (Carnegie Mellon), grad students are expected to serve as Teaching Assistants, working under a professor (who would run the big lecture classes) to teach small sections of students on days they don’t have a lecture. (These are called "recitations".) I really loved this and found myself spending way more time prepping for teaching and working with students than I spent on my own homework and research. After a disastrous oral exam with my research advisors that I totally bombed, I thought about dropping out of grad school. I had a few dark months where I zombied my way through life, unsure of what to do and whether it had all been a waste of time.
Amazingly, at that time I learned about a different degree that my school offered that I had never really heard of: Doctor of Arts (D.A.) It’s like a PhD: it’s a doctorate, and I had to take the same advanced coursework. But, the dissertation is not original research and scholarly articles for a journal. Instead, it’s expository, it’s based on sharing existing knowledge in a new and creative way (instead of forging new knowledge, like for a PhD dissertation).
I ended up writing a textbook for a popular math course at my school that everyone has to take called “Concepts of Mathematics”. The math department let me, as a grad student, teach one of the 100+ student lecture classes, which is very rare. And I was able to “test run” my book along the way to get feedback from students and make it better. They still use that book, 4 years after I’ve graduated. And, I use the book to teach MATH 2109 Discrete Methods here at Emmanuel!
