School starts tomorrow, and I am really excited to have my own classes for the year again. One of the assignments I give my students on the first or second day is to write a math autobiography, including their best, worst, and earliest memories of math. I wrote about my earliest math memories here. I thought I would share some of my best memories today.
I recall several moments working with students after I started teaching; I think about these often, but they are more about teaching than about doing math, so I'll save those for another post. The other good memories that stick in my brain are two episodes from college math classes. I'll write about the one that occurred later here, and save the other story for another post, I think.
Abstract Algebra was a three-course sequence, of which the first two courses were required of all math and math-ed majors. The third course was an elective. This is the course that studied groups, rings, and fields, and included lots of strategies for proving that a particular set of numbers could be classified as a group, ring, or field. (I wrote about a discussion with my younger son around the topic of groups here.) Since it was a required course, the first class started with about 30 students, which was about as big a math class as there was at DePaul at the time. My favorite college professor, Jeff Bergen, was teaching it. He had a great sense of humor, was very patient about answering questions, and explained complicated ideas well. Nevertheless, the class was difficult, and by the midterm, only about 24 students remained in the class.
The second course began with 18 students, and was again taught by Dr. Bergen. He had taught most of us in Calculus and Differential Equations in prior years, and we all knew each other to some extent. The class was interesting and fun, but still difficult, and only 12 of us remained by the midterm. I can't recall a set of math classes I have worked harder in, but I asked lots of questions, spent many hours on homework, and did well overall. Knowing Dr. Bergen would teach the third course, I signed up for it, even though it wasn't required. Only two other students signed up, and I thought the class would be cancelled. It wasn't. The three of us met in Bergen's office, and furiously took notes while one of us or Bergen solved problems on the board. Talk about pressure! No place to hide, no other students to answer the hard questions, and it was great! But still beastly difficult. By the midterm, only one of us (not me!) had a decent grade, and I had to think long and hard about whether or not I would drop the class. I spent at least one sleepless night walking around campus trying to weigh my options, and thinking about the different strategies I would have to use for studying if I was going to stay in the class and have any hope of passing with a reasonable grade. (At that point, I would have been happy with a C, folks.) I talked to Dr. Bergen about my worry, and he suggested a couple more strategies. I stayed in the class, along with the one guy who was passing, changed how I was studying, used more office hours to get more questions answered, and had a great time. I did pass the class, and I will never forget the satisfaction I felt in completing all three courses, working through the difficulties I faced, and coming out with a better understanding of not only the math, but also of my own learning capabilities. That was probably the lowest math grade I've ever received, and yet that is the one I am the most proud of.
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