Throughout my time in secondary and post-secondary schooling, I have realized that most math teachers/professors follow a monotonous routine of teaching/lecturing, assigning homework, and, once we finish a unit, reviewing followed by an exam. If you look back, you would realize that most, if not all, teachers did something similar. Rarely have a teacher done something out of the ordinary, which is why I loved learning discrete mathematics and number theory in my programming classes in secondary school. I solved these problems by coding up a program which helped me understand the relational mathematics behind the way it works rather than the instrumental mathematics or how it works. It was also why I shifted my mathematical views from caring about the "how-to" to wanting to know the "why it works."
Similarly, in post-secondary school, the professor who stood out to me was the one who did not follow the monotonous routine of lectures, homework, and exams. I went to Simon Fraser University, and there was one professor whose classes I took introduced a different way to teach. The main goal of the course was to teach us group theory. However, rather than taking the traditional monotonous approach to a relation mathematics approach, we have to first play with games that emphasize the learning material without explaining it. He had us explore the things and then formally introduced them to us. The final was also not the traditional style of an exam. A poster and report asked us to explore other games (not covered in class) and teach us the math behind them. Most of it was a variation of the Rubik's cube, and for the odd one out (us), we analyzed a computer algorithm for solving a 3 by 3 Rubik's cube. For those interested in the course, http://www.sfu.ca/~jtmulhol/math302/ (He made a free textbook to go with the class.)
All too true that most math classes follow a very predictable (and monotonous) pattern! Sometimes it 'works', in that it's quite possible to learn interesting things despite the monotony, if you're an interested student -- but I think there are more optimal combinations of teaching techniques. Your SFU group theory course sounds great, and I had an SFU introduction to group theory that was similarly experimental and fascinating! (It was taught by a prof now retired, Harvey Gerber). I love the approach via games.
ReplyDeleteI'm also very interested in the ways you learned discrete math and number theory via programming! This has great promise for your future teaching... perhaps a computer math class? I think a lot of people can get a fresh look at math through the constraints and affordances of coding!