It has been a fun start to the year so far. One of my goals of the last couple of years has been to keep moving away from the lecture-based style I inherited from my time teaching college math and go towards more group work, more investigation, more discussion, and more projects. I’m optimistic about continuing to make slow progress on all of those goals, but I think the hardest is still discussion. It is challenging for me to efface myself enough from the process, and to guide the students into a good, self-generating, student-led discussion. It’s hard to be sufficiently mindful of the language I use and the choices I make in addition to thinking about the actual mathematics that they are doing (or attempting) and that I want to come through in the discussion.
I’ve been happy so far with the relatively rich problems and investigations that my students have been doing. In my Trig/Precal class I brought in my bike to introduce a problem about gear ratios, and that was fun. It was also the right level of challenge, with no one getting it right away, but everyone being able to get somewhere. And I’m still happy with the theme I have for AB Calculus, where we are pretending to be part of a company selling sporks.
One quick comment about my Multivariable Calculus class, where we are starting with a unit on linear algebra: it was interesting to me that multiple (strong) students, confronted with a system of equations, said “let’s use matrices so we can use the calculator.” The idea seemed to be that matrices are something that are specifically for the calculator, and perhaps can only be used by a calculator. They will of course learn in the next few weeks how cool and powerful matrices are, even (or especially) when done by hand, with an eye to general features, not just when fed into a calculator or computer.