I have had my first class in Math, Art, and Design (MAD) and in Calculus, and I wanted to give a report on how those two classes went for me. In MAD I introduced the class and then started to talk about infinity, our first unit this semester. I showed a number of videos and then we went through the “Hotel Infinity” thought experiment together. Part of the reason that I start the semester with infinity is that there is so much richness to explore mathematically, but it is also an idea that we all share — mathematicians don’t have the market on infinity cornered and anyone can engage with the ideas. But I find it interesting that even though I want students to engage in the ideas their own way, I still struggle when their ideas are different from mine. I still have this deep internal belief that this is math class and there really is a right/best/most illuminating way to engage with the material. I constantly have to remind myself that differences of approach and opinion are OK, even though I chose the topic specifically to allow for these differences. I had the students give me some written feedback and it is mostly positive. I need to guard against going so fast and intensely that I leave people behind, and make sure that I give students ample time to work on their own. Honestly, it was wonderful reading the responses because brief as they were I felt people were putting their hearts into them.
I just moments ago got done teaching my first calculus class, with 16 people in it. Yay! I talked too much, and next class I vow to give the students more time to work. Once again, I adhere to the idea of giving students space and control, but it makes me anxious and I control my anxiety by preparing too much material and talking too much. I talked explicitly about two things that I think are important. First, I talked about the way that math is taught with the teacher presenting procedures and the students practicing those. Good teaching means doing a good job explaining, and being a good student means practicing. I told them that I want to open us up to something different, but that it’s risky and uncomfortable for all of us. For me, its uncomfortable because I’m violating the social contract. They have certain expectations of teachers and I’m not always going to meet those. For them, it is uncomfortable because I’m asking them to do something new and sometimes it will feel like I’m throwing them into the deep end and insisting that they swim. The other thing I talked about explicitly is working in groups, and I tried to draw out some of what they think helps and what can go wrong. I want to do more of that in subsequent classes.