Some amazing things have happened in the last month or two. I feel like my chances to really grown and explore as a teacher are running out and I have so much left to learn. When I haven’t written in a long time I always struggle to start the post, wondering what do I write about. Meeting Dr. Steffe in Georgia and talking to him about student thinking? My wild and crazy geometry game I just finished up? Teaching solids of revolution in Calculus? Arizona State and picking a graduate school?
Let’s stick to this week for starters. Kids came back from Spring Break with a severe dose of senioritis. So many of them had not finished assignments and many were absent because of the ash cloud over Europe. One of my students emailed me from Rome asking about homework. He’d even taken his book with him which I thought was fantastic. I haven’t told them that I’m going to graduate school next year because I don’t want them to think that I’m checking out of the class. In fact, I’m not checking out. My senses are more honed, my planning more complete, because I know this is my last chance. There is no next year. Usually in teaching when something seems like it will be a huge upstream swim I just postpone it for “next year.” Some of these things(like keeping papers organized well) never seem to happen. There is always a next semester. And then next semester is never quite calm enough to re-prioritize. But now, all of my ideas need to be played out in the classroom while I’ve still got this chance. It’s going to be so much harder to convince someone else to try them out when I’m working with teachers in the next few years.
I’ve also realized what a valuable source of data my students are. I’ve started to ask them more about what they are thinking. Instead of just tracking which ideas they get right and wrong I’m trying to figure out how they are making sense of it all.
One student came in to talk to me about how hard the homework had been. He mentioned that when doing w-substitutions he couldn’t tell if he’d picked an inappropriate substitution because he didn’t have enough faith in the rest of the process to know if his problems were related to the selection of w or the rest of the algebra.
He also told me that he’d like me to put “think about algebra” on the top of tests to remind students to make basic simplifications to make integration easier. The class amended this today and asked me to tattoo think about Algebra on my head to help them improve. The future educational researcher in me asked if saying “think about algebra” would help a lot. Isn’t the issue their algebraic fluency? I know that telling someone to be better at algebra isn’t going to work. Why do they need to be told to even consider using algebra? What taught them that algebra is not a useful tool for making problems easier? Even after lots of algebra drama we still had a bunch of questions that required understanding fractions and/or exponent rules to transform the integral into a polynomial function in typical form.
I NEED to videotape my classroom as Dr. Engle suggested to me. Maybe during the Volumes of revolution project. I need to carefully think about what types of questions might be really interesting for that project. Kids end up spending a lot of time trying to design a function that looks like the shape that they want.
In Geometry I asked a few students what they thought of the book Thinking Mathematically. I am trying to understand if they are learning about general problem solving strategies. Alexis said that she learned that when you get stuck on a problem you are supposed to keep going. Another student said the problems gave him a headache because he really had to think. Alexis and I discussed what she was learning. We both agreed it was really hard to measure as compared to formulas and procedures but she seemed to think that she was learning something. I did notice that students are willing to think about geometric proofs for more than a minute. The time it takes to solve a problem seems to have increased and they are okay with that. Honestly, I think that is a meaningful lesson.
As I try to long term plan the rest of the semester, I am struggling a bit. I want to do something really amazing so that I can write about it in Mathematics Teacher(or perhaps a less prestigious journal.) I want to join the projects at ASU with a strong understanding of what kids are thinking in Calculus. And I don’t know. I’ve been so focused on everything else that I forgot to focus on student thinking. How did it take me 3.75 years of teaching to come to this?