I’m reading Graham Nuthall’s book The Hidden Lives of Learners. It’s a fascinating summary of a career of research working to take the student’s perspective and learn more accurately what students experience in the classroom.
Rata: Yea, we did a chart on it, but I can’t remember what we put on it now…this big picture on this big piece of paper on the wall. And our group had to do something on weather, and you had to write these, the north, south, east, and west on it, and see, and put, which weather brings the hottest (laugh).
Interviewer: Right, and your group did that?
Rata: Yes, and you had to put it up on the wall.
Interviewer: Right, and do you remember which was the warm, dry one?
Rata: No (laugh).
Interviewer: Can you picture it in your mind, the one your group did? Who did the writing on the chart?
Interviewer: Did he? Did you help?
Rata: Um, no, the other two didn’t help us, only me and Bruce done it. I did some of the writing on it and he, he wrote it out, and I wrote ‘weather’, and he, um, we both thought it up, and looked on our chart [weather records] to see which one was warm.
The interviewer and Rata are discussing a question she couldn’t remember how to answer about the relationship between wind and weather in New Zealand. I’m fascinated by what she remembers and what she doesn’t. This exchange reminds me of an idea I try to think about in my teaching:
Students learn only what they think about.
If my class does not make students think about math, they’re not going to learn math. In this instance, for whatever reason, Rata was thinking about a lot of things making that poster but not about the relationship between wind and weather.
I wonder how many lessons I’ve taught where, looking back on it, a student could say, “Oh I remember, we were doing this on whiteboards, and Carter was writing it in green and we were on the side of the room by the door…”, but not actually remember the mathematical content I’m interested in. I would bet there are more activities than I would like to admit that don’t cause students to do the necessary mathematical thinking.