OK, I came up with an investigation in my class that I thought was really awesome. (See previous post.) It was simple, engaging, and collaborative, and the students actually argued about it and then rolled up their figurative sleeves and worked it out with only occasional intervention from me. In addition, there were multiple ways to solve it, and there was room for extension at the end.
But I felt slightly less cool when I realized that the next section of the textbook had a homework problem that was almost exactly like it. (It was couched in more pseudo-context about a greeting card manufacturer who for some unfathomable reason cared whether their card, when folded, was similar to the unfolded state….) So I’m not as blindingly original as I felt in the moment.
Nevertheless, I assigned the problem as part of the next night’s homework assignment. That’s when the real ego smack-down happened.
They had no idea how to solve it. I don’t think a single student could do it. (At least, no one would admit to solving it, which is another problem in classroom culture I need to deal with.) This was almost EXACTLY the problem they did as groups THE DAY BEFORE.
So what is the deal? Does group work feel good to us as teachers, while not really teaching the students anything? Does it make us think they are learning individually, when really they are just leveraging each other’s partial understanding?
What can I do as part of group work to help each student to consolidate the whole process? (I am thinking journalling about the problem, but that’s something for next year, because there’s not time in the schedule to establish that as a classroom habit at this point.) Is there something not as time consuming I can do (or have them do) as a wrap-up?
Help me, math twitter blogosphere. You are my only hope.