I have been quiet on the web for the last couple of days. I had an interview for and was hired into a grade 6/7 long-term occasional (LTO) position, and it has been a whirlwind of prepping and trying to teach a very challenging group of junior/intermediate students. Today was day 2.
I planned a math lesson the way I wanted to do it, knowing that with my group it could flop miserably, but to my delight, it went off quite well! First we did our first WODB (Which One Doesn’t Belong) for the non-math-teaching-geeks out there. They had to sign their name to the one they thought didn’t belong and write in their reason. They were reluctant at first, but loosened up when they realized that they were allowed to use the same reason as some of their classmates. Knowing that they might be tempted to cluster in their answers, I provided an incentive for original thinking: as a class, they had to try to find my secret teacher choice. If they did, they would get a small prize. Here is the board for the day:
Students came up with all kinds of great reasons, some of which I hadn’t even considered! A few of their reasons were not well explained, so we discussed what they meant, and I clarified and made visible their thinking in green (my teacher colour). Despite their best efforts, they did not come up with my secret teaching reason. I chose 2×2 because it is a perfect square. I picked this one, because it tied into exponents (which the grade 7s had learned in the fall), and it opened up the idea of an array, which should open up their view of multiplication. After saying that it made a perfect square, another student said that it didn’t have to be a square and separated the two groups of two. I should have paid him. It got the class talking about another way in which we could talk about multiplication. Overall, we had a great discussion. The image to the right shows some additional insights and reflections on student thinking.
I followed this up by splitting them into visually random groups and having each group take one of the multiplications and representing it as many ways as possible on a sheet of chart paper. They struggled with what this meant at first, and I had to call them back in to model it a little in the middle, but they seemed to wind up with a broader conception of multiplication by the end.
For grade 6/7 students, the multiplication was a little simple, but I noticed during my transition day of observation that students did not seem to have a lot of flexible thinking when it comes to the idea of multiplication so I wanted to back them up a little and try to open up their minds a bit. I think it worked, even if it did take a while. They now have a base from which to add in an extra digit.