Using the grid frame with algebra tiles to work through multiplication in algebra blew-my-mind. It made algebra so much more clear to my head, and I don't remember ever particularly struggling with it, I guess I just never understood there was a bigger concept to understand. After that activity during our last class, where we experienced many different ways algebra can be thought about, the readings, Group Worthy Tasks (Lotan, 2003) and Orchestrating Discussions (Smith, Hughes, Engle, Stein, 2009), really hit home. Just as described, I needed time to think about an algebraic equation myself, discuss with others, and work through with manipulatives a variety of thought processes to get to the point where the algebra tiles on the grid made sense to me. And it was the connection I made myself, just as we talked about in class and was discussed in both readings, that x2 is an area and on the grid I could see an actual area. If only I knew I was such a mathematical wizard when I was younger, well, I'd probably actually be in the same place, but I would have gotten a lot more of a thrill out of math classes.
I must admit, I am still working through the beans as negative and positive numbers. Is it that you don't subtract because you can't really subtract in real life anyway, you can just move it or change it? Money doesn't actually go away, it just leaves one pocket for another; apples that get eaten don't disappear, they go through the digestive tract. Is all this why we don't subtract, we just add the opposite?
Some points in the readings remind me of the Culture of Power Delpit described, and that when we were talking in class and the readings explained having multiple entry points to the learning, it is about equity, so that complex instruction with group-worthy tasks and effectively organized discussions in mathematics isn't just a good suggestion, it is necessary for equity.
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