Me, aloud: “What should I write about tonight?”
Another evening of supervising/coaching/cheer leading middle school math homework. They’re focusing on simplifying expressions where there is subtraction of a subexpression in parenthesis. As I wrote about previously, there are technically a few different ways of approaching this (and that language was for the math-savvy, not something I would actually say to a middle-schooler).
In the end we settled on the “distribute the minus sign” approach, since they’ve also been practicing the distributive property as well. She still doesn’t see “the point” of simplifying expressions, and perhaps at this point she doesn’t need to. But she’s willing to play along if for no other reason than she cares about doing well in school. I’ll take that.
She had over-learned a rule that I suspect many of her classmates did, which is “when there are things in parentheses you reverse the signs.” Nope! Not if the “things in parentheses” are simply being added. So we had to purge the “rule” and try to get to an explanation for why parentheses can essentially disappear when the subexpression is added, but the signs all flip when being subtracted. Still not the way I would choose to structure a curriculum, but it’s what we’re stuck with at the moment.
What was really gratifying, though, is how she was adding, subtracting and multiplying integers essentially in her head and getting the signs right about 95% of the time. This reminds me of what my high school math teacher once claimed: when you are studying level N of mathematics, you’re really solidifying everything you learned at level N-1. Her mother thinks she’s just coming out of metamorphosis – her brain had turned to liquid goo at the onset of adolescence and is starting to solidify back into something resembling a brain again.
I’m keeping it short tonight – time for a good night’s sleep. Yay for a short work week this week!