Math Relearning/Progressions/High School Functions
These are my comments on the Common Core Math Progressions document Functions: Grades 8-High School (PDF).
"this document does not treat in detail all of the material studied" - At this point I'm not trying very hard to understand, since I'm sure they're about to get into territory I barely remember and they're not going into much detail. I'll understand it when I get there in the curriculum, and the faster I get through the progressions, the sooner I can start.
"reasonable in the context" - It's kind of annoying that you can't figure everything out just by looking at the calculations, but it could be interesting to think about the relationship between the math and its context. And are mathematicians missing something by divorcing math from any context and thinking of it as a symbol manipulation game?
"algebraic expressions may not be suitable" - I'm looking forward to learning the other options.
"a linear function does not have a slope" - Why not? Just because it's not visual in itself? Is the function different from whatever you use to calculate the slope of its graph?
"describe the relationships qualitatively" - Yes, it's good to remember that people are still human when they think about math.
"Although it is common to say" - These kinds of language distinctions are important to me, so I want to come back to this when I get here in the curriculum. Actually I'm thinking of revisiting all the progressions as I go through the curriculum.
"the vertical line test is problematic" - I don't know what this is about, but it sounds like the kind of thing I want to know. The discussion distinguishes between a flawed method and a better one, and it tries to get down to the real issue in the mathematical task it's addressing.
"The square root function" - I've read that +/- 3 isn't the right solution but not why, so I'm glad they cover this. There's so much useful, in-depth information in the Common Core that I think people who dismiss it are cheating themselves. Unless they don't care to know math, in which case they may still be cheating themselves.
"all students are expected to develop fluency" - At this point I do wonder why we make everyone learn so much math. Most people don't ever need these functions after school. How does it benefit them? If they're relevant to the kinds of statistics that inform public policy, that would be a good reason, but otherwise the only reasons I can come up with sound like rationalizations.
"looking for and making use of structure" - This seems to be what some people mean when they talk about patterns, rather than simply noting and interpreting ambiguous, surface patterns like sequences.
"To avoid this problem" - I'm glad these exercises are on Illustrative Mathematics. It might make me more likely to remember to come back to them when I'm in the curriculum.
"subtleties and pitfalls" - Sounds like fun. :) Until I get into it and feel the strain.
"from scratch ... special recipes" - Yes, that's what I'm hoping this time, to learn the principles behind the recipes, so I can make my own math.
"Some students might" - I'm glad I figured out early that it's a basic feature of math that operations can be converted into each other. It helped me understand some other reading I was doing today. It's important to look at math from different angles like that one--what math means, how it works, etc. I'm sure there are other angles I haven't learned about yet.
My notes are starting to get repetitive, so I'm going to speed through the rest of the progressions.
Linear and Exponential Models
I like that mathematicians have so fully studied circles. It's nice to completely understand something, at least the things you consider important about it. I wonder if it's possible to design a good, single diagram that displays all of a circle's important mathematical features.
"Prove and apply trigonometric identities" - I'd like to try translating mathematical proofs into some other logical notation, just to clarify how the grammar of math relates to the grammar of logic. They're not the same thing.