Math Relearning/Mathematical Practice
Comments on the Common Core Standards for Mathematical Practice.
After having read the Progressions, I'm reading these because they're starting to sound important. When I first read the K-8 standards, it was just to get ideas for creating my own curriculum, and I didn't think I needed the MP standards for that.
I want to break these descriptions out into lists so the pieces are easier to work with for various purposes.
Side note: I really like the font in the CC standards. I might try to match it for my personal font, if Google or whoever has something close.
- 1 Make sense of problems and persevere in solving them.
- 2 Reason abstractly and quantitatively.
- 3 Construct viable arguments and critique the reasoning of others.
- 4 Model with mathematics.
- 5 Use appropriate tools strategically.
- 6 Attend to precision.
- 7 Look for and make use of structure.
- 8 Look for and express regularity in repeated reasoning.
Make sense of problems and persevere in solving them.
"explain correspondences between" - This reminds me of just how many math concepts there are to learn. It's a little intimidating. At the same time I suspect there are fewer than it seems because so many words are used to describe them. This reminds me that the CC standards are stated in terms of tasks, and the concepts are buried in the tasks. Furthermore, some of the concepts are split across tasks, probably mainly in the lower grades (e.g., working within certain number ranges in certain grades). I'll need to separate out the concepts and combine them when it makes sense. Separating things out would involve attending to the different levels and modes of concepts, especially whether something is a procedure or a reason for a procedure.
I've often thought during my math reading that if you want puzzles to solve, you don't have to go any farther than your math textbooks, assuming the exercises are well written.
Reason abstractly and quantitatively.
Ah, all that talk of context relates to this standard, and it's only half the picture. I hadn't connected abstraction (decontextualization) and contextualization.
"Quantitative reasoning entails" - I suspect once I get more familiar with math, I'll be able to introspect about the quantitative aspects of a situation like I do about its personal aspects.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
"drawing an auxiliary line" - So hopefully learning more geometry will give me clues for solving the world's hardest easy geometry problem.
"step back for an overview and shift perspective" - I do this for non-mathematical situations a lot. It's nice to see this technique applies to math too.
"single objects or as being composed" - Tall's procepts.
Look for and express regularity in repeated reasoning.
Isn't a generalization from specific data a conjecture, and doesn't it have to be proven afterward? I'm looking forward to learning how this happens.