Hint: It's not knowing 17 different ways to solve a quadratic equation.
As the wee progeny of many of my friends and family began to wind their way through elementary (and middle???) school, I've had a number of conversations lately with adults who work outside of education about what it means to have a "good" math education and/or a "good" math teacher and in particular what should they look for in a school or classroom to know that their child is going to get a decent mathematical education.
It's a very tricky, very loaded question that I always struggle to answer in any helpful way. I mean, I can certainly list any number of elements I would hope to see in any math classroom my child were going to spend time in. For example:
- A focused, coherent, and rigorous curriculum that aligns at least pretty well with the Common Core
- A balance of procedural, conceptual, and problem solving/application elements
- A focus on making sense of mathematics rather than on "answer-getting"
- Rich, open-ended opportunities for tinkering, discovery, and general "mathematical play"
- Procedural fluency that is built on conceptual understanding and robust number sense rather than rote memorization
- De-emphasizing speed, but without altogether abandoning the idea of "mathematical efficiency"
- Explicit discussion of the myriad ways of accessing and making sense of mathematics (multiple representations, multiple solutions, etc.)
- Explicit discussion of the brain science that underlies fixed vs. growth mindsets
- Celebration of mistakes as a necessary part of the learning process that enriches and enhances our understanding
- Opportunities for collaboration with diverse peers (and I mean diverse in every sense of the word)
...Etc.
...Etc.
...Etc.
