- We didn't cover enough math topics

- We should have prepared for the STAR Test

- We didn't do Algebra II (or whatever math we were supposed to be doing)

- I didn't like when there wasn't a clear/right answer

As you might guess, I try to create a class in which students are doing math. We have worked on some interesting problems this year (How many combinations are there at Chipotle, What is the area of the Koch Snowflake, How can we predict global population, What is the best strategy for the game of Pig, etc) and students have done some really interesting mathematics as a result. Unfortunately, our society views mathematics as a thing and not an act of creating. Our national content standards, for many, serve as a definition of what mathematics is (and, by comparison, what it is not). In schools, society dictates, math should be compartmentalized and taught by transmission; if you perform well on the STAR/SAT/Whatever then you are good at math and if you don't then you're not.

I have tried really hard to open up this narrow definition of mathematics and to provide all students the opportunity to be mathematical every day, yet some of my students don't even recognize what we do in class as mathematics. It's difficult to be a part of a system while simultaneously doing things that run against it. You can't, and I don't, blame students for their outlook on things. I'm not sure my writing here captures the drama of all this, but I find it really alarming that this is what our educational system is teaching students about mathematics and about themselves. As I reminded my students today, the root of "educate" is "educe," or "to draw out." My job with them has been to teach by offering them an opportunity to express what was already a part of them, the ability to create mathematics, to create powerful ideas.