__the__goal I have for my students? Well, to learn mathematics. In order for that to happen, I need to

*maximize the amount of time that students are actually doing mathematics*. Everything I plan should be centered around this.

This begs the question, though - what is "doing mathematics"? First, it's easy to list a few things that it is not. Doing mathematics is not:

- taking notes
- listening to me talk
- drill & kill assignments
- taking tests

Already, so there is one guide post - minimize the amount of time doing these activities.

As for doing mathematics, I like the way that Keith Devlin describes it:

"Doing math" involves all kinds of mental capacities: numerical reasoning, quantitative reasoning, linguistic reasoning, symbolic reasoning, spatial reasoning, logical reasoning, diagrammatic reasoning, reasoning about causality, the ability to handle abstractions, and maybe some others I have overlooked. And for success, all those need to be topped off with a dose of raw creativity and a desire - for some of us an inner need - to pursue the subject and do well at it.

However, I'm having a difficult time describing exactly what "doing mathematics" means. In my mind, it's more of "I know it when I see it", so I need to work on clarifying what it means. Some activities that I think do fall under this umbrella:

- Solving novel problems
- Student-generated questions
- Investigations
- Cooperative groupwork
- Communicating reasoning and thinking
- Proving conjectures
- Finding patterns

This list could go on and on, but my takeaway has been this.

*All planning should be focused on maximizing the amount of time that my students are doing mathematics.*