Hi Bryan,

I enjoyed reading your research proposal... and your blog in general. Two things jumped out at me in your proposal. First, when you define mathematical agency, you talk about "mathematical" problems and situations. That implies that there are "non-mathematical" problems and situations. Do you believe that this distinction is real, and how do you differentiate them? Second, when I read your Habits of a Mathematician, I don't sense any organization or deeper framework behind them. It is a nice list -- and I don't disagree with anything on it -- but the list feels like a hodge podge that does not provide me with any deeper insights. Sharpening and organizing the list will take a ton of effort, but it may be worth it.

I'm also curious about how you are feeling about your career in math education now that the school year is over. I think you need to ask yourself some hard questions about the impact you are having on your students. How effective have you been at supporting student agency and mathematical habits of mind?

The goals you have established for yourself are incredibly hard to achieve... especially in one year. In fact, I'm not even sure you can do what you are trying to do in one year by yourself. Based on my own experiences in the classroom, I don't believe that your focus on "doing" math is enough. I think you need to take things to another level, which means being a pioneer and breaking new ground. But I hope that you stick with it. I like how thoughtful and self-critical you are. I would urge you to be even more self-critical, not less.

Dave

Hi Bryan,

It feels like the habits on your list overlap. For example, conjecture and test seems directly related to look for pattern and regularity, be systematic, and tinker; and visualize seems directly related to look for pattern and regularity, simplify the problem, and stay organized. I suspect that if you were to create a web linking the habits together according to "direct" relationships, the interrelationships among them would get pretty complex. This makes me feel like there must be some kind of underlying structure beneath these habits that I'm not seeing yet... kind of like particles and sub-particles. On an intellectual level, it just makes me want to probe deeper.

What are you trying to accomplish by asking students to "do" math? After reading your research proposal, I would guess that one of your primary goals is to increase your students' mathematical agency. Are you accomplishing this goal? Are you accomplishing this goal such that you are confident that most of your students will continue developing their own mathematical agency and doing math once they leave your classroom?

I had to ask myself these same questions when I started out as a teacher. In my experience, students could not build enough mathematical agency doing math for one isolated year to buck the system and become lifelong math learners. You are trying to undo a decade of past math experiences for them. All you can hope to do in one year is to prime the pump in a way that the pump keeps pumping on its own after it leaves you. That's quite a challenge, and I haven't found any answers in the literature. I don't even hear many people asking these questions and working toward an answer. But that is just my experience.

And research plan I would have been sunk.

(sorry iPad jam)

Good luck. Action research or bust!