Thanks to Avery, the phrase 'mathematical habits of mind' has been in my brain more lately. Now, every time I point out a mathematical habit of mind (MHOM) in class, I want students to add it to their growing list of MHOM. I ask them to turn to the last page of their notebooks and add it.
I've found myself doing this in each of my classes, and I think it's a great change to be making.
In my office, when I tell a student how to check their work, I have them write down: "Check the steps" on the last page of their notebook. And when I ask them to re-read the question when they're done, to see if they've answered it, I ask them to write: "Look back to see if I've answered the question I was trying to answer."
I've mentioned precision and organizing information. I think I've also mentioned trying a simpler problem first.
I've often mentioned these things in the past. (In fact, here's a blog post where I summarized some of these ideas.) What I'm doing differently is asking the students to compile a list of these ideas, to help them become more self-aware as they work on math.
Maybe a month or so into the semester, we can take some time out to discuss their lists and make a class list, with examples. I like where this is going.