Jeremy Kun's Habits of Highly Mathematical People.
He doesn't actually spend a ton of time on how the math we do in the classroom teaches the habits/skills he mentions; he's mostly defining and discussing examples of these skills in mathematical people. It's still pretty fascinating and useful.
Mark Chubb on Closing a Lesson
This post includes links to interesting things about orchestrating math discussion, and in general it talks about some things I've been thinking about (and struggling with) recently
Francis Su's Freedom Through Inquiry
I was fortunate enough to be at the IBL conference where Francis Su gave this speech, and it's so good. I love the humor of parts of it ("This set's closed, this set's open, this one's neither, this one's clopen!"), but Su also says so many important things about freedom in learning and how inquiry allows this freedom.
Dylan Kane on Lecturing
I'd never heard the bit about lecturing in MS/HS because in HS/college there would be lectures, but I agree with the reasons Kane lists to not use this excuse. My favorite part of the post, though, is the bit about not being sure how to respond when asked if he lectures, with these two quotes:
"Based on that knowledge I may choose to deliver some explicit instruction. Maybe for two minutes at a time, maybe for twenty."
"There’s no magic bullet, no one right answer. That intellectual work of figuring out what is going to work tomorrow for my students is probably my favorite part of the job."
Joshua Bowman on Expectations of an Upper-Level Math Class
This is mostly an excerpt from Bowman's analysis syllabus, setting up expectations from which specifications for grading will be taken. I really like the idea of explicitly basing an upper-level course around the ideas of definition, theorem, proof, and community. (I love that he includes community because it's so important.)
