I haven’t released my insecurity. I have had to learn to accept it. In getting to this point, I realized that I, in actuality, had very little control of what was really happening in my classroom. Oh, I could make it appear that i was in control of the structure and behaviors, but that was a role that both the students and I mutually agreed upon. Unspoken, but still a shared understanding. In reality, I was never in control of their learning.

Now while I have a general idea of where I’d like my lessons to go, I never know where they’ll actually end up. Do I still get insecure about this? Yep. But I have learned to have faith in my students capabilities to do and to communicate mathematics. I have also had to develop a bit of faith in my own ability to help lead a discussion. Does it always end up where I’d envisioned? Nope. But my day is never boring. Insecurities and all.

As someone who tutors a lot of students for SAT/ACT prep, my coins of the realm in general are: process of elimination and “everything is a reading test”: that is, if you don’t take advantage of the answer choices and don’t read things carefully and attentively, you’re almost certainly under-performing. It’s obscene how many questions kids get wrong on various sections of these exams by not thinking analytically about why wrong answers are there and noting what exactly the question is calling for, and this is true on all sections of these tests and those like them (GRE, GMAT, LSAT, etc.)

So teachers could do a lovely service for students by taking math problems (and some science problems from the ACT) and making them launching points (or valuable side-trips) for investigations (I assume, Dan, that you don’t teach everything with the same structure, even when you find one you really like). ;^)

If anyone is interested, I could probably provide a few rich examples of what I’m talking about. Feel free to write me: mikegold@umich.edu

I like that so much that I forwarded it off to the ITEEA’s IdeaGarden list, which is the professional list for technology education teachers. Great stuff, Dan. I’ve also been bouncing your NCTM reports to our middle school math teacher.

Keep up the good work. It’s inspiring to see conference notes being made useful by turning them into public conversations.