The ‘think-pair-share’ strategy helps here – youngsters discuss their ideas with a partner first, before sharing with class. No teacher involvement until they have already vocalised their thinking.

It is much harder to get a ‘tell’ when you are communicating online. Maybe online learning has an edge here.

This whole issue is a symptom of “teacher as priest”. Do we need learners to need us as arbiters of correctness and truth?

http://numberwarrior.wordpress.com/2009/05/12/my-favorite-educational-psychology-experiment/

We got into wait time. Like, “don’t just answer your own question when there’s silence,” but nothing like this kind of utterly essential Jedi mind trick.

I’d like to trade notes on one point with both of you: it takes me a matter of months to rid most students of their dependence on my reaction for their response. Months. The process is much quicker than I’d imagine.

If they get too deer-in-the-headlights then sometimes I let them know that they have the right answer, I just want them to explain how they got there. But that’s a short-term fix for poor self-efficacy and risks turning into a new cue. (Revised student algorithm: answer, look scared when asked to explain, wait to see if you are told you’re correct.)

The math may favor a certain approach, but the real world tells you that any line, on any day, can become the line from hell. Odds on a coin flip are 50-50, but that doesn’t mean that every other flip is tails.

Secondly, your little spinny things gave me a flashback to an art exhibit I went to about 15 years ago, which I have inexplicably not thought about since becoming a math teacher. The artist was Arthur Ganson. He makes machines. One of them is a series of twelve gear setups that each reduce the revolution rate to 1/50 of the previous. A motor turns the first gear at 200rpm; the last gear is embedded in concrete. All Ganson’s machines are charming, whimsical, and sort of mathematically provocative. (For example.)

@MatrixFrog, Maria and Touzel – a propos of the motivation question I read a compelling post by Jesse Johnson on how the question “what’s it for?” is actually usually a code for “I’m bored” or “I’m lost.” MatrixFrog I think you’re right that it’s the wrong question to focus on, or at least those of us teachers who are not engaged by the question should feel free to not focus on it. It is enough to focus on keeping the problems provocative, the level of challenge appropriate, and making sure the students are getting opportunities to be creative.