In theory, this is great, and previously I've actively encouraged such cooperation. After all, what better way to learn to communicate math, sharpen argumentative skills, look at concepts and methods from different perspectives - well, y'all know the drill. Every modern text on teaching and learning mathematics seems to wet itself with excitement over group work. A classroom full of quiet students working alone with their (gasp!) textbook is, or should be, a remnant of older and more ignorant days.

But now I'm starting to change my mind. I see how students use each other as crutches, easy support instead of the harder work of figuring something out by oneself. Two main negative effects from this: students believe that they have mastered and understood something which they really haven't, and also that they are deprived of the chance to build thinking, memory and confidence by single-handedly struggling with math problems and concepts.

But now I'm starting to change my mind. I see how students use each other as crutches, easy support instead of the harder work of figuring something out by oneself. Two main negative effects from this: students believe that they have mastered and understood something which they really haven't, and also that they are deprived of the chance to build thinking, memory and confidence by single-handedly struggling with math problems and concepts.

In an ideal world students would be doing this kind of individual work as homework. This is not an ideal world.

So I'd like to incorporate more of that quiet individual work in class, but at this point I'm not sure how to fit that in with the explorations we frequently have going on. It's a matter of priorities, I'm sure, but even without individual work we're struggling against the clock every lesson. Right now I'd just really like a structure that I can use for each (or at least most) lessons and which includes a brief warm-up review of the previous lesson, an exploration, discussion/summary, group practice, and individual practice. But unless these components on average take less than 10 minutes each (they don't), something's gotta give. It's a pretty nasty dilemma and I welcome any and all suggestions.