How long should I let kids struggle with a problem?

I’ve been thinking a lot about that question the last few weeks. I teach math to three different “ability groupings” of kids, and yet in many ways they have similar sets of reactions in grappling with a difficult problem.

When they first hear the problem, there generally is interest and excitement, especially if I have chosen a good problem. (By the way, by “problem”, I don’t mean a routine exercise, but rather something that requires them to think, to use what they have previously learned but in a different way.) Students generally start talking among themselves about what they might do, or they raise their hands to ask clarifying questions and to propose a plan of attack. At this point, things have a really good feel– students are engaged, and they are anticipating solving a thorny problem if they just make a sincere effort. And indeed, that is often how things go– students spend a few minutes trying an approach or two, make a mini-breakthrough, and then solve the problem.

But often, after 5-10 minutes of thinking, students find themselves at an apparent dead end.