The two extremes we try to avoid in teaching creative problem solving:
(a) The student who holes up in a quiet place for hours by himself hammering his head on the desk trying to solve a problem that should take all of 20-25 minutes
(b) The student who looks at the problem for 30 seconds, throws up his hands, and turns in a blank page saying "I have no idea, this is too hard."
Somehow we have to convince students to make a serious individual effort, but to stop and seek help when they get truly stuck. How? I've got my own techniques, which usually involve rules about how much time students must spend writing down their own ideas before collaborating. Occasionally I've assigned work due on one day, then on that day granted a reprieve to allow further collaboration. That works great; except, you can only do it once or twice before students stop doing the individual work, hoping for and expecting a reprieve.
Jen Deschoff, originally a Michiganer but now a North Carolinininian, created a kick-arse approach to holding students accountable for their individual effort on problem sets. In my Summer Institute that Jen attended, I pointed out the four essential elements of a well-presented physics problem:
There's hardly a well-solved AP-level problem anywhere which doesn't include at least three of these four elements. I remember making a throwaway comment that, if I were pressed for time during the school year*, instead of grading a problem set carefully I might just look quickly for these elements in order to assign a grade.
* Ed. Note: Why use the subjunctive? You're a teacher. When school is in session, you are pressed for time by definition. Might as well say "If Ray Lewis could beat you up, then he wouldn't steal your lunch money, 'cause he's reformed now."
Well, Jen took that comment and ran with it. She now grades many AP-level problems in two stages:
Stage 1: On the day the problem is due, students give the problem to another student, who looks for each of the four elements. The students are NOT grading the answer at all! They're just verifying that words, diagrams, equations, and numbers show up somewhere, and giving a grade for that. Everyone keeps their original work.
Stage 2: The NEXT day, everyone just turns in the problem, and Jen grades it for correctness as well as for the four problem solving elements.
This approach fosters discussion among students -- they grade each other's initial work, and so I'm sure they comment on the correctness of the solution. Someone who was previously stuck will likely see the hint he needs. And now the guy who writes nothing because "it's just too hard" stands naked* before the class, seeing that he could have, should have, earned credit just by going through the problem solving motions. (Jen says she has thrown** blank papers back to students.) Next time, when he does go through those motions, he'll be surprised to find that physics isn't as hard as he thought.