I’m currently teaching a course to a middle-school math teacher in Teaching Mathematics through Problem Solving. I’ve taught this course a number of times before. One of the things I do is to ask students to work on problems which I think they will find difficult, but doable. My students – all teachers themselves – become frustrated if they encounter a problem that takes them more than a few minutes. They are so used to routine problems that will yield to a known method of attack, that they don’t know what they are capable of.
I think it may be sometimes better to assign one difficult problem rather than 10 routine ones. And we need to get students to commit to trying to solve a problem even if they have to put it away for a while, let it percolate in their unconscious, and come back to it later. At the risk of sounding like an old fogy, students today are very much used to expecting instant gratification. We need to teach them the rewards of persistence.