ColinsMum--respectfully, I certainly didn't mean to offend anyone, and I definitely agree with you--with the qualification that IMO it should be clear when the problem is something 'new' that may not be solvable with techniques already covered in the class. We haven't done AoPS but my impression is that learning how to solve new/different problems is kind of the point there, right? In the EPGY class, they present a lecture and then a series of problems that use the techniques just presented. Then sometimes there is a problem that can't be solved using techniques that were already presented--but it is not distinguished in any way from the problems that came before; it's just the next problem that comes up. In the context of the EPGY format, both my DD and I have found this to be confusing and frustrating. I am not a mathematician, so perhaps that is my problem, but at least from my perspective I think it helps give students confidence when the teacher makes it clear that the problem before them is one that they may not be able to solve, versus one that they should be able to solve had they been paying attention. To do otherwise feels to me (and independently to DD--she expressed this on her own) to be for lack of a better word unkind and not in a spirit of supporting the student. (DD--"why did they do that?") In the context of AoPS or a math puzzle contest, I totally agree with you, and have been trying to encourage DD to be more interested in learning how to solve problems. But IMO that is not how EPGY presents itself, and if that's what they're trying to accomplish I think it is counterproductive to try to slip it in unannounced. Maybe that's why I ended up giving up on math in college--my freshman calculus course was given by a professor who had a very thick German accent (that I couldn't understand at the time; maybe now I would have no problem) and who seemed to just write formulas up on the board for the entire hour. Perhaps I was supposed to know which parts I already knew, and where to go to find what I didn't already know?? Anyway, it doesn't matter for me because that was my last math class, but DD is better at it and I want her to be able to go as far as she can--so it would be great if the courses she takes encourage her rather than making her wonder if she missed something. If you still disagree, then I guess I would conclude that we have very different learning styles.
