Gifted Issues Discussion homepage Forums Recommended Resources EPGY - did your kids need additional instruction?

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.

That's certainly helpful, and I won't argue with the idea that it's sensible for most children most of the time. My reservation is that, of course, in real life problems (of any kind) don't come so labelled - one of the things one has to learn is to tackle something even though to begin with you just don't know whether you can do it or not.

Well, yes and no. Yes, because the clue is in the name :-) No, because this is not an add-on, something intended to be presented alongside a "normal" class that does things differently: the idea is that you do AoPS geometry instead of any other geometry class. They do it this way because they think this is the way it should be done (at least for "high performing" students, and I don't think they are trying to be very exclusive here; this ought to apply to anyone who needs to be accelerated in maths, for example). See here and related pages.

More likely, different ideas of what it means to learn mathematics. I submit that there is practically no point in being able to solve problems only if you know in advance that you can solve them and have been taught a technique to do so. That's not doing mathematics; that's pretending to be a computer, and we have computers for that these days.

I have to agree with ColinsMum-- but that is an outlook which, pedagogically speaking, is most common in math and physical science, and quite rare elsewhere.

I have hypothesized that this is because those disciplines must, almost by definition, rely so thoroughly on a growth-mindset or a "problem-solving" one. It's about examining the problem and considering which tools one has available, and ultimately, considering and rejecting different approaches to that problem.

Other things are about turning the crank, in the euphemism frequently used by physicists and chemists re: learning a new tool. It's useful educationally, but generally ONLY unto basic proficiency. More useful is the examination of a problem which one LACKS the tools to solve adequately, elegantly, or easily.

Example: it is entirely possible and mostly adequate to approach Newtonian physics from an algebraic and iterative standpoint. 50 years ago, perhaps not so much as now, actually, given advances in computing power. But it will always lack the sheer accuracy and elegance of using calculus to do the job.

Really, calculus seems so much more... useful once you've considered what it takes to work problems without it.



Cultivating such an outlook early seems especially wise.

Personally, curricula which neglect this kind of pedagogy have all but killed my DD's avid learning of mathematics. It's one of the things that I've loved about Singapore's basic approach over Saxon and other curricula like it. Growth mindset. Not fixed.