I have to admit that I have a somewhat dismissive nature sometimes, and have been known to make critical remarks for non-public consumption; “Programmers cannot do math at ALL” (hi Dale!) Of course, this is more out of shock than a belief in any natural order. I firmly believe that anyone of everyday intelligence can learn math. I am of the opinion that I could teach calculus* to a dead twig if the twig where sufficiently motivated.
Which is why I was happy to see that someone had written a blog entry on learning math being what you make of it. The only thing I would criticize is that he is completely wrong.
Ok..just kidding, but I do have to say that I would not follow his councel on exercises. When I read a GTM on a new subject (papers don’t usually have many exercises :), I don’t really view the problem sets as seperate from the explanitory text – I do every single problem. This is because the author of the text did not view the problem sets as seperate either. It goes beyond “having been shown the idea, cement it in your mind with the excercises”. Most of the time, realizations that the author wants you to have are set up in the problem sets because they would be TOO padantic and verbose in the main text.
*This isn’t restricted to calculus of course.