Talk:What makes Mathematics hard to learn?

high school anecdote

I had a friend who, one year behind me in high school, was already very talented at mathematics, excelled in math competitions. after he had taken first-year high school math, he was taking geometry. he didn't like it. Every year we would have the same conversation, as he tried to find reasons to drop or stop studying for his math courses.

10th grade : why should I learn this geometry? I already know everything I need to about algebra and trigonometry and mathematics - everything my calculator can do, very useful stuff. why should I learn this? it's a waste of time.

11th grade : why should I learn this calculus? I mean sure, algebra and geometry are useful everywhere, and this is an abstraction above those -- and taking derivatives and integrals to evaluate some basic physics. But a few weeks in I know the basics, most of it is mechanical -- why should I learn this just to be 'educated'?

12th grade : why should I learn abstract algebra? How could this ever have meaning in my life? I already know algebra and geometry, which use abstractions, and calculus and function analysis is useful in lots of my science work, but this is just manipulating sets -- I already know how to do anything that might come up in a real world problem. Why should I spend time studying this?

By the end of each year, he was the strongest proponent of how interesting and useful and enlightening a math course was, and could rattle off a dozen ways in which it helped improve on or influence work in some of his other courses (he went on to study cognitive science).

On the one hand, he is right -- today he doesn't use any of the above math on even a weekly basis. On the other hand, it took him about 6 months into the year before he was loving what he was doing and seeing relevance in everything else he studied. The teachers and books never inspired that in him, however, he had to internalize it and start seeing the world differently before he found inspiration to carry on. --Sj talk 22:06, 26 February 2008 (EST)