[dkarl]

Unfortunately, the pleasure or displeasure of doing math compounds quickly. A kid who doesn't enjoy it is going to do the minimum required, and if that isn't enough, it will become ever harder and less enjoyable in the future. You need practice, and practice is a dirty word in pedagogy.

Someday education is going to catch up with music and sport in its attitude towards practice. As adults we all understand that in music or sports, the most elite of the elite, the top 0.01% of human beings in attainment, are never too good to need more practice and polish of basic skills. But when we look at children learning math, repetition becomes anathema. My question is, how could anybody ever enjoy math without repetition? You need to make the boring stuff easy and then keep it easy. How does that happen without repetition? If you don't practice, the boring stuff becomes hard again, and you don't have brains to spare for the interesting stuff.

[ksenzee]

I can’t relate to this at all. In music, you practice until you get it, and then you stop. It’s important not to over-practice, in fact. In high school math classes, I was assigned an order of magnitude more practice problems than I actually needed. There was no “practice until you get it, then quit.” It was “do all the problems whether you understand them or not, or you get a bad grade.” Repetition is absolutely anathema when you’ve ceased to learn anything from it.

[greentxt]

I agree. Kids need to eat their vegetables, but we can make vegetables quite delicious if we try. Also, the music metaphor is imperfect because some musicians are performers others composers. I prefer sport as the metaphor: a mix of short laregely repituous training and longer term strategy, different styles for different athletes, influence of genetics and talent heterogeneity acknowledged at the elite end of the spectrum.