orthogon wrote:Whilst we could debate just how hard or easy certain concepts are, I think we could probably agree that mathematics, and to a lesser extent natural sciences in general, are viciously cumulative. Properly understanding one thing requires a pretty thorough grokking of the principles on which it builds. This for me is a very strong argument for that other unfashionable idea in education: ability-based streaming. Time spent teaching concept B to a student who doesn't get the prerequisite concept A is almost completely wasted. (This might not always be quite the whole story. Many concepts have some kind of circular dependence. Normally you'd think of matrix arithmetic as a prerequisite to geometrical transformations, but it's possible that somebody might suddenly "get" matrices as a result of learning about transformations. But even there there's a kind of cumulative effect resulting from iteration: by going back and forth between two topics you can make a small progress in your understanding of each in each iteration,
I'm in total agreement with this - as long as the streaming is done per subject, and it's made relatively easy to move between streams if appropriate, I think the upsides far outweigh the downsides, at least for maths and science.
like climbing up the inside of an alcove by moving your feet alternately on facing walls - I forget the climbing term for this).
Stemming is the word you are looking for.