This summer I've been studying how to put math concepts across to young minds, and there are a lot of different strands and substrands to it. The five strands model seems to be widely accepted, but it seems to me that there are really only three, with one having many substrands. The three are conceptual understanding, procedural fluency, and problem solving, as described in
http://www.p12.nysed.gov/ciai/mst/math/standards/revisedlintro.html . In this context "conceptual understanding" basically means Bloom's taxonomy, procedural fluency means doing the basic operations quickly and accurately. Problem solving is stickier--it means taking the concepts you've already learned, recognizing which ones to apply to a given problem, and how to apply them. This isn't easy, especially because many problem have more than one way to solve them, and it's what I need to learn more about.
The five strands, by the way, add "productive disposition" (basically, a positive attitude) to the list, and split "problem solving" into "strategical competency" and "adaptive reasoning". Productive disposition is of course an important component, but not something to be planned or tested for, so you can't make it part of a formal structure. As for splitting up problem solving--I don't see any reason for that, maybe when I work out the concept better I'll see the point. I should think that through while I'm playing chess.
