Just an interesting piece... a recent study has found that teaching conceptual understanding in math makes children learn better, as opposed to teaching procedures.
You Do The Math: Explaining Basic Concepts Behind Math Problems Improves Children's Learning
The children were taught about solving equations such as
4 + 5 + 3 = ___ + 3
either procedurally, or conceptually. Procedural instruction went kind of like this:
"Add the three numbers on this side, 4 + 5 + 3. That's 12. Then subtract the number here from that, 12 - 3 = 9. That's the number that goes to the blank."
In the conceptual group they were taught about equivalence, the equation having two sides that have to be equal.
Of course... the conceptual teaching is the way to go!
Here's a link to the research paper (in press):
Matthews, P. & Rittle-Johnson, B. (in press). In pursuit of knowledge: Comparing self-explanation, concepts, and procedures as pedagogical tools. Journal of Experimental Child Psychology.
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