If you're involved in Math Education (or perhaps even if you're not!) you have probably read about the controversies surrounding Khan Academy. Even if you could care less about Khan, I strongly recommend this series at the Generation YES Blog, Khan Academy Posts: Implications for Math Education.
If you teach math--whether in the classroom or as a homeschooler--this series will challenge you to examine your own beliefs about teaching and learning. If you don't have time to read it now, bookmark and come back later. I'm sure glad I did. :)
I especially recommend part 1, Khan Academy and the Mythical Math Cure, which talks about "how we believe certain things about math that are not true, but we keep doing them anyway." A major myth: "Learning math is about acquiring a sequential set of skills (and we know the sequence.)"
This myth resonated with me because I recently heard something similar while attending a math conference where Jo Boaler spoke. (Highly recommend her book, What's Math Got to Do With It? How Parents and Teachers Can Help Children Learn to Love Their Least Favorite Subject.) She talked about how low achievers do very different math than those who excel. One hurdle? Low achievers see math as a series of rules...rules that are equally important. Kids who struggle in math are less flexible in their mathematical thinking...which makes them emphasize rules even more. And what happens when kids struggle? They are likely to be exposed (by the teacher) to more drill/skill, which leads them to a stronger belief (misconception) that procedure is what counts in learning mathematics.
And think about math education. If kids are ever encouraged to think flexibly about math, it's when they're young. (Unfortunately, for some, the drill/skill emphasis begins immediately.) But the older they get, the more the emphasis is on procedures, mostly through memorization. As Alfie Kohn writes, it's no wonder that U.S. kids do worse and worse on internationally normed tests as they get older.
Thoughts? Love to hear them!
P.S. While you're at it, read a fascinating piece of research: "The Harmful Effects of 'Carrying' and 'Borrowing' in Grades 1-4" by Constance Kamii and Ann Dominick. The research is from 1998. And what are we still doing in most schools (and homes?) Teaching carrying and borrowing!