I fully agree with jenbrdsly about Life of Fred being algorithm driven. I have used the Fractions, Decimals, and the first Prealgebra book with my son as a supplement and I was horrified to see that the author very rarely develops concepts. For example, when teaching fraction multiplication, the *only* instruction in the entire book was simply to multiply the numerators and denominators. That's it. No discussion of why one might want to multiply fractions. No discussion of why you can multiply denominators together but you can't add them together. Nothing. I would never use Fred for primary instruction.
As for constructivism--I agree that math instruction should be grounded in developing conceptual understanding (this is why I love the Singapore series). However, I don't think it is necessary for a child to "discover" every last concept and algorithm for himself. One can "construct" knowledge without "discovering" it.
