On NPR, you'll find "The Way You Learned Math Is So Old School" from Weekend Edition Saturday talking about how children learn math today as compared to the way we--their parents, the oldsters--learned math. You can listen to the podcast or read the text. Also check out the visuals showing how the teaching of multiplication has changed.
Just a little personal reflection... While I never had trouble "doing" the math (as shown in the old way of multiplying) I had no understanding of what it meant. Now, having learned the second way--WITH manipulatives--I can now picture a problem like that (36x24) in my head and do it mentally. No paper. No calculator. That, for me, is a huge step forward.
Also, check out the new Math Teachers at Play Blog Carnival hosted at MathInsider. You're sure to find a lot of new ideas there!