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!
I love coming here to find out what else I can learn and discover! The article hits it spot on. The reason I became interested in math education is because while I did well in math, I knew I wasn't trained adequately. Great at paper and pencil but no mental math abilities. My mother, on the other hand, can do multiple digit multiplication in her head. It's all about the right training.
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