When I was in elementary school, I absolutely LOVED math. I felt that it was something that I am good at, and my teachers seemed to think so as well. After I have taken some mathematics method courses in college, I have given the way I was taught a lot of thought. My teachers would teach an algorithm on the board, we would copy it and do several worksheets on it until we took a test. Sure, this worked for me, but what about my peers?
It wasn't until this past summer that I actually realized why we "carry" numbers when we subtract large numbers. I never thought about this because of the numbers' place value. I thought this was strange. I was excellent at math; could work every problem out, but never really knew why I was doing what I was doing.
This really makes me think about how I would want to teach math to my students. Sure, algorithms work for some students, but not all. I believe that using manipulatives can really help students see why we move certain numbers around like we do. Maybe even let them create their own algorithms.
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