Chapter 5: A Look at A Child’S Understanding of Mathematical Ideas Through his Representations

It was Spring. Some students in my second-grade class were not making the progress I expected them to make. My goal was for all of my students to become efficient problem solvers and to be able to operate by decomposing and composing numbers into friendlier parts instead of counting up or down by ones. I wondered why some students were able to use an efficient strategy in some situations but would revert to less efficient ones in other cases. As I began to explore this question I noticed that, for some reason, I had paid more attention to children’s talk than to their written work. During the normal course of reviewing student work, I often checked each day’s work without connecting it with past work or with my observations of them in class. I had a fragmented understanding of my students’ understanding and was missing an important aspect of their sense-making process. I decided to improve my ability to analyze how my students communicated their mathematical ideas through written representations and how these representations connected with their work in general. I thought that by having a more comprehensive view of children’s work, I would be able to understand why they were not making the progress I was expecting.