THE MICROEVOLUTION OF MATHEMATICAL REPRESENTATIONS IN CHILDRENS ACTIVITY

In this article, I discuss children's design of mathematical represent ations on paper, asking how material displays are constructed and tran sformed in activity. I show that (a) the design of displays during pro blem solving shapes one's mathematical activity and sense making in cr ucial ways, and (b) knowledge of mathematical representations is not s imply recalled and applied to problem solving but also emerges (whethe r constructed anew or not) out of one's interactions with the social a nd material settings of activity. A detailed characterization of stude nt-designed tables of values to solve problems about linear functions is also presented.