ABSTRACT
This chapter explores the implications for curriculum designers, teachers, and students of a basic fact of human communication: that words and symbols do not necessarily convey our meanings and intentions to others. It is based on an analysis of a brief moment in a classroom conversation among a group of third-and fourth-grade students who were designing a chart to describe their own motion along a 10-foot straight line. This conversation took place during a series of lessons the author helped develop as a member of a research team conducting a curricular design study around the mathematics of motion. The students in the class were designing the chart as a means of directing someone else to walk along such a line according to their directions. In the process they were discovering that words placed in a chart meant different things to the various members of the class and that their intentions did not necessarily convert into the actions of others. Nonetheless, we see in the analysis of this conversation that, in and around their struggles to get one another to understand their meanings, these students were slowly begin-ning to build a collective world of meaning that included their motion, their charts, and their words in
which there was enough commonality among their understandings to begin to communicate certain aspects of their motion to another.
