Students' understanding of the notion of function in dynamic geometry environments.

To make optimal use of computational environments, one must understand how students interact with the environments and how students' mathematical thinking is reflected and affected by their use of the environments. Similarly, to make sense of research on students' thinking and learning, one must understand how the environments and contexts used in the research may affect the conclusions one derives. The research on students' learning of functions has approached the topic in terms of symbols and graphs (see, for example, Leinhardt et al. (1990) for a review of work up to that point; Harel and Dubinsky (1992) for a collection of research; and Dugdale et. al. (1995), for some recent thinking about implications for curriculum reform using technology). Dynamic geometry environments (DGEs) like Cabri Geometry or Geometer's Sketchpad, offer us an opportunity to get a new perspective on these old and important issues. DGEs let students build geometrical constructions and then drag certain objects around the screen in a continuous manner while observing how the entire construction responds dynamically. In this way DGEs model functional relationships that are not specified by symbols or represented by graphs. Based on interviews with undergraduate mathematics majors, this paper presents preliminary observations that confirm some old results and raise some new questions about students' notions of function. [ABSTRACT FROM AUTHOR]