A central theme of the "Math in Motion project is the relationship between seeing and imaging in mathematics learning; through our work we have become deeply interested in conducting studies based on eye movements. This SGER proposal fulfills an opportunity cost in the sense of taking advantage of an ongoing prjoect that will provide a timely conceptual background and practical need for the proposed work. I t will allow us to conduct interviews with high school students in whichg they will interpret and draw graphs for the motion of an imaginary object. We will analyze the data collected with an eye tracker in conjunctions with the videotaped interview and its transcription. We will examine how thte interviewee's scanpaths change as she tries to see and imagine different aspects of the motion symbolized by the graph. These exploratory studies will illuminate the following research questions of the project included in the Math in Motion proposal: "How does bodily action/perception become part of imagining the mothion and shape of mathematical enitities? In which ways do students' understanding of properties come to mold their bodily action/perception?" As far as we know, the existing studies in mathematics education tracking eye motion have focused on ascertaining how experts and novices pay atteention to different aspect of videotaped episodes or to validate formal models of information processing. Our aim is different and more in the tradition of Yarbus (1967): the conduction of case studies analyzing patterns of indivi8dual canpaths depending on the viewer's questions and what she is trying to imagine.
