TO SENSE AND TO VISUALIZE FUNCTIONS: THE CASE OF GRAPHS ' STRETCHING

In this paper we glance at the very first attempts of two calculus students to understand the concept of dilation of functions using tools that support direct manipulations of graphs. Each one of them was engaged in interpreting dynamic graphs in purpose to construct procedure to deal with graphs stretching in various situations. At the core of each procedure there is a similar conceptual metaphor: stretching and straightening a rope. Based on theories of embodied cognition and on theories attempting to explain the instrumentation of artifacts we are seeking for the roots of this metaphor, and its role in the process of building meaning to the concept. THEORETICAL FRAMEWORK & GOALS Studies suggest that developing "function sense " insight into function properties and operations is a central task of the mathematics curricula (Eisenberg and Deryfus, 1994). Developing competence in solving function related problems, means being proficient in multiple linked representations of functions (graphic, algebraic and tabular) and learning to move freely between them. As Yerushalmy & Schwart