Abstract

Our aim is to provide an educative experience concerning the study of rate of change, to be implemented prior to its formal treatment in the classroom. By means of a Socratic dialog and the manipulation of a computer generated visualization tool, we shall provoke answers to questions such as How much?, How steep? and How fast? by identifying all key ingredients necessary to provide a sound concept image of the concept of derivative of a function at a point. Our study is framed in van Hiele's educational model methodology. This first of two articles deals with the interview and the list of descriptors which allow the detection of the levels of reasoning the model postulates. In a forthcoming article we shall concern ourselves with the analysis of all students' responses, cognitive obstacles encountered and tutorial actions needed to overcome them.

Keywords: Model; change; rate of change; visualization; approximation; local rate of change.

Pages:  63$-$92     

Volume  XIII ,  Issue  2 ,  2010