How students invent representations of motion A genetic account

The purpose of this paper is to illustrate, through example, a particular approach to understanding how students learn to use scientific and mathematical representations. Much of the work in these fields has been focused on a microanalysis of how students use specific representations, such as line graphs and equations, and on the particular difficulties that students have with these representations. Here, in contrast, I will illustrate an approach that attempts to place students' work with representations in the context of the broader history of their representational experience, and the capabilities that this experience engenders. I refer to this approach as "genetic," because it attempts to understand episodes of representational learning within the broader context of the genesis of representational competence. I will illustrate this new program by looking at episodes in which students are engaged in the invention of graphical representations of motion. The heart of my analysis will be the identification of what I call constructive resources, basic and somewhat generic resources that contribute to a student's ability to invent representations of motion. The analysis will include a number of core observations. I will argue for the importance of prior experiences with drawing and that some features of drawings are carried over to representations invented by students. I will describe a type of representation I call a temporal sequence that I believe develops from student experience with notational systems. Finally, I will discuss how students' abilities to make use of certain features of elements of a representational display contribute to their ability to invent novel forms.