Mathematical Representation Competency in the Era of Digital Representations of Mathematical Objects

In this chapter, we examine what the possession and development of mathematical representation competency constitutes in the context of digital representations of mathematical objects. We start from the specific case of representations of objects in a dynamic geometry environment and attempt to generalize our argument to representations of any other mathematical object. Our claim concerns the hypothesis about the correlation between two steps in the representation competency, which we partly substantiate empirically and partly argue from a theoretical point of view. The first step concerns the ability to interpret and use geometrical representations of dynamic geometrical objects. We present data from students that reach different degrees of such ability, as they are working on dynamic geometry tasks. The second step is theoretically based and concerns the ability to interpret and use representations of non-geometrical objects that can be interpreted geometrically.