Representational Fluency and Symbolisation of Derivative

Abstract

The nature of mathematical concepts has been the subject of some scrutiny in the mathematics education literature. One of the key ideas described in the literature is the distinction between the process and object perspectives of concepts. What is not so clear is how this distinction translates into different symbolisations and representations of the concept, and how students can construct the fluency to be able both to interact with these, and to translate between them. This paper describes the initial stages of a study which aims to use the dynamic multiple representations of a calculator's computer algebra system (CAS) to promote improved understanding of differentiation. In particular it looks at student interpretation of the symbolisation dy/dx and their ability to relate this across different representations. The results of the study show that the students surveyed lack representational fluency for the concepts associated with this symbolisation, and that this appears to be due to their process perspective of the symbol. They have not yet encapsulated the differentiation process, as represented by the symbol, into the derivative object. Some implications for teaching and learning which can address this using the CAS calculator are considered.