Programming as a mathematical instrument: the implementation of an analytic framework

This paper relates to an ongoing project using design-based research as a methodol- ogical approach in which students with no prior experiences of using programming as a mathematical tool are observed trying to solve mathematical problems with the help of programming. The Instrumental Approach is used as conceptual framework in which the concept of instrumental genesis describes the process where the programming environment as an artefact together with student-developed mental schemes forms an instrument in order to solve mathematical problems. The development of schemes is of special interest in this paper where Vergnaud’s components of a scheme provide a framework for analysing transcripts of talk between student pairs and the programming code that they generate.