Processes of Mathematical Thinking Competency in Interactions with a Digital Tool

Abstract

AbstractAddressing how students can exercise processes of the mathematical thinking competency in a learning environment using digital tools, this chapter seeks to uncover which and how processes of the mathematical thinking competency can appear in interaction with the use of digital tools. I present an empirical case of two students working with a dynamic worksheet in TI-\(n\)spire. Using networking of theories and its strategy of “combining”, the case is analyzed from different perspectives using the framework of the mathematical thinking competency and the theoretical perspectives of instrumental genesis, conceptual fields and semiotic mediation. Using different perspectives captures different processes of the students’ work. Mathematical thinking competency helps identify which aspects are in play. Instrumental genesis and semiotic mediation elaborate on how the processes of mathematical thinking competency interact with the processes of working with the tool. Furthermore, the lens of semiotic mediation also captures generalization processes of the mathematical thinking competency, which was not identified by using the mathematical thinking competency on its own.KeywordsMathematical thinking competencyThe KOM frameworkDynamic geometryComputer algebra systemDifferential calculus