The Didactical Contract Surrounding CAS when Changing Teachers in the Classroom

Abstract

The article discusses three empirical examples of Computer Algebra System (CAS) use in Danish upper secondary school mathematics class with a recent change of teacher. All examples lead to didactical problems surrounding the situation and unclear expectations between teacher and students, involving loss of students’ mathematical skills and confidence, loss of global mathematical perspective, and the students losing sight of the mathematical objects in question. The article is the result of collaboration between two mathematics education researchers and an upper secondary school mathematics teacher, who experienced severe difficulties when taking over a class from another teacher. CAS was experienced as a crucial part of and reason for these difficulties. As a means for investigating the potential reasons behind the difficulties, a selection of constructs from the Theory of Didactical Situations (TDS) is applied. In particular, it is observed that unclear contractual relations about the role of CAS bring with them misguided winning strategies and metacognitive shifts, eventually causing the students to ‘lose the game’.