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’.
Highlights
The article discusses three empirical examples of Computer Algebra System (CAS) use in a Danish upper secondary school mathematics class that had experienced a recent change of teacher
The fact that this picture is somehow reversed appears to give rise to new didactical problems, which we are experiencing in the mathematics programs of the Danish educational systems at the moment, not least due to a use of strong mathematical tools introduced without consistent pedagogical intentions
Students appear to experience unclear and non-negotiated contractual relations, and in the second example the winning strategy of the didactical milieu becomes unclear to the students
Summary
The article discusses three empirical examples of Computer Algebra System (CAS) use in a Danish upper secondary school mathematics class that had experienced a recent change of teacher. It has become difficult to imagine a professional in a mathematics-related discipline or carrier today carrying out his or her work without involving some kind of mathematics software, and curricular ideas about ‘mathematical competence’ often involve developing abilities with such tools. The fact that this picture is somehow reversed appears to give rise to new didactical problems, which we are experiencing in the mathematics programs of the Danish educational systems at the moment, not least due to a use of strong mathematical tools introduced without consistent pedagogical intentions. Jankvist and Misfeldt (2015) argue that we may sometimes even talk about “CAS-induced difficulties in learning mathematics”, and illustrate this by means of the ‘desolve’ command and students’ conception of differential equations
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