Designing mathematical tasks to promote preservice teachers’ algebraic reasoning and argumentation
Résumé
The aim of this study is to shed light on one group of preservice teachers’ engagement with designed mathematical tasks and in what ways these tasks promote the preservice teachers’ argumentation and reasoning. The study took place within a university course on argumentation and reasoning and on how to draw on these mathematical processes within mathematics teaching in upper secondary school. We analyse the preservice teachers’ written solutions to the given tasks unfolding within small-group work. The analyses reveal that they used predicted approaches, such as deductive proof and geometrical representation. However, they also used unique approaches, such as manipulating one side of the equation to look like the other, using functions to generalize, proving by example, and using drawings instead of variables.
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