Analysis of proving in the Habermas’ rationality perspective: The meta-knowledge – knowledge interplay
Résumé
The reported research aims at investigating the relationships between knowledge and meta-knowledge in the process of proving through the lens of the Habermas’ construct of rationality, as it has been adapted to mathematics education in the last decade. We will analyse three prospective teachers’ behaviours in proving situations of Euclidean geometry and theory of real numbers. The construct of rationality of proving will allow to put into evidence difficulties, obstacles and conditions for success, related to the epistemic, teleological, communicative components of rationality in the interplay between content knowledge and meta-knowledge. The analyses will put into evidence what meta-knowledge of proof and proving means in the rationality perspective, thus providing a potential, comprehensive view of such meta-knowledge and of how to develop students’ mastery of it.
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