Cognitive unity of theorems, theories and related rationalities

Paolo Boero (1)

1 Dipartimento di Mathematica

The construct of cognitive unity of theorems was introduced twenty years ago to identify suitable conditions for students' "smooth" approach to proving. In this paper the Habermas' construct of rationality, adapted to mathematics education in previous research, is used to identify some factors in the activation of cognitive unity of theorems. In particular, I consider the dependence of cognitive unity on the specific rationality (e.g. analytic geometry rationality, or synthetic geometry rationality) according to which a conjecturing and proving problem is dealt with. The analysis of some examples will provide evidence for it, together with hints for further research.

Keywords: Theorems; conjecturing and proving; cognitive unity; proving as rational behavior

Domains: Mathematics [math]; Humanities and Social Sciences

Paolo Boero. Cognitive unity of theorems, theories and related rationalities. CERME 10, Feb 2017, Dublin, Ireland. ⟨hal-01873224⟩