A theoretical perspective for proof construction

Annie Selden (1) , John Selden (1)

1 New Mexico State University

This theoretical paper suggests a perspective for understanding university students’ proof construction based on the ideas of conceptual and procedural knowledge, explicit and implicit learning, behavioral schemas, automaticity, working memory, consciousness, and System 1 and System 2 cognition. In particular, we will discuss proving actions, such as the construction of proof frameworks, that could be automated, thereby reducing the burden on working memory and enabling university students to devote more resources to the truly hard parts of proofs.

Mots clés: University level; proving actions; behavioral schemas; System 1 and System 2 cognition; proof framework

Domaines: Education; Histoire et perspectives sur les mathématiques [math.HO]

Annie Selden, John Selden. A theoretical perspective for proof construction. CERME 9 - Ninth Congress of the European Society for Research in Mathematics Education, Charles University in Prague, Faculty of Education; ERME, Feb 2015, Prague, Czech Republic. pp.198-204. ⟨hal-01281086⟩