Re-conceptualising conceptual understanding in mathematics

Geoff Kent (1) , Colin Foster (2)

1 UCL - University College of London [London]
2 UON - University of Nottingham, UK

In this theoretical paper, we explore interrelationships between conceptual and procedural understanding of mathematics in the context of individuals and groups. We question the enterprise of attempting to assess learn-ers' mathematical understanding by inviting them to perform a (perhaps unfamiliar) procedure or offer an explanation. Would it be appropriate to describe a learner in possession of an algorithm for responding satisfactorily to such prompts as displaying conceptual under-standing? We relate the discussion to Searle's " Chinese Room " thought experiment and draw on Habermas' Theory of Communicative Action to develop potential implications for addressing the problem of interpreting learners' mathematical understanding.

Mots clés: Conceptual; Habermas; procedural; Searle; understanding

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

Geoff Kent, Colin Foster. Re-conceptualising conceptual understanding in mathematics. 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.2656-2661. ⟨hal-01289445⟩