Validating in the mathematics classroom. (English)

Oesterle, Susan (ed.) et al., Proceedings of the 38th conference of the International Group for the Psychology of Mathematics Education “Mathematics education at the edge", PME 38 held jointly with the 36th conference of PME-NA, Vancouver, Canada, July 15‒20, 2014, Vol. 3. [s. l.]: International Group for the Psychology of Mathematics Education (ISBN 978-0-86491-360-9/set; 978-0-86491-363-0/v.3). 169-176 (2014).

Summary: The focus of this report is on the process of resolution of a task; specifically, on the validation of the mathematical model proposed by a group of students and the numerical result that is constructed within this model. Habermas’ construct of rational behavior is used to describe validity conditions that emerge and are used by the students as means for validation. We take a classroom episode from a design experiment to examine how the emergence of these conditions points to a socially constituted mathematical epistemology in the secondary school mathematics classroom, to shared and tacit principles of the didactic contract concerning the knowledge there, and to non-mathematical references that are taken for granted.