Coherent formalisability as acceptability criterion for students’ mathematical discourse

Abstract

ABSTRACT The challenges involved in navigating between home, school and academic languages, especially in a low resource context, have been well documented in the literature. Processes and strategies that allow the use of students’ “language as resource” have also been suggested by research. In the context of explorations, where students work with an unfamiliar open problem, we have observed them engaging in mathematical practices and “mathematical conversations” and making their own discoveries, regardless of limited access to a formal language. The discourse in such contexts may not exhibit accepted characteristics of mathematical discourse. There is a need for defining acceptability criteria that validate the mathematical in these informal ways of talking and enable movement towards more formal discourse. To this end, we suggest coherent formalisability as an acceptability criterion and examine discursive proving actions in an exploratory context in the light of this criterion.