Coherent formalisability as acceptability criterion for students’ mathematical discourse

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.

KEYWORDS:

• Mathematical discourse
• explorations
• coherent formalisability

Acknowledgements

We acknowledge the support of the Govt. Of India, Department of Atomic Energy, under Project No. 12-R&D-TFR-6.04-0600. We are grateful to the students who participated in this study and their school authorities. We thank Sanjay Chandrasekharan, Chaitanya Ursekar and anonymous reviewers for helpful suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Here we draw on the experience of the third author as a research mathematician.

Additional information

Funding

This work was supported by Department of Atomic Energy, Government of India [Project No. 12-R&D-TFR-6.04-0600].