Interactions and tensions between mathematical discourses and schoolwork discourses when solving dynamic geometry tasks: what is internally persuasive for students?

ABSTRACT

I explore students’ discourses in small groups working on mathematical problems using GeoGebra, focusing on the Cartesian connection between algebra and geometry. Specifically, the interest lies in what is internally persuasive for students in upper-secondary school (11th grade) with histories of low attainment. Three problem-solving episodes are presented in detail to illuminate different intertwining and interacting discourses that students produce. In all cases, students engaged in visual explorations and expressed joy in the work. Students used discourses of visual appearance and technical symbolism to talk about screen objects and problem solutions. Two cases illustrate how a student makes a conjecture internally before verifying it for themselves and then convincing their peers of the validity of their solution. In a contrasting case, students used visual trial and error and asked an authority to confirm their solution. Discourses concerning the institutional demands of school interfered with students’ mathematical dialogue.

KEYWORDS:

• Dialogism
• dynamic geometry software
• mathematical discourse

Acknowledgements

This paper builds on a paper presented in the Thematic Working Group on Mathematics and Language at the CERME12 conference in February 2022. I am grateful to the participants there as well as my doctoral supervisors, Ólafur Páll Jónsson and Simon Goodchild, Bjarnheiður Kristinsdóttir and the anonymous reviewers for helpful comments on earlier drafts of this manuscript.

Disclosure statement

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

Notes

1 It is a matter of philosophical contention whether (already existing) mathematical objects are represented or whether there are no independent mathematical objects to represent – they exist only as concrete speech, writings, drawings, imaginations, by which they are instantiated or realised. In Duval’s (2006) theory, objects are represented, while in Sfard’s (2008) theory, there are visual mediators of realisations instead of representations in light of the fact that there is no privileged thing to be represented. I will use representations because this is a more common word in mathematics literature.