Discussing Dependencies of Variable Points on the Basis of a GeoGebra Task: Meaning Making in a Teacher-Class Dialogue

Abstract

In this article, I present a meaning-making trajectory of a teacher–class dialogue on digital, dynamic, geometric–functional tasks in an Icelandic upper-secondary classroom of low-attaining students. Learning is seen from a dialogical perspective, as taking up a more mathematical discourse, which here revolves in particular around the language of variables, functions, and Cartesian co-ordinates to describe and construct interactive graphical situations with dynamic geometry software. In the teacher–class dialogue, descriptions of the graphical situations are debated and developed, building on everyday language and intuitions, expanded with more mathematical ways of expression. The main types of discourse identified were (1) in terms of magnitudes and speed, (2) in terms of goal-directed behavior, (3) in terms of vague invariants, (4) in terms of relations between specific points, and (5) in terms of canonical mathematics. The teacher appreciating the students’ discourses while prompting for more precision and suggesting specializing was instrumental in eliciting types (4) and (5). The dialogue illustrates the highly non-linear nature of mathematics learning and the complex work it takes to establish shared meanings.