Structure and dynamic of analogical, abductive and deductive arguments: a course on solid geometry as a context for reflection

Abstract

We describe the argumentation process, focusing on arguments by analogy, emerging when a group of students addresses a problem that can be solved in both 2D geometry and 3D geometry. To this end, within a qualitative-naturalist methodology called classroom-based research, the Toulmin Model was used to typify the arguments produced by students, and an ontosemiotic analysis was carried out to describe the mathematical activity associated. Outcomes legitimate the use of abductive or analogical arguments in problem-solving processes (particularly, in 3D geometry) specifying the way how they articulate and dynamize objects (concepts, procedures, propositions) present in that process. In addition, we explain the phases of the argumentation by analogy through the relationship between the domains involved in it.