Defining Families of Polyhedrons: a Study with High School Students

Abstract

An exploratory and descriptive research is presented in which the participation of high school students in the mathematical practice of defining is characterized, without major intervention of a teacher, and how this participation leads them to establish definitions with particular characteristics of different families of polyhedrons. The data study is based on an analysis of the students’ discourse , taking as a basis the communicative features of Sfard’s theory. The main results show that the use of colloquial and ambiguous words is characteristic of the students’ discourse , and they carry out different routines when participating in different aspects of the mathematical practice of defining that leads them to establish definitions, in their great majority, ambiguous with necessary, but not sufficient conditions. It also highlights the complexity of involving students in discursive practices and the importance of continuing to conduct research focused on the teaching and learning process that provides information to try to improve student participation in different discursive practices.

Discourse; Mathematical practice of defining; Communicative features of mathematical discourse; Families of polyhedrons