Investigation of generalisation processes of secondary school students using multiple representations in a pattern task

Abstract

The aim of this study is to show how the GeoGebra software-supported collaborative learning environment contributes to a group of students using multiple representations and reaching generalisations while solving problems collectively. Blending individual and collaborative learning activities were carried out with a learning method called ACODESA (from French: Apprentissage Collaboratif, Débat Scientifique, Auto-réflexion). Within this context, four 8th-grade students participating in the study were asked to solve the pattern problem by using the GeoGebra software and following the stages of the ACODESA method. The data were collected via a pattern problem developed by the researcher, students’ audio records and screen recordings, GeoGebra files and written productions. The data were analysed using Duval’s theory of registers of semiotic representation and Toulmin’s model. The Toulmin model was used to analyse students’ argument structures, that is, to determine their reasoning structures. The data analysis revealed that a GeoGebra software-supported collaborative learning environment supported secondary school students in using multiple representations, making algebraic reasoning and generalisation. The discussions in this process contributed to the students’ transformation of representations and the evolution of their representations. Providing students with the opportunity to express and examine the pattern with multiple representations, GeoGebra software helped students to obtain data, test their conjectures and thus reach generalisation.