Epistemic actions in the construction of new mathematical knowledge and in the development of algebraic thinking

Abstract

This article discusses how 5^th grade students construct new mathematical knowledge, from knowledge acquired in previous learning experiences. We adopted the AiC (Abstraction in Context) theoretical model and the RBC+C (Recognizing, Building-with, Constructing, Consolidation) theoretical and methodological model in order to understand how the abstraction process occurred during students’ completion of algebraic tasks. We focused on how students mobilized and reorganized mathematical knowledge and procedures to solve the tasks. The aim was to understand how the epistemic actions of the RBC+C model and the subcategories of analysis defined in the scope of this research emerged, how they related to each other, and what influence those relationships had in the construction of new mathematical knowledge. In this study, new mathematical construction is associated with the development of algebraic thinking. Following a qualitative approach, we concluded that the relationship between the epistemic actions Recognizing and Building-with was essential for the development of new mathematical knowledge. The manifestation of the Constructing and Consolidation epistemic actions revealed that students of this age level can successfully establish some algebraic relations, and they can understand and use symbolic language. These students, who still had no significant knowledge in algebra, evidenced mathematical gains with the resolution of tasks, which intended to promote algebraic thinking, thus reinforcing the approach of early algebra.