The Evolution from “I think it plus three” Towards “I think it is always plus three.” Transition from Arithmetic Generalization to Algebraic Generalization

Abstract

This paper is part of broader research being conducted in the area of algebraic thinking in primary education. Our general research objective was to identify and describe generalization of a 2nd grade student (aged 7–8). Specifically, we focused on the transition from arithmetic to algebraic generalization. The notion of structure and its continuity in the generalization process are important for this transition. We are presenting a case study with a semi-structured interview where we proposed a task of contextualized generalization involving the function y = x + 3. Special attention was given to the structures evidenced and the type of generalization expressed by the student in the process. We noted that the student identified the correct structure for the task during the interview and that he evidenced a factual type of algebraic generalization. Due to the student’s identification of the appropriate structure and the application of it to other different particular cases, we have observed a transition from arithmetic thinking to algebraic thinking.