Analysis of the change of students’ recognition about “expression by using □”:

From a viewpoint of algebraic reasoning

Abstract

This study empirically examines the designs of lessons about “expression by using □” as a part of research which aim to bridge between arithmetic and algebra based on the “early algebra” approach. The purposes of this study are to analyze the change of students’ recognition of □, expression, and the mutual relationships between operations, and to identify and characterize algebraic reasoning that appears in the lessons. Findings of this study revealed that our attempt to introduce □ as a general number helped the students use □ in the classroom naturally. In addition, the students’ recognition of □, expression, and the mutual relationships between operations tended to be improved interactively. Furthermore, this result suggests that such improvement is closely related to the algebraic reasoning.