An investigation of the role of patterns in developing algebraic thinking

Abstract

This study was designed to investigate the role of patterns in the development of algebraic thinking, specifically in the acquisition of the concept of "variable." Comparisons were made between a control classroom in which eighteen fourth-grade students followed a five-week prescribed curriculum reinforced with cumulative review, and an experimental classroom in which eighteen fourth-grade students followed the same curriculum enhanced with the study of patterns in place of the cumulative review. Students' abilities to use algebraic generalizations to describe problem situations and their level of understanding of algebraic notation were measured by pre- and post-intervention interviews and by pre-and posttests. Student responses from structured interview sessions along with a mixed design repeated measures analysis of variance were used to determine the treatment effects on the groups. In addition, performance gain (loss) and observations by experts were used to clarify the results of the study. Statistically significant differences were found between groups as well as differences that surfaced during interview sessions. The results of analyses performed indicate that: (I) the pattern enhanced group outperformed the control group in their ability to generalize problem situations; and (ii) the pattern enhanced group showed higher levels of understanding of algebraic notation than the control group. Implications of this study address the need for opportunities for the elementary student to explore the concept of "variable." The elementary mathematics curriculum should involve content and activities that prepare students to think algebraically. Furthermore, such a curriculum should be enhanced with the study of numerical patterns. However, to fully implement such a change in the mathematics curriculum involves better subject-matter preparation for the elementary preservice teacher. Opportunities to explore worthwhile mathematical tasks should be provided within the preservice mathematics preparation.