Students' algebra sense via their understanding of the distributive law

Abstract

The distributive law or distributive property is a fundamental algebraic property in the arithmetic of numbers and algebraic expressions. This paper reports on an investigation of students' understanding of the distributive law through task-based interviews from the perspectives of constructivists. It explores students' lack of appreciation of the algebraic structure underpinning the distributive law, particularly amongst students who were already proficient in arithmetic and the distributive law. A total of 203 students from one secondary school of average standard in Hong Kong participated in this study, which adopted a cross-sectional approach. Thirty-three students were then interviewed. The study showed that although some students made progress in the understanding and application of the distributive law, others could not make sense of the meaning of variables and algebraic rules. Therefore, their algebra remained a routine instrumental application of rules, and their understanding of the algebraic structure was incomplete. This paper concludes with a discussion on how the tasks used in the interviews provided teachers with an innovative alternative to deepening students' understanding of letters as variables and the distributive law.