Focusing on Brackets as Structuring Elements: The Effect on High School Students’ Algebraic Expertise

Abstract

To understand the problems that high school students have with algebra and more specifically sense of structure in equations, we dive deeper in a specific part of their algebraic expertise: structure sense. This paper attempts to answer the question whether this structure sense can be developed by focusing on brackets as a structuring element. It elaborates on an effect study done on 108 Dutch 10th grade high school students in an attempt to develop structure sense by means of five interventions of ten minutes, given over two weeks during the regular mathematics lessons. These interventions were based on the idea of think-pair-share, with each intervention using problems in which structure sense played a role. Before the interventions, students had to do a pretest and after the interventions, a posttest. These tests were graded on mathematical correctness and effective use of structure. A statistically significant difference was found between the results of the pre- and posttest. These results would imply that structure sense was developed by means of the interventions. This is a promising result for mathematics education, although the long-term effects of the interventions remain yet to be seen.