Developing an abstract understanding of unit iteration through problem solving

Unit iteration is an important process in understanding and applying area measurement. However, results from large-scale assessments of middle school students’ mathematical achievement indicate that applying unit iteration to solve real-world problems poses significant difficulties for many students. This study investigated how middle school students’ abstract understanding of unit iteration might develop through problem solving. Design-Based Research was used to implement a series of problems designed to elicit students’ abstract understanding of unit iteration. Data from audio-transcripts and copies of student work from two Grade 8 Mathematics classes (n = 31) were analysed to determine the methods and strategies that students used to solve the problems. The findings suggest that students’ abstract understanding of unit iteration developed through solving the area measurement problems posed in this study. Furthermore, it was discovered that problem-solving strategies provided students with the leverage through which their conceptual understanding developed.