What Can a Response Pattern Analysis Reveal about Learners’ Performance on Arithmetic Equivalences and Algebraic Equations?

Abstract The transition from arithmetic to algebra is a well-known difficulty in school mathematics. In order to succeed, learners require inter alia a better understanding of algebraic symbols, equality, equations and working with negatives/subtraction. This article reports on a response pattern analysis (RPA) of learners’ responses to six test items involving arithmetic equivalences and algebraic equations. The participants were 106 Grade 10 learners from two township schools in Johannesburg, South Africa. The key finding was that success in solving linear equations does not imply success in solving arithmetic equivalences, and vice versa. Methodologically, the study showed that an RPA is an accessible, simple and time-efficient means of conducting initial analyses of larger data sets that is well suited to studies conducted by novice researchers.