Is the inverse method more effective than the balance method on learning linear equations? A cross-cultural experimental study between Australia and Malaysia

Abstract

We conducted a cross-cultural experimental study, consisting of Australian students ( N = 57) and Malaysian students ( N = 75) on learning to solve one-step and two-step linear equations. Central to our research inquiry is the perceived difference between two instructional methods: the balance method of learning vs. the inverse method of learning. The balance method and the inverse method differ in their use of mathematical operations to solve linear equations (e.g., +4 on both sides, balance operation, vs. –4 becomes +4, inverse operation). According to cognitive load theory, the balance operation imposes twice the level of element interactivity (i.e., interaction between elements) than that of the inverse operation. Our findings, ascertained from univariate analysis of variance (ANOVA) testing, show that for the Australian students, the balance group outperformed the inverse group. Such results do not support our hypothesis and contradict with previous findings, where the inverse group outperformed the balance group in a Malaysian context. No statistically significant difference was found between the two groups of Malaysian students. In line with our hypothesis, the Malaysian students outperformed the Australian students with respect to the inverse method. We attributed the results, in part, to the impact of prior knowledge of the balance method (Australian students) and the inverse method (Malaysian students) upon subsequent learning of linear equations. Nonetheless, given that the differential level of element interactivity favors the inverse method, we advocate the exploration of the potentiality of the inverse method for enhancing the learning of linear equations.