Comparing balance and inverse methods on learning conceptual and procedural knowledge in equation solving: a cognitive load perspective

Abstract

We examined the use of balance and inverse methods in equation solving. The main difference between the balance and inverse methods lies in the operational line (e.g. +2 on both sides vs -2 becomes +2). Differential element interactivity favours the inverse method because the interaction between elements occurs on both sides of the equation for the balance method but only on one side of the equation for the inverse method. In an experimental study, 63 students (mean age = 13) were randomly allocated to either balance or inverse group to undertake a pre-test, study an instruction sheet, complete acquisition equations, sit for a post-test and a concept test. Procedural knowledge was assessed on performance on practice equations and post-test, whereas conceptual knowledge was assessed on performance on the concept test. The inverse group outperformed the balance group on practice equations but not the post-test. Both the balance and inverse groups scored higher on the inverse concept test than the balance concept test. Positive association between performance on procedural knowledge and performance on conceptual knowledge was found for the inverse group but not the balance group. Overall, the evidence obtained indicates a number of educational implications for implementation.