Advancing the study of solving linear equations with negative pronumerals: A smarter way from a cognitive load perspective

Central to cognitive load theory is the concept of element interactivity, which reflects the complexity of material. The complexity of linear equations depends on the number of operational and relational lines and the nature of the operation (balance versus inverse) in the solution procedure. A relational line refers to the quantitative relation whereby the right-hand side of the equation equals to its left-hand side. An operational line refers to the application of an operation and such a procedural step preserves the equality of the linear equation. The balance method and inverse method differ in the operational line (e.g., + 3 on both sides vs.– 3 becomes + 3) where the inverse operation imposes half the level of element interactivity as the balance method. Seventy-five students randomly assigned to either the balance group or inverse group to complete (i) one-step equations (Experiment 1), (ii) two-step equations (Experiment 2), and (iii) one-step and two-step equations with a focus on equations with negative pronumerals (Experiment 3). Performance favoured the inverse group when the gap between the low and high element interactivity equations was substantial enough. Both groups performed better and invested lower mental effort on the inverse operation than the balance operation.