Solving Linear Equations: Will This Pose as a Challenge to Elementary Pre-Service Teachers?

Abstract

From the perspective of cognitive load theory, the complexity of equation solving depends on the degree of element interactivity, which is proportionate to the number of operational and relational lines. An operational line alters the problem state of the equation, and yet at the same time preserves its equality (e.g., + 2 on both sides). A relational line indicates the relation between elements in that the left side of the equation equals to the right side. Apart from the element interactivity effect, operating with special features (e.g., fractions) increases the complexity involved in equation solving. Thirty-eight pre-service teachers (Female = 30, male = 8) were randomly assigned to solve one-step, two-step or multi-step equations and to complete a concept test regarding the role of '=' sign with respect to the operational and relational lines. Test results revealed that higher performance correlated with fewer number of operating and relational lines. However, performance favored those equations without special features when the number of operational and relational lines was kept constant. The correlation between performance on test items and concept test was significant for both two-step equations and multi-step equations but not for one-step equations.