Unpacking the Complexity of Linear Equations from a Cognitive Load Theory Perspective

Abstract

The degree of element interactivity determines the complexity and therefore the intrinsic cognitive load of linear equations. The unpacking of linear equations at the level of operational and relational lines allows the classification of linear equations in a hierarchical level of complexity. Mapping similar operational and relational lines across linear equations revealed that multi-step equations are derivatives of two-step equations, which in turn, are derivatives of one-step equations. Hence, teaching and learning of linear equations can occur in a sequential manner so that learning new knowledge (e.g. two-step equations) is built on learners' prior knowledge (e.g. one-step equations), thus reducing working memory load. The number and nature of the operational line as well as the number of relational lines also affects the efficiency of instructional method for linear equations. Apart from the degree of element interactivity, the presence of complex element (e.g. fraction, negative pronumeral) also increases the complexity of linear equations and thus poses a challenge to the learners.