Instructional efficiency: The role of prior knowledge and cognitive load

We used a 2 (prior knowledge: low vs. high) × 4 (instructional approach: unitary vs. unitary-pictorial vs. equation vs. equation-pictorial) ANOVA to examine the relationship between instructional approach, student prior knowledge, and personal belief of best practice for learning of the find-whole percentage problems, which pose a challenge for many middle school students. The unit percentage concept is central to both the unitary approach and the unitary-pictorial approach, where the latter has a diagram to scaffold the unit percentage concept. Both the equation approach and the equation-pictorial approach, in contrast, are algebra approaches that integrate relevant information to form an equation, allowing learners to solve for an unknown (e.g., x). Furthermore, the equation-pictorial approach relies on the proportional concept, scaffolded by a diagram to form an equation. A student's best practice, reflected by what is known as the 'actual – optimal bests dichotomy', details her belief in capability to perform task complexity (i.e., simple task vs. complex task). The concept of element interactivity within cognitive load theory framework predicts differential instructional efficiency: equation-pictorial > equation approach > unitary-pictorial > unitary. Our findings (N = 218 secondary students) showed that performance outcomes favored high prior knowledge students for complex problems and, to a lesser extent, practice problems and simple problems. Low prior knowledge students benefitted most from the equation-pictorial approach, and they invested higher mental effort than high prior knowledge students across three approaches (unitary, unitary-pictorial, equation) but not the equation-pictorial approach. Importantly, cognitive load imposition, by proxy of students' mental effort, was unrelated to students' belief in optimal best.