Can Correct and Incorrect Worked Examples Supersede Worked Examples and Problem-Solving on Learning Linear Equations? An Examination from Cognitive Load and Motivation Perspectives

Research has advocated for the use of incorrect worked examples targeting specific conceptual barriers to enhance learning. From the perspective of cognitive load theory, we examined the relationship between instructional efficiency (correct and incorrect worked examples [CICWEs] vs. worked examples [WEs] vs. problem-solving [PS]), levels of expertise (low vs. high), and belief in achievement best (realistic vs. optimal) in learning linear equations across two experiments (N = 43 vs. N = 68). In the CICWE group, students compared an incorrect step in the incorrect worked example with the parallel correct step in the correct worked example and justified why the step was wrong. The WE group completed multiple worked example–equation pairs, while the PS group solved equivalent linear equations independently. As hypothesized, the WE group outperformed the PS group for low prior knowledge students, while the reverse occurred for high prior knowledge students, demonstrating the expertise reversal effect. In contrast, the CICWE group did not outperform either the PS or WE group. A student’s indication of optimal best, reflecting what is known as the ‘realistic–optimal achievement bests dichotomy’, aligns with his or her belief in their ability to perform tasks of varying complexity (simple task vs. complex task). Regarding the belief in achieving optimal best as an outcome of instructional manipulation, for low prior knowledge students, there were no significant differences across groups on either the realistic best or optimal best subscales. However, for high prior knowledge students, the groups differed significantly on the optimal best subscale, but not on the realistic best subscale. Importantly, the mental effort invested during learning was unrelated to students’ belief in achieving their optimal best.