When is observing failure productive? Investigating the role of solution diversity in vicarious failure

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Abstract Prior research has shown that Productive Failure (PF), where learners attempt (and fail) to solve a problem prior to receiving instruction, is more effective for conceptual knowledge acquisition than receiving instruction first (Direct Instruction; DI). Higher diversity in generated solution attempts seemed positively associated with conceptual knowledge acquisition. The present study investigated whether observing another student’s attempts to solve the problem prior to receiving instruction (i.e., Vicarious Failure; VF) is as beneficial as PF for conceptual knowledge acquisition in mathematics and whether this depends on the diversity in the observed solution attempts. In the high solution diversity condition (VF-high), students observed five solution attempts that (taken together) included all four components of the to-be-learned canonical solution, while in the low diversity condition (VF-low), the solution attempts included only two of these components. Secondary education students (n = 152) were randomly assigned to one of four conditions: PF, VF-high, VF-low, and Direct Instruction (DI). As expected, students in the VF-high condition significantly outperformed students in the VF-low and DI conditions and performed as well as students in the PF condition on the conceptual knowledge posttest. Surprisingly, the PF effect found in previous studies was not replicated, i.e., the PF condition descriptively seemed to outperform the DI condition, but this difference was not statistically significant. Our findings provide further insight into the mechanisms that explain why engaging with problems prior to instruction is effective, suggesting that students’ activation of prior knowledge is more critical than whether they experience failure first hand.