Comparing Learning From Productive Failure and Vicarious Failure

A total of 136 eighth-grade math students from 2 Singapore schools learned from either productive failure (PF) or vicarious failure (VF). PF students generated solutions to a complex problem targeting the concept of variance that they had not learned yet before receiving instruction on the targeted concept. VF students evaluated the solutions generated by PF students before receiving the same instruction. Student-generated solutions were either suboptimal or incorrect, and in this sense can be conceived as failed problem-solving attempts. Although there was no difference on self-reported engagement, PF students reported significantly greater mental effort and interest in knowing the canonical solution to the problem than VF students. When preexisting differences in general ability, math ability, and prior knowledge were controlled, PF students outperformed VF students on conceptual understanding and transfer without compromising procedural fluency. These results suggest that when learning a new math concept, people learn better from their own failed solutions than those of others provided appropriate instruction on the targeted concept is given after the generation or evaluation activity.