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How can students effectively learn and transfer mathematical procedures to solve new problems? Here, we tested the effects of deliberately committing and correcting errors during mathematical problem-solving practice on transfer of the learned procedures. In two experiments, university students were instructed on mathematical algorithms (synthetic division and matrix multiplication) and solved practice problems during open-book study. Learners were then tested on flexibly adapting the algorithms to solve novel problems that were structurally more complex or embedded in “real-life” scenarios (i.e., mathematical word problems). Deliberately committing and correcting procedural errors during problem-solving practice yielded better transfer than errorless repeated practice (Experiment 1) or studying incorrect worked examples by finding, explaining, and correcting the errors that one’s peers had made (Experiment 2). Yet, most learners failed to accurately predict or recognize the advantage of deliberate erring even after the test, instead misjudging this technique as less effective. This suggests that experiencing the benefit of deliberate erring is insufficient to dispel learners’ metacognitive illusion that generating errors is not helpful for their learning. Overall, our results point to the critical role of first-hand errors in mathematical learning. Relative to avoiding errors or even studying others’ errors and juxtaposing them with the correct solutions, guiding learners to deliberately commit and correct their own errors after instruction improves mathematical problem solving and transfer. (PsycInfo Database Record (c) 2024 APA, all rights reserved)
