Productive versus vicarious failure: Do students need to fail themselves in order to learn?

Hartmann, Christian; Gog, Tamara van; Rummel, Nikol

doi:10.1002/acp.4004

Cited by 6 publications

(2 citation statements)

References 32 publications

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“…This finding corroborates the advantage of learning from self- over other-generated errors in extant research on other error types, including those that are allowed to occur spontaneously (Metcalfe & Xu, 2018; Sadler & Good, 2006) or induced before direct instruction (Kapur, 2014a, 2014b; cf. Hartmann et al, 2021, 2022).…”

Section: Discussionmentioning

confidence: 99%

Deliberately making and correcting errors in mathematical problem-solving practice improves procedural transfer to more complex problems.

Yap,

Wong

2024

Journal of Educational Psychology

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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. Educational Impact and Implications StatementTransfer of learning lies at the heart of education, but is often difficult to achieve. Here, we show in the domain of mathematics that deliberately committing and correcting procedural errors during problemsolving practice enhances students' transfer of the learned procedures to solve novel, more challenging problems. Deliberate erring was not only more effective than errorless repeated practice, but also finding, explaining, and correcting others' errors in incorrect worked examples. These results expand our repertoire of approaches to harness the power of errors for improving mathematical problem solving and transfer in education.

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Section: Discussionmentioning

confidence: 99%

Deliberately making and correcting errors in mathematical problem-solving practice improves procedural transfer to more complex problems.

Yap,

Wong

2024

Journal of Educational Psychology

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“…In the generation and exploration phase, which lasted two periods, Students were assigned into groups (triads) by the teacher based on teachers’ knowledge about their students. The choice of working within groups (a key PF fidelity criterion 16 ) is based on vicarious failure (VF), which addresses that observing other students’ failure to solve a problem would also be productive for her\his own learning from subsequent instruction 56 , 57 . Studies illustrate the benefit of exposing students to other’s general prior knowledge and expertise in developing, detecting, and correcting multiple RSMs 58 .…”

Section: Introductionmentioning

confidence: 99%

Prior math achievement and inventive production predict learning from productive failure

2023

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A frequent concern about constructivist instruction is that it works well, mainly for students with higher domain knowledge. We present findings from a set of two quasi-experimental pretest-intervention-posttest studies investigating the relationship between prior math achievement and learning in the context of a specific type of constructivist instruction, Productive Failure. Students from two Singapore public schools with significantly different prior math achievement profiles were asked to design solutions to complex problems prior to receiving instruction on the targeted concepts. Process results revealed that students who were significantly dissimilar in prior math achievement seemed to be strikingly similar in terms of their inventive production, that is, the variety of solutions they were able to design. Interestingly, it was inventive production that had a stronger association with learning from PF than pre-existing differences in math achievement. These findings, consistent across both topics, demonstrate the value of engaging students in opportunities for inventive production while learning math, regardless of prior math achievement.

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Do students learn more from failing alone or in groups? Insights into the effects of collaborative versus individual problem solving in productive failure

et al. 2023

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Productive Failure (PF) is an instructional design that implements a problem-solving phase which aims at preparing students for learning from a subsequent instruction. PF has been shown to facilitate students’ conceptual knowledge acquisition in the mathematical domain. Collaboration has been described as a vital design component of PF, but studies that have investigated the role of collaboration in PF empirically so far, were not able to confirm the necessity of collaboration in PF. However, these studies have diverged significantly from prior traditional PF studies and design criteria. Therefore, the role of collaboration in PF remains unclear. In an experimental study that is based on the traditional design of PF, we compared a collaborative and an individual problem-solving setting. It was hypothesized that collaboration facilitates the beneficial preparatory mechanisms of the PF problem-solving phase: prior knowledge activation, awareness of knowledge gaps, and recognition of deep features. In a mediation analysis, the effects of collaborative and individual problem solving on conceptual knowledge acquisition as mediated through the preparatory mechanisms were tested. In contrast to the hypotheses, no mediations or differences between conditions were found. Thus, collaboration does not hold a major preparatory function in itself for the design of PF.

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Productive versus vicarious failure: Do students need to fail themselves in order to learn?

Cited by 6 publications

References 32 publications

Deliberately making and correcting errors in mathematical problem-solving practice improves procedural transfer to more complex problems.

Deliberately making and correcting errors in mathematical problem-solving practice improves procedural transfer to more complex problems.

Prior math achievement and inventive production predict learning from productive failure

Do students learn more from failing alone or in groups? Insights into the effects of collaborative versus individual problem solving in productive failure

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