Deliberately Making and Correcting Errors in Mathematical Problem-Solving Practice Improves Procedural Transfer to More Complex Problems.
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| Title: | Deliberately Making and Correcting Errors in Mathematical Problem-Solving Practice Improves Procedural Transfer to More Complex Problems. |
|---|---|
| Authors: | Yap, Janson Boon Khang1 (AUTHOR), Wong, Sarah Shi Hui1,2 (AUTHOR) psywshs@nus.edu.sg |
| Source: | Journal of Educational Psychology. Oct2024, Vol. 116 Issue 7, p1112-1128. 17p. |
| Subject Terms: | *Transfer of training, *Transfer of students, *Transfer students, *Problem solving, Mathematical errors, Matrix multiplications |
| Abstract: | 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 Statement: Transfer 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 problem-solving 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. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Educational Psychology is the property of American Psychological Association and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Education Research Complete |
| FullText | Text: Availability: 0 |
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| Header | DbId: ehh DbLabel: Education Research Complete An: 179869611 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Deliberately Making and Correcting Errors in Mathematical Problem-Solving Practice Improves Procedural Transfer to More Complex Problems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Yap%2C+Janson+Boon+Khang%22">Yap, Janson Boon Khang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Wong%2C+Sarah+Shi+Hui%22">Wong, Sarah Shi Hui</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> psywshs@nus.edu.sg</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Educational+Psychology%22">Journal of Educational Psychology</searchLink>. Oct2024, Vol. 116 Issue 7, p1112-1128. 17p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Transfer+of+training%22">Transfer of training</searchLink><br />*<searchLink fieldCode="DE" term="%22Transfer+of+students%22">Transfer of students</searchLink><br />*<searchLink fieldCode="DE" term="%22Transfer+students%22">Transfer students</searchLink><br />*<searchLink fieldCode="DE" term="%22Problem+solving%22">Problem solving</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+errors%22">Mathematical errors</searchLink><br /><searchLink fieldCode="DE" term="%22Matrix+multiplications%22">Matrix multiplications</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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 Statement: Transfer 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 problem-solving 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. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Educational Psychology is the property of American Psychological Association and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1037/edu0000850 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 17 StartPage: 1112 Subjects: – SubjectFull: Transfer of training Type: general – SubjectFull: Transfer of students Type: general – SubjectFull: Transfer students Type: general – SubjectFull: Problem solving Type: general – SubjectFull: Mathematical errors Type: general – SubjectFull: Matrix multiplications Type: general Titles: – TitleFull: Deliberately Making and Correcting Errors in Mathematical Problem-Solving Practice Improves Procedural Transfer to More Complex Problems. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Yap, Janson Boon Khang – PersonEntity: Name: NameFull: Wong, Sarah Shi Hui IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 00220663 Numbering: – Type: volume Value: 116 – Type: issue Value: 7 Titles: – TitleFull: Journal of Educational Psychology Type: main |
| ResultId | 1 |
