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Productive failure in learning math.

Manu Kapur1

  • 1National Institute of Education, Nanyang Technological University.

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Summary
This summary is machine-generated.

Problem-solving before direct instruction significantly enhances math conceptual understanding and knowledge transfer. Learning from failed attempts, whether personal or peer-based, also improves outcomes, challenging traditional teaching methods.

Keywords:
LearningMathematics educationProblem solvingProductive failureVicarious failure

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Area of Science:

  • Cognitive Psychology
  • Educational Psychology
  • Mathematics Education

Background:

  • Traditional mathematics instruction often prioritizes direct teaching of concepts and procedures before problem-solving.
  • The effectiveness of this 'teach-then-practice' approach versus a 'problem-solve-then-teach' methodology is debated.
  • Understanding how different learning sequences impact conceptual knowledge and transfer is crucial for pedagogical advancement.

Purpose of the Study:

  • To compare the efficacy of two distinct learning sequences for new mathematical concepts: direct instruction followed by problem-solving versus problem-solving followed by direct instruction.
  • To investigate the impact of learning from peer failure on conceptual understanding and procedural knowledge.
  • To identify factors that predict successful learning outcomes in mathematics.

Main Methods:

  • Two randomized-controlled studies were conducted involving learners acquiring new math concepts.
  • Participants were assigned to either a 'teach-first' or 'problem-solve-first' learning condition.
  • Conceptual understanding, procedural knowledge, and transfer to novel problems were assessed. A second study incorporated peer-learning from failed attempts.

Main Results:

  • Both learning sequences resulted in high procedural knowledge.
  • The 'problem-solve-first' group demonstrated significantly superior conceptual understanding and transferability to new problems compared to the 'teach-first' group.
  • Learning from peer failures improved outcomes for the 'teach-first' group but did not surpass the 'problem-solve-first' group. The quantity of student-generated solutions positively correlated with learning gains.

Conclusions:

  • Learners benefit from engaging in problem-solving before receiving explicit instruction in new math concepts and procedures.
  • Learning from one's own or peers' failed problem-solving attempts can be a potent pedagogical strategy, potentially more effective than traditional direct instruction.
  • These findings suggest alternative instructional models that emphasize productive struggle and inquiry-based learning for improved mathematical cognition.