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Updated: Jul 30, 2025

Problem-Solving Before Instruction PS-I: A Protocol for Assessment and Intervention in Students with Different Abilities
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Prior math achievement and inventive production predict learning from productive failure.

Manu Kapur1, Janan Saba2, Ido Roll2

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Summary

Productive Failure (PF) math instruction benefits all students, not just high achievers. Inventive production, or designing solutions, is key to learning, regardless of prior math achievement.

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Area of Science:

  • Educational Psychology
  • Mathematics Education

Background:

  • Constructivist instruction is often perceived as more effective for students with higher prior domain knowledge.
  • Investigating the efficacy of specific constructivist approaches across diverse student achievement levels is crucial.

Purpose of the Study:

  • To examine the relationship between prior math achievement and learning outcomes in Productive Failure (PF).
  • To determine if inventive production mediates the effect of prior achievement on learning in PF.

Main Methods:

  • Two quasi-experimental, pretest-intervention-posttest studies were conducted in Singapore public schools.
  • Students with varying prior math achievement designed solutions to complex problems before receiving instruction.
  • Learning was assessed post-intervention, with a focus on inventive production and prior achievement.

Main Results:

  • Students with significantly different prior math achievement showed similar levels of inventive production.
  • Inventive production demonstrated a stronger association with learning from PF than prior math achievement.
  • These findings were consistent across different mathematical topics.

Conclusions:

  • Productive Failure (PF) is a valuable instructional approach for diverse learners in mathematics.
  • Encouraging inventive production is essential for effective learning, irrespective of students' initial math abilities.
  • The study challenges the notion that constructivist methods exclusively benefit high-achieving students.