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Summary
This summary is machine-generated.

Activating prior math knowledge negatively impacts how students encode and solve equivalence problems. This suggests that common math class patterns can hinder problem-solving by affecting what students focus on.

Keywords:
encodingequal signequivalence problemsmathematics educationproblem solving

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Area of Science:

  • Cognitive Psychology
  • Mathematics Education
  • Learning Sciences

Background:

  • Mathematical equivalence problems (e.g., 3 + 4 + 5 = 3 + __) are challenging for elementary students.
  • Prior math education can instill problematic patterns: "operations = answer" format, "equal sign means total," and "solve all operations on all numbers."
  • These ingrained patterns may negatively influence how students approach and solve equivalence problems.

Purpose of the Study:

  • To investigate if activating prior knowledge of problematic math patterns affects problem encoding and solving.
  • To test the hypothesis that these patterns negatively impact problem-solving by influencing encoding processes.
  • To examine the mediating role of encoding performance in the relationship between knowledge activation and problem-solving.

Main Methods:

  • Undergraduate participants completed control tasks or tasks activating knowledge of three problematic math patterns.
  • Participants then reconstructed and solved a series of mathematical equivalence problems.
  • Encoding performance, problem-solving accuracy, and error types were analyzed.

Main Results:

  • Participants in the knowledge activation condition encoded equivalence problems less effectively than control participants.
  • Knowledge activation led to more errors in solving equivalence problems, mirroring typical child errors.
  • Encoding performance significantly mediated the impact of knowledge activation on equivalence problem-solving.

Conclusions:

  • Activating prior knowledge of common math class patterns impairs encoding and problem-solving of equivalence problems.
  • The way students encode mathematical problems is a key factor influenced by their educational experiences.
  • Findings highlight how deeply ingrained patterns from math instruction can inadvertently hinder conceptual understanding and problem-solving skills.