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Systematic Mathematical Errors and Cognitive Load.

Paul L. Ayres1

  • 1University of New South Wales, Sydney, Australia

Contemporary Educational Psychology
|March 29, 2001
PubMed
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Algebraic bracket tasks create uneven cognitive load, leading to more errors in later computations. Working memory failures, not rule deficits, explain these errors in students.

Area of Science:

  • Cognitive Psychology
  • Mathematics Education
  • Educational Psychology

Background:

  • Algebraic bracket expansion is a fundamental skill for students.
  • The cognitive processes involved in solving algebraic problems are not fully understood.
  • Previous research has not specifically examined the cognitive load distribution during algebraic bracket tasks.

Purpose of the Study:

  • To test the hypothesis that algebraic bracket tasks cause an uneven distribution of cognitive load.
  • To identify the sources of errors in algebraic bracket computations.
  • To investigate the impact of algebraic bracket tasks on working memory.

Main Methods:

  • Three experiments were conducted with 8th and 9th-grade students.
  • Experiment 1 involved analyzing error patterns in expanding successive brackets.

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  • Experiment 2 used verbal protocols to understand error causes.
  • Experiment 3 employed a dual-task methodology to assess working memory load.

    • Main Results:

    • Students made significantly more errors in the second bracket than the first.
    • Errors increased within each bracket, with more errors in the second operation.
    • Verbal protocols revealed working memory failures as the primary cause of errors.
    • Dual-task performance indicated that bracket computation negatively impacts working memory.

    Conclusions:

    • The cognitive load during algebraic bracket tasks is unevenly distributed across operations.
    • Working memory limitations are a key factor contributing to errors in these tasks.
    • The findings have implications for instructional strategies in algebra.