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Measures of Potential Flexibility and Practical Flexibility in Equation Solving.

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  • 1Institute of Developmental Psychology, Beijing Key Laboratory of Applied Experimental Psychology, Faculty of Psychology, Beijing Normal UniversityBeijing, China.

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Summary

Students may know multiple math strategies but not use them. This study introduces measures for potential (knowing) and practical (using) flexibility, finding they are distinct but related concepts in mathematical problem-solving.

Keywords:
equation solvingmeasurespotential flexibilitypractical flexibilitystrategic flexibility

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Area of Science:

  • Cognitive Psychology
  • Educational Psychology
  • Mathematics Education

Background:

  • Strategic flexibility in math involves knowing and using multiple problem-solving strategies.
  • Existing research suggests a gap between students' knowledge of strategies and their actual use.
  • The competence-performance distinction, common in psychology, has not been applied to strategic flexibility.

Purpose of the Study:

  • To develop and validate measures for potential flexibility (competence) and practical flexibility (performance) in mathematical equation solving.
  • To investigate the relationship between these two distinct aspects of flexibility.
  • To explore the competence-performance distinction within strategic flexibility.

Main Methods:

  • A Tri-Phase Flexibility Assessment was administered to 158 Chinese middle school students.
  • The assessment involved solving equations, generating strategies, and evaluating strategy knowledge.
  • Confirmatory factor analysis (CFA) was used to validate the measures.

Main Results:

  • CFA supported a two-factor model distinguishing potential and practical flexibility.
  • Measures demonstrated satisfactory internal consistency and validity.
  • Potential and practical flexibility were found to be distinct yet correlated constructs.

Conclusions:

  • The study successfully differentiated and measured potential and practical flexibility in mathematics.
  • Findings highlight the importance of considering both strategy knowledge and application in mathematical proficiency.
  • The validated measures offer valuable tools for future research and educational interventions.