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The developmental relations between conceptual and procedural knowledge: a multimethod approach.

Michael Schneider1, Elsbeth Stern

  • 1Institute for Behavioral Sciences, ETH Zurich, Universitaetsstrasse 6, CAB G84.2, 8092 Zurich, Switzerland. schneider@ifv.gess.ethz.ch

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Summary
This summary is machine-generated.

Measuring conceptual and procedural knowledge in math is challenging because they appear intertwined. This study reveals significant validity issues with common measurement tools, impacting research on mathematical competencies.

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Area of Science:

  • Mathematics Education
  • Cognitive Psychology

Background:

  • Conceptual and procedural knowledge are crucial for mathematical competencies, but their interrelations remain debated due to inconclusive empirical results.
  • Existing research faces challenges in validly measuring these distinct knowledge types independently, as they manifest intertwined in behavior.

Purpose of the Study:

  • To investigate the extent of measurement problems in assessing conceptual and procedural knowledge in elementary students.
  • To evaluate the validity of common hypothetical measures for conceptual and procedural knowledge in decimal fractions.

Main Methods:

  • A multimethod approach was employed with 289 fifth and sixth graders.
  • Four common hypothetical measures for conceptual knowledge and four for procedural knowledge of decimal fractions were administered.
  • Two studies examined measure consistency across treatments and modeled knowledge as latent factors over three measurement points.

Main Results:

  • Substantial problems with the validity of the measures used to assess conceptual and procedural knowledge were identified.
  • These validity issues may have been present but undetected in previous research, contributing to inconclusive findings.
  • The study highlights the difficulty in measuring conceptual and procedural knowledge independently.

Conclusions:

  • The findings underscore the need for improved measurement tools to advance theoretical and practical progress in understanding mathematical competencies.
  • A multimethod approach is crucial for addressing the challenges in validly measuring intertwined knowledge types.
  • Revisiting and refining measurement strategies is essential for future research in mathematics education.