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Predicting adaptive expertise with rational number arithmetic.

Jake McMullen1, Minna M Hannula-Sormunen1, Erno Lehtinen1,2

  • 1Department of Teacher Education, University of Turku, Finland.

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|November 8, 2021
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Summary
This summary is machine-generated.

Adaptive rational number knowledge is predicted by prior knowledge, calculation skills, and a tendency to focus on multiplicative relations. These factors are key to developing adaptive expertise in mathematics.

Keywords:
adaptive expertiseflexibilitymathematical developmentrational numbersspontaneous mathematical focusing tendency

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Area of Science:

  • Mathematics Education
  • Cognitive Psychology

Background:

  • Adaptive expertise, particularly in rational numbers, is crucial but shows individual differences.
  • Adaptive rational number knowledge involves integrating numerical understanding for novel tasks.

Purpose of the Study:

  • To investigate how domain-general and specific skills predict rational number knowledge.
  • To differentiate predictors for conceptual, procedural, and adaptive rational number knowledge.

Main Methods:

  • Longitudinal study with 173 6th and 7th graders over 1.5 years.
  • Multiple hierarchical regression analysis used to assess predictors of rational number knowledge.

Main Results:

  • Prior rational number knowledge, calculation skills, and spontaneous focusing on multiplicative relations (SFOR) uniquely predicted adaptive rational number knowledge.
  • Conceptual knowledge and general math achievement predicted conceptual and procedural knowledge, but not adaptive knowledge.

Conclusions:

  • Mathematical development research should include adaptive expertise features.
  • Investigating spontaneous mathematical focusing tendencies is recommended for understanding adaptive expertise.