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Mental representations in fraction comparison.

Thomas J Faulkenberry1, Benton H Pierce

  • 1Department of Psychology and Special Education, Texas A&M University - Commerce, TX 75429-3011, USA. Thomas_Faulkenberry@tamu-commerce.edu

Experimental Psychology
|May 20, 2011
PubMed
Summary
This summary is machine-generated.

Adults use various strategies, including magnitude-based representations, to compare fractions. Reaction times in fraction comparison tasks are influenced by numerical distance and problem size, especially with component-based strategies.

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Area of Science:

  • Cognitive Psychology
  • Mathematical Cognition

Background:

  • Understanding how individuals mentally represent and compare numerical values is crucial in cognitive psychology.
  • Fraction comparison is a complex task that can involve diverse strategies, influencing cognitive processing.

Purpose of the Study:

  • To investigate the mental representations and strategies adults employ during a fraction comparison task.
  • To determine how numerical distance and problem size affect reaction times in fraction comparison.

Main Methods:

  • Participants performed a fraction comparison task, identifying the larger fraction.
  • Trial-by-trial strategy reports were collected, alongside reaction time data.
  • Regression analyses were used to identify predictors of reaction times.

Main Results:

  • Reaction times were significantly predicted by the numerical distance between fractions across all strategies.
  • A problem-size effect was observed, with reaction times predicted by the average cross product, particularly for component-based strategies.
  • Adults utilized a range of strategies, from intuitive knowledge to procedural methods like cross-multiplication.

Conclusions:

  • Adults primarily use magnitude-based mental representations for fraction comparison.
  • Strategy choice plays a role in the formation of mental representations, influencing the impact of problem size.
  • The findings contribute to understanding numerical cognition and mathematical learning.