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Representations of Fractions: Evidence for Accessing the Whole Magnitude in Adults

Representations of Fractions: Evidence for Accessing the Whole Magnitude in Adults Proficiency with fractions serves as a foundation for later mathematics and is critical for learning algebra, which plays a role in college success and lifetime earnings. Yet children often struggle to learn fractions. Educators have argued that a conceptual understanding of fractions involves learning that a fraction represents a magnitude different from its whole number components. However, it is not well understood whether adults represent a fraction's magnitude similarly to whole numbers. This study investigated the distance effect during a comparison task using fraction pairs that discouraged comparing a fraction's components. Accuracy improved and reaction times decreased with greater distance between fraction pairs, showing a distance effect similar to that seen with whole numbers. This study suggests that a representation of a fraction's magnitude is present in the fully developed number system. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mind, Brain, and Education Wiley

Representations of Fractions: Evidence for Accessing the Whole Magnitude in Adults

Sprute, Lisa; Temple, Elise
Mind, Brain, and Education , Volume 5 (1) – Mar 1, 2011
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Publisher
Wiley
Copyright
© 2011 The Authors. Journal Compilation © 2011 International Mind, Brain, and Education Society and Blackwell Publishing, Inc.
ISSN
1751-2271
eISSN
1751-228X
DOI
10.1111/j.1751-228X.2011.01109.x
Publisher site
See Article on Publisher Site

Abstract

Proficiency with fractions serves as a foundation for later mathematics and is critical for learning algebra, which plays a role in college success and lifetime earnings. Yet children often struggle to learn fractions. Educators have argued that a conceptual understanding of fractions involves learning that a fraction represents a magnitude different from its whole number components. However, it is not well understood whether adults represent a fraction's magnitude similarly to whole numbers. This study investigated the distance effect during a comparison task using fraction pairs that discouraged comparing a fraction's components. Accuracy improved and reaction times decreased with greater distance between fraction pairs, showing a distance effect similar to that seen with whole numbers. This study suggests that a representation of a fraction's magnitude is present in the fully developed number system.

Journal

Mind, Brain, and Education – Wiley

Published: Mar 1, 2011

References

  • Order and equivalence of rational numbers: A clinical teaching experiment.
    Behr, Behr; Wachsmuth, Wachsmuth; Post, Post; Lesh, Lesh
  • The mental representation of numerical fractions: Real or integer?
    Bonato, Bonato; Fabbri, Fabbri; Umilta, Umilta; Zorzi, Zorzi
  • Developmental and individual differences in pure numerical estimation.
    Booth, Booth; Siegler, Siegler
  • Identifying fractions on number lines.
    Bright, Bright; Behr, Behr; Post, Post; Wachsmuth, Wachsmuth
  • Varieties of numerical abilities.
    Dehaene, Dehaene
  • Development of elementary numerical abilities: A neuronal model.
    Dehaene, Dehaene; Changeux, Changeux
  • The mental representation of parity and number magnitude.
    Dehaene, Dehaene; Bossini, Bossini; Giraux, Giraux
  • Development of number line representations in children with mathematical learning disability.
    Geary, Geary; Hoard, Hoard; Nugent, Nugent; Byrd‐Craven, Byrd‐Craven
  • Confounding whole‐number and fraction concepts when building on informal knowledge.
    Mack, Mack
  • Parts and holes: gaps in rational number sense among children with vs. without mathematical learning disabilities.
    Mazzocco, Mazzocco; Devlin, Devlin
  • Rational numbers: Componential versus holistic representation of fractions in a magnitude comparison task.
    Meert, Meert; Gregoire, Gregoire; Noel, Noel
  • Time required for judgements of numerical inequality.
    Moyer, Moyer; Landauer, Landauer
  • Teaching and learning fraction and rational numbers: The origins and implications of whole number bias.
    Ni, Ni; Zhou, Zhou
  • Representational change and magnitude estimation: Why young children can make more accurate salary comparisons than adults.
    Opfer, Opfer; DeVries, DeVries
  • Speed of adding and comparing numbers.
    Restle, Restle
  • Development of numerical estimation in young children.
    Siegler, Siegler; Booth, Booth
  • The development of numerical estimation: Evidence for multiple representations of numerical quantity.
    Siegler, Siegler; Opfer, Opfer
  • The logarithmic‐to‐linear shift: one learning sequence, many tasks, many time scales.
    Siegler, Siegler; Thompson, Thompson; Opfer, Opfer
  • Competent reasoning with rational numbers.
    Smith, Smith
  • The development of students' understanding of the numerical value of fractions.
    Stafylidou, Stafylidou; Vosniadou, Vosniadou