Quantity Representation

  • Rhonda Douglas Brown
  • Vincent J. Schmithorst


In this chapter, we draw on evolutionary developmental psychology theory and Dehaene and colleagues’ triple-code model to describe quantity representation, which is the basis for a set of numerical abilities selected during evolution, including numerosity, which involves quickly determining the quantity of a set without counting, and ordinality, which involves recognizing that one set contains more than another without counting. We present research using innovative behavioral and cognitive neuroscience methods indicating that sensitivity to magnitude is present at birth and increases in precision into adulthood, including work investigating two quantity representation systems: the Parallel Individuation (PI) system that allows humans to precisely track a small number of individual objects through space and time; and the Approximate Number system, or number sense, that allows humans to approximate the numerosities of sets of items without using symbols. Research establishing a relationship between quantity representation and mathematics achievement during childhood and adolescence is also described. We present results from a functional Magnetic Resonance Imaging (fMRI) study demonstrating that brain activation in the inferior occipital gyrus, lingual gyrus, and bilateral intraparietal sulcus (IPS) during magnitude comparison is positively related to adolescents’ mathematics achievement, whereas deactivation of the Default Mode Network (DMN) during magnitude comparison is negatively related to adolescents’ mathematics achievement, indicating that abstract quantity representation may be foundational for the development of calculation skills.


Quantity representation Numerosity Ordinality Parallel Individuation Approximate Number System Functional Magnetic Resonance Imaging (fMRI) Magnitude comparison Mathematics achievement Intraparietal sulcus (IPS) Default Mode Network (DMN) 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Rhonda Douglas Brown
    • 1
  • Vincent J. Schmithorst
  1. 1.Developmental & Learning Sciences Research CenterSchool of Education, University of CincinnatiCincinnatiUSA

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