Dissonances in theories of number understanding

Lance Rips*, Amber Bloomfield, Jennifer Asmuth

*Corresponding author for this work

Research output: Contribution to journalComment/debatepeer-review


Traditional theories of how children learn the positive integers start from infants' abilities in detecting the quantity of physical objects. Our target article examined this view and found no plausible accounts of such development. Most of our commentators appear to agree that no adequate developmental theory is presently available, but they attempt to hold onto a role for early enumeration. Although some defend the traditional theories, others introduce new basic quantitative abilities, new methods of transformation, or new types of end states. A survey of these proposals, however, shows that they do not succeed in bridging the gap to knowledge of the integers. We suggest that a better theory depends on starting with primitives that are inherently structural and mathematical.

Original languageEnglish (US)
Pages (from-to)671-682
Number of pages12
JournalBehavioral and Brain Sciences
Issue number6
StatePublished - Dec 19 2008

ASJC Scopus subject areas

  • Behavioral Neuroscience
  • Neuropsychology and Physiological Psychology
  • Physiology

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