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Dissonances in theories of number understanding

Published online by Cambridge University Press:  11 December 2008

Lance J. Rips ,
Amber Bloomfield  and
Jennifer Asmuth
Lance J. Rips
Affiliation:
Psychology Department, Northwestern University, Evanston, IL 60208; rips@northwestern.eduasmuth@northwestern.eduhttp://mental.psych.northwestern.edu
Amber Bloomfield
Affiliation:
Psychology Department, DePaul University, Chicago, IL 60614. abloomfi@depaul.edu
Jennifer Asmuth
Affiliation:
Psychology Department, Northwestern University, Evanston, IL 60208; rips@northwestern.eduasmuth@northwestern.eduhttp://mental.psych.northwestern.edu
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Abstract

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.

Type
Authors' Response
Information
Behavioral and Brain Sciences , Volume 31 , Issue 6 , December 2008 , pp. 671 - 687
Copyright
Copyright © Cambridge University Press 2008

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