Rips et al/From Numerical Concepts to Concepts of Number: BBS Call for Commentators

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TITLE: From Numerical Concepts to Concepts of Number AUTHORS: Lance J. Rips Amber Bloomfield, and Jennifer Asmuth ABSTRACT: Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe these abilities set the stage for later mathematics: the natural numbers and arithmetic. But the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (a) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept from these beginnings. Proposals for arriving at natural number by (empirical) induction presuppose the mathematical concepts they seek to explain. Moreover, standard experimental tests for children’s understanding of number terms do not necessarily tap these concepts. (b) True concepts of number do appear, however, when children are able to understand generalizations over all numbers, for example, the principle of additive commutativity (a + b = b + a). Theories of how children learn such principles usually rely on a process of mapping from physical object groupings. But both experimental results and theoretical considerations imply that direct mapping is insufficient for acquiring these principles. We suggest instead that children may arrive at natural numbers and arithmetic by constructing mathematical schemas on a base of innate abilities and math principles. KEYWORDS: mathematical concepts; acquisition of natural numbers; representations of mathematics; theories of mathematical cognition FULL TEXT: http://www.bbsonline.org/Preprints/Rips-08242006/Referees/Rips-08242006_pre… ================================================================== *** CALL RESPONSE INSTRUCTIONS *** ================================================================== Please DO NOT respond to this email. If you wish to submit a proposal for commentary and/or suggest potential commentators, please go to the new Online Commentary Proposal System at the following URL: http://www.bbsonline.org/perl/commentary/commproposal?authordir=Rips-082420… * If you only wish to suggest potential commentators, please ignore prompts to submit a proposal with expertise information. * If you experience technical difficulties, please email bbs(a)bbsonline.org. * Please respond to this Call no later than March 31, 2008 NOTE: Behavioral and Brain Sciences (BBS) is an international, interdisciplinary journal providing Open Peer Commentary on important and controversial current research in the biobehavioral and cognitive sciences. Commentators must be BBS Associates, or suggested by a BBS Associate. If you are not a BBS Associate, please follow the instructions linked below: http://www.bbsonline.org/Instructions/associnst.html ================================================================== ================================================================== Paul Bloom - Editor Barbara Finlay - Editor Behavioral and Brain Sciences bbs(a)bbsonline.org http://www.bbsonline.org -------------------------------------------------------------------