David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Behavioral and Brain Sciences 31 (6):623-642 (2008)
Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and arithmetic. However, 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: (1) 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. (2) 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 in a more top-down way, by constructing mathematical schemas
|Keywords||acquisition of natural numbers mathematical concepts representations of mathematics theories of mathematical cognition|
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Allen Newell (1990). Unified Theories of Cognition. Harvard University Press.
W. V. Quine (1960). Word and Object. The MIT Press.
Sigmund Freud (2012). The Future of an Illusion. Broadview Press.
Stewart Shapiro (1997). Philosophy of Mathematics: Structure and Ontology. Oxford University Press.
Noam Chomsky (1988). Language and Problems of Knowledge. The MIT Press.
Citations of this work BETA
Helen De Cruz & Johan De Smedt (2013). Mathematical Symbols as Epistemic Actions. Synthese 190 (1):3-19.
Kathryn Davidson, Kortney Eng & David Barner (2012). Does Learning to Count Involve a Semantic Induction? Cognition 123 (1):162-173.
Brian Butterworth (2010). Foundational Numerical Capacities and the Origins of Dyscalculia. Trends in Cognitive Sciences 14 (12):534-541.
Dedre Gentner (2010). Bootstrapping the Mind: Analogical Processes and Symbol Systems. Cognitive Science 34 (5):752-775.
Manuela Piazza (2010). Neurocognitive Start-Up Tools for Symbolic Number Representations. Trends in Cognitive Sciences 14 (12):542-551.
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