David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Cognition 107 (3):932-945 (2008)
In learning mathematics, children must master fundamental logical relationships, including the inverse relationship between addition and subtraction. At the start of elementary school, children lack generalized understanding of this relationship in the context of exact arithmetic problems: they fail to judge, for example, that 12 + 9 - 9 yields 12. Here, we investigate whether preschool children’s approximate number knowledge nevertheless supports understanding of this relationship. Five-year-old children were more accurate on approximate large-number arithmetic problems that involved an inverse transformation than those that did not, when problems were presented in either non-symbolic or symbolic form. In contrast they showed no advantage for problems involving an inverse transformation when exact arithmetic was involved. Prior to formal schooling, children therefore show generalized understanding of at least one logical principle of arithmetic. The teaching of mathematics may be enhanced by building on this understanding.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Véronique Izard, Pierre Pica, Elizabeth S. Spelke & Stanislas Dehaene (2008). Exact Equality and Successor Function: Two Key Concepts on the Path Towards Understanding Exact Numbers. Philosophical Psychology 21 (4):491 – 505.
Similar books and articles
Judith G. Smetana (1999). The Role of Parents in Moral Development: A Social Domain Analysis. Journal of Moral Education 28 (3):311-321.
Shaun Nichols & T. Folds-Bennett (2003). Are Children Moral Objectivists? Children's Judgments About Moral and Response-Dependent Properties. Cognition 90 (2):23-32.
Stephen Andrew Butterfill (2010). Children's Selective Learning From Others. Review of Philosophy and Psychology 1 (4):551-561.
Erika Nurmsoo, Elizabeth Robinson & Stephen Andrew Butterfill (2010). Children's Selective Learning From Others. Review of Philosophy and Psychology 1 (4):551-561.
Jeremy I. M. Carpendale & Charlie Lewis (2004). Constructing an Understanding of Mind: The Development of Children's Social Understanding Within Social Interaction. Behavioral and Brain Sciences 27 (1):79-96.
Jennifer S. Lipton & Elizabeth S. Spelke (2006). Preschool Children Master the Logic of Number Word Meanings. Cognition 98 (3):57-66.
Elizabeth S. Spelke (2010). Core Multiplication in Childhood. Cognition 116 (2):204-216.
Camilla K. Gilmore, Shannon E. McCarthy & Elizabeth S. Spelke, Symbolic Arithmetic Knowledge Without Instruction.
Added to index2009-01-28
Total downloads5 ( #210,215 of 1,096,291 )
Recent downloads (6 months)1 ( #224,942 of 1,096,291 )
How can I increase my downloads?