David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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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.
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References found in this work BETA
F. Xu & E. S. Spelke (2000). Large Number Discrimination in 6-Month-Old Infants. Cognition 74 (1):1-11.
Pierre Pica, Cathy Lemer, Véronique Izard & Stanislas Dehaene (2004). Exact and Approximate Arithmetic in an Amazonian Indigene Group. Science 306 (5695):499-503.
Elizabeth Spelke & Hilary Barth (2003). The Construction of Large Number Representations in Adults. Cognition 86 (3):201-221.
Hilary Barth, Kristen La Mont, Jennifer Lipton, Stanislas Dehaene, Nancy Kanwisher & Elizabeth Spelke (2006). Non-Symbolic Arithmetic in Adults and Young Children. Cognition 98 (3):199-222.
Elizabeth M. Brannon (2002). The Development of Ordinal Numerical Knowledge in Infancy. Cognition 83 (3):223-240.
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.
Iro Xenidou‐Dervou, Ernest C. D. M. Lieshout & Menno Schoot (2014). Working Memory in Nonsymbolic Approximate Arithmetic Processing: A Dual‐Task Study With Preschoolers. Cognitive Science 38 (1):101-127.
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