David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Symbolic arithmetic is fundamental to science, technology and economics, but its acquisition by children typically requires years of effort, instruction and drill1,2. When adults perform mental arithmetic, they activate nonsymbolic, approximate number representations3,4, and their performance suffers if this nonsymbolic system is impaired5. Nonsymbolic number representations also allow adults, children, and even infants to add or subtract pairs of dot arrays and to compare the resulting sum or difference to a third array, provided that only approximate accuracy is required6–10. Here we report that young children, who have mastered verbal counting and are on the threshold of arithmetic instruction, can build on their nonsymbolic number system to perform symbolic addition and subtraction11–15. Children across a broad socio-economic spectrum solved symbolic problems involving approximate addition or subtraction of large numbers, both in a laboratory test and in a school setting. Aspects of symbolic arithmetic therefore lie within the reach of children who have learned no algorithms for manipulating numerical symbols. Our findings help to delimit the sources of children’s difficulties learning symbolic arithmetic, and they suggest ways to enhance children’s engagement with formal mathematics. We presented children with approximate symbolic arithmetic problems in a format that parallels previous tests of non-symbolic arithmetic in preschool children8,9. In the first experiment, five- to six-year-old children were given problems such as ‘‘If you had twenty-four stickers and I gave you twenty-seven more, would you have more or less than thirty-five stickers?’’. Children performed well above chance (65.0%, t1952.77, P 5 0.012) without resorting to guessing or comparison strategies that could serve as alternatives to arithmetic. Children who have been taught no symbolic arithmetic therefore have some ability to perform symbolic addition problems. The children’s performance nevertheless fell short of performance on non-symbolic arithmetic tasks using equivalent addition problems with numbers presented as arrays of dots and with the addition operation conveyed by successive motions of the dots into a box (71.3% correct, F1,345 4.26, P 5 0.047)8..
|Keywords||No keywords specified (fix it)|
No categories specified
(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
Helen De Cruz & Johan De Smedt (2010). The Innateness Hypothesis and Mathematical Concepts. Topoi 29 (1):3-13.
Camilla K. Gilmore, Shannon E. McCarthy & Elizabeth S. Spelke (2010). Non-Symbolic Arithmetic Abilities and Achievement in the First Year of Formal Schooling in Mathematics. Cognition 115 (3):394.
Daniel C. Hyde, Saeeda Khanum & Elizabeth S. Spelke (2014). Brief Non-Symbolic, Approximate Number Practice Enhances Subsequent Exact Symbolic Arithmetic in Children. Cognition 131 (1):92-107.
Christophe Mussolin, Sandrine Mejias & Marie-Pascale Noël (2010). Symbolic and Nonsymbolic Number Comparison in Children with and Without Dyscalculia. Cognition 115 (1):10-25.
Manuela Piazza (2010). Neurocognitive Start-Up Tools for Symbolic Number Representations. Trends in Cognitive Sciences 14 (12):542-551.
Similar books and articles
Elizabeth Spelke & Camilla Gilmore (2008). Children's Understanding of the Relationship Between Addition and Subtraction. Cognition 107 (3):932-945.
Camilla K. Gilmore & Elizabeth S. Spelke (2008). Children's Understanding of the Relationship Between Addition and Subtraction. Cognition 107 (3):932-945.
Elizabeth S. Spelke (2010). Core Multiplication in Childhood. Cognition 116 (2):204-216.
Pierre Pica, Cathy Lemer, Véronique Izard & Stanislas Dehaene (2004). Exact and Approximate Arithmetic in an Amazonian Indigene Group. Science 306 (5695):499-503.
Ann Dowker, Sheila Bala & Delyth Lloyd (2008). Linguistic Influences on Mathematical Development: How Important is the Transparency of the Counting System? Philosophical Psychology 21 (4):523 – 538.
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.
Jennifer S. Lipton & Elizabeth S. Spelke (2006). Preschool Children Master the Logic of Number Word Meanings. Cognition 98 (3):57-66.
Mirja Hartimo (2006). Mathematical Roots of Phenomenology: Husserl and the Concept of Number. History and Philosophy of Logic 27 (4):319-337.
Jennifer S. Lipton & Elizabeth S. Spelke, Preschool Children's Mapping of Number Words to Nonsymbolic Numerosities.
Alistair H. Lachlan & Robert I. Soare (1994). Models of Arithmetic and Upper Bounds for Arithmetic Sets. Journal of Symbolic Logic 59 (3):977-983.
C. Ward Henson, Matt Kaufmann & H. Jerome Keisler (1984). The Strength of Nonstandard Methods in Arithmetic. Journal of Symbolic Logic 49 (4):1039-1058.
H. Jerome Keisler (2006). Nonstandard Arithmetic and Reverse Mathematics. Bulletin of Symbolic Logic 12 (1):100-125.
Alistair H. Lachlan & Robert I. Soare (1998). Models of Arithmetic and Subuniform Bounds for the Arithmetic Sets. Journal of Symbolic Logic 63 (1):59-72.
Added to index2010-12-22
Total downloads7 ( #188,122 of 1,102,748 )
Recent downloads (6 months)1 ( #296,987 of 1,102,748 )
How can I increase my downloads?