Preschoolers' Precision of the Approximate Number System Predicts Later School Mathematics Performance

The Approximate Number System (ANS) is a primitive mental system of nonverbal representations that supports an intuitive sense of number in human adults, children, infants, and other animal species. The numerical approximations produced by the ANS are characteristically imprecise and, in humans, this precision gradually improves from infancy to adulthood. Throughout development, wide ranging individual differences in ANS precision are evident within age groups. These individual differences have been linked to formal mathematics outcomes, based on concurrent, retrospective, or short-term longitudinal correlations observed during the school age years. However, it remains unknown whether this approximate number sense actually serves as a foundation for these school mathematics abilities. Here we show that ANS precision measured at preschool, prior to formal instruction in mathematics, selectively predicts performance on school mathematics at 6 years of age. In contrast, ANS precision does not predict non-numerical cognitive abilities. To our knowledge, these results provide the first evidence for early ANS precision, measured before the onset of formal education, predicting later mathematical abilities.

[1]  M. Denckla,et al.  Rapid "automatized" naming of pictured objects, colors, letters and numbers by normal children. , 1974, Cortex; a journal devoted to the study of the nervous system and behavior.

[2]  Kelly S. Mix,et al.  Number Versus Contour Length in Infants' Discrimination of Small Visual Sets , 1999 .

[3]  C. Gallistel,et al.  Nonverbal Counting in Humans: The Psychophysics of Number Representation , 1999 .

[4]  A. Su,et al.  The National Council of Teachers of Mathematics , 1932, The Mathematical Gazette.

[5]  J. Sattler.  Assessment of Children: Cognitive Applications , 2001 .

[6]  E. Spelke,et al.  Infants' Discrimination of Number vs. Continuous Extent , 2002, Cognitive Psychology.

[7]  M. Ashcraft.  Math Anxiety: Personal, Educational, and Cognitive Consequences , 2002 .

[8]  Elizabeth S Spelke,et al.  Origins of Number Sense , 2003, Psychological science.

[9]  Michèle M. M. Mazzocco,et al.  Complexities in identifying and defining mathematics learning disability in the primary school-age years , 2003, Annals of dyslexia.

[10]  E. Spelke,et al.  Language and Conceptual Development series Core systems of number , 2004 .

[11]  Richard E Thompson,et al.  Kindergarten Predictors of Math Learning Disability , 2005, Learning disabilities research & practice : a publication of the Division for Learning Disabilities, Council for Exceptional Children.

[12]  S. Dehaene,et al.  Principles underlying the design of "The Number Race", an adaptive computer game for remediation of dyscalculia , 2006, Behavioral and brain functions : BBF.

[13]  Elizabeth M Brannon,et al.  The representation of numerical magnitude , 2006, Current Opinion in Neurobiology.

[14]  M. Mazzocco,et al.  A Longitudinal Assessment of Executive Function Skills and Their Association with Math Performance , 2007, Child neuropsychology : a journal on normal and abnormal development in childhood and adolescence.

[15]  C. Blair,et al.  Relating effortful control, executive function, and false belief understanding to emerging math and literacy ability in kindergarten. , 2007, Child development.

[16]  Brian Butterworth,et al.  Core information processing deficits in developmental dyscalculia and low numeracy. , 2008, Developmental science.

[17]  S. Wiebe,et al.  Short-Term Memory, Working Memory, and Executive Functioning in Preschoolers: Longitudinal Predictors of Mathematical Achievement at Age 7 Years , 2008, Developmental neuropsychology.

[18]  Justin Halberda,et al.  Individual differences in non-verbal number acuity correlate with maths achievement , 2008, Nature.

[19]  Charalambos Y. Charalambous,et al.  Mathematical Knowledge for Teaching and the Mathematical Quality of Instruction: An Exploratory Study , 2008 .

[20]  Nancy C. Jordan,et al.  Using Kindergarten Number Sense to Predict Calculation Fluency in Second Grade , 2008, Journal of learning disabilities.

[21]  E. Spelke,et al.  Nonsymbolic, approximate arithmetic in children: abstract addition prior to instruction. , 2008, Developmental psychology.

[22]  Justin Halberda,et al.  Developmental change in the acuity of the "Number Sense": The Approximate Number System in 3-, 4-, 5-, and 6-year-olds and adults. , 2008, Developmental psychology.

[23]  Melissa E. Libertus,et al.  Behavioral and Neural Basis of Number Sense in Infancy , 2009, Current directions in psychological science.

[24]  L. Verschaffel,et al.  The predictive value of numerical magnitude comparison for individual differences in mathematics achievement. , 2009, Journal of experimental child psychology.

[25]  E. Spelke,et al.  Newborn infants perceive abstract numbers , 2009, Proceedings of the National Academy of Sciences.

[26]  Peggy P. Chen,et al.  Self-regulation, motivation, and math achievement in middle school: variations across grade level and math context. , 2009, Journal of school psychology.

[27]  Nancy C. Jordan,et al.  Socioeconomic variation, number competence, and mathematics learning difficulties in young children. , 2009, Developmental disabilities research reviews.

[28]  Daniel Ansari,et al.  Mapping numerical magnitudes onto symbols: the numerical distance effect and individual differences in children's mathematics achievement. , 2009, Journal of experimental child psychology.

[29]  Andrea Facoetti,et al.  Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia , 2010, Cognition.

[30]  Janet A. Welsh,et al.  The Development of Cognitive Skills and Gains in Academic School Readiness for Children from Low-Income Families. , 2010, Journal of educational psychology.

[31]  Elizabeth S. Spelke,et al.  Non-symbolic arithmetic abilities and mathematics achievement in the first year of formal schooling , 2010, Cognition.

[32]  S. Friedman,et al.  Instruction, Teacher-Student Relations, and Math Achievement Trajectories in Elementary School. , 2010, Journal of educational psychology.

[33]  Sian L. Beilock,et al.  Female teachers’ math anxiety affects girls’ math achievement , 2010, Proceedings of the National Academy of Sciences.

[34]  Melissa E. Libertus,et al.  Preschool acuity of the approximate number system correlates with school math ability. , 2011, Developmental science.

[35]  Maria Chiara Passolunghi,et al.  The relationship between working memory, IQ, and mathematical skills in children , 2011 .

[36]  A. Desoete,et al.  Can we predict mathematical learning disabilities from symbolic and non-symbolic comparison tasks in kindergarten? Findings from a longitudinal study. , 2012, The British journal of educational psychology.