Brief non-symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children

Recent research reveals a link between individual differences in mathematics achievement and performance on tasks that activate the approximate number system (ANS): a primitive cognitive system shared by diverse animal species and by humans of all ages. Here we used a brief experimental paradigm to test one causal hypothesis suggested by this relationship: activation of the ANS may enhance children's performance of symbolic arithmetic. Over 2 experiments, children who briefly practiced tasks that engaged primitive approximate numerical quantities performed better on subsequent exact, symbolic arithmetic problems than did children given other tasks involving comparison and manipulation of non-numerical magnitudes (brightness and length). The practice effect appeared specific to mathematics, as no differences between groups were observed on a comparable sentence completion task. These results move beyond correlational research and provide evidence that the exercise of non-symbolic numerical processes can enhance children's performance of symbolic mathematics.

[1]  S. Dehaene,et al.  THREE PARIETAL CIRCUITS FOR NUMBER PROCESSING , 2003, Cognitive neuropsychology.

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

[3]  Stanislas Dehaene,et al.  Effects of an Adaptive Game Intervention on Accessing Number Sense in Low-Socioeconomic-Status Kindergarten Children , 2009 .

[4]  Nicole M. McNeil,et al.  ANS acuity and mathematics ability in preschoolers from low-income homes: contributions of inhibitory control. , 2013, Developmental science.

[5]  Elizabeth M. Brannon,et al.  The Effect of Heterogeneity on Numerical Ordering in Rhesus Monkeys , 2006 .

[6]  Stella F. Lourenco,et al.  Origins and Development of Generalized Magnitude Representation , 2011 .

[7]  Marinella Cappelletti,et al.  rTMS over the intraparietal sulcus disrupts numerosity processing , 2007, Experimental Brain Research.

[8]  D G Gadian,et al.  Calculation difficulties in children of very low birthweight: a neural correlate. , 2001, Brain : a journal of neurology.

[9]  Kelly S. Mix,et al.  Early fraction calculation ability. , 1999, Developmental psychology.

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

[11]  S. Carey,et al.  Re-visiting the competence/performance debate in the acquisition of the counting principles , 2006, Cognitive Psychology.

[12]  Philippe Pinel,et al.  Distributed and Overlapping Cerebral Representations of Number, Size, and Luminance during Comparative Judgments , 2004, Neuron.

[13]  R. Baumeister,et al.  Ego depletion: is the active self a limited resource? , 1998, Journal of personality and social psychology.

[14]  Stella F. Lourenco,et al.  Nonsymbolic number and cumulative area representations contribute shared and unique variance to symbolic math competence , 2012, Proceedings of the National Academy of Sciences.

[15]  S. Dehaene,et al.  An open trial assessment of "The Number Race", an adaptive computer game for remediation of dyscalculia , 2006, Behavioral and Brain Functions.

[16]  ROBERT S. MOYER,et al.  Time required for Judgements of Numerical Inequality , 1967, Nature.

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

[18]  Daniel Ansari,et al.  Nonsymbolic numerical magnitude comparison: reliability and validity of different task variants and outcome measures, and their relationship to arithmetic achievement in adults. , 2012, Acta psychologica.

[19]  L Girelli,et al.  The development of automaticity in accessing number magnitude. , 2000, Journal of experimental child psychology.

[20]  Andreas Nieder,et al.  Neuronal population coding of continuous and discrete quantity in the primate posterior parietal cortex , 2007, Proceedings of the National Academy of Sciences.

[21]  Stanislas Dehaene,et al.  Cerebral Pathways for Calculation: Double Dissociation between Rote Verbal and Quantitative Knowledge of Arithmetic , 1997, Cortex.

[22]  S. Dehaene,et al.  Functional and Structural Alterations of the Intraparietal Sulcus in a Developmental Dyscalculia of Genetic Origin , 2003, Neuron.

[23]  S Dehaene,et al.  Attention, automaticity, and levels of representation in number processing. , 1995, Journal of experimental psychology. Learning, memory, and cognition.

[24]  S. Dehaene,et al.  Representation of number in the brain. , 2009, Annual review of neuroscience.

[25]  L. Frank The Society for Research in Child Development , 1935 .

[26]  Brian Butterworth,et al.  Foundational numerical capacities and the origins of dyscalculia , 2010, Trends in Cognitive Sciences.

[27]  Emmy Defever,et al.  The Approximate Number System is not Predictive for Symbolic Number Processing in Kindergarteners , 2014, Quarterly journal of experimental psychology.

[28]  Stella F. Lourenco,et al.  General Magnitude Representation in Human Infants , 2010, Psychological science.

[29]  Fei Xu,et al.  Numerosity discrimination in infants: Evidence for two systems of representations , 2003, Cognition.

[30]  Gavin R. Price,et al.  Impaired parietal magnitude processing in developmental dyscalculia , 2007, Current Biology.

[31]  Justin Halberda,et al.  Intuitive sense of number correlates with math scores on college-entrance examination. , 2012, Acta psychologica.

[32]  S. Dehaene,et al.  Attention, automaticity, and levels of representation in number processing , 1995 .

[33]  Fei Xu,et al.  Number sense in human infants. , 2005, Developmental science.

[34]  A. Baddeley,et al.  Executive functions and self-regulation , 2012, Trends in Cognitive Sciences.

[35]  Stanislas Dehaene,et al.  Calibrating the mental number line , 2008, Cognition.

[36]  Douglas Fuchs,et al.  Effects of First-Grade Number Knowledge Tutoring With Contrasting Forms of Practice. , 2013, Journal of educational psychology.

[37]  Elizabeth M Brannon,et al.  The development of ordinal numerical knowledge in infancy , 2002, Cognition.

[38]  Nancy Kanwisher,et al.  Non-symbolic arithmetic in adults and young children , 2006, Cognition.

[39]  Daniel Ansari,et al.  Individual differences in children’s mathematical competence are related to the intentional but not automatic processing of Arabic numerals , 2011, Cognition.

[40]  Nancy Kanwisher,et al.  Nonsymbolic Arithmetic in Adults and Young Children , 2003 .

[41]  Pierre Pica,et al.  Education Enhances the Acuity of the Nonverbal Approximate Number System , 2013, Psychological science.

[42]  Manuela Piazza,et al.  Neurocognitive start-up tools for symbolic number representations , 2010, Trends in Cognitive Sciences.

[43]  G. Rizzolatti,et al.  Evolution of human cortical circuits for reading and arithmetic : The “ neuronal recycling ” hypothesis , 2004 .

[44]  Justin Halberda,et al.  Is Approximate Number Precision a Stable Predictor of Math Ability? , 2013, Learning and individual differences.

[45]  Susan Carey,et al.  One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles , 2007, Cognition.

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

[47]  Sian L. Beilock,et al.  Beyond quantity: Individual differences in working memory and the ordinal understanding of numerical symbols , 2009, Cognition.

[48]  Susan Carey,et al.  Where Our Number Concepts Come From. , 2009, The journal of philosophy.

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

[50]  Daniel Ansari,et al.  Domain-specific and domain-general changes in children's development of number comparison. , 2008, Developmental science.

[51]  Elizabeth M Brannon,et al.  Basic Math in Monkeys and College Students , 2007, PLoS biology.

[52]  Avishai Henik,et al.  A common representation for semantic and physical properties: a cognitive-anatomical approach. , 2006, Experimental psychology.

[53]  Elizabeth S. Spelke,et al.  Symbolic arithmetic knowledge without instruction , 2007, Nature.

[54]  S. Dehaene,et al.  Abstract representations of numbers in the animal and human brain , 1998, Trends in Neurosciences.

[55]  Emmy Defever,et al.  Association between basic numerical abilities and mathematics achievement. , 2012, The British journal of developmental psychology.

[56]  G. Orban,et al.  Parietal Representation of Symbolic and Nonsymbolic Magnitude , 2003, Journal of Cognitive Neuroscience.

[57]  Ariel Starr,et al.  Number sense in infancy predicts mathematical abilities in childhood , 2013, Proceedings of the National Academy of Sciences.

[58]  Daniel Ansari,et al.  The Evolution of Numerical Cognition: From Number Neurons to Linguistic Quantifiers , 2008, The Journal of Neuroscience.

[59]  J. Grafman,et al.  Metabolic abnormalities detected by 1H-MRS in dyscalculia and dysgraphia , 1999, Neurology.

[60]  B. Schmeichel,et al.  Attention control, memory updating, and emotion regulation temporarily reduce the capacity for executive control. , 2007, Journal of experimental psychology. General.

[61]  Hilary Barth,et al.  Abstract number and arithmetic in preschool children. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[62]  Elizabeth M Brannon,et al.  Training the Approximate Number System Improves Math Proficiency , 2013, Psychological science.

[63]  S. Dehaene,et al.  Computer-Assisted Intervention for Children with Low Numeracy Skills , 2009 .

[64]  Neil Marlow,et al.  Individual Differences in Inhibitory Control, Not Non-Verbal Number Acuity, Correlate with Mathematics Achievement , 2013, PloS one.

[65]  Kyoung-Min Lee Cortical areas differentially involved in multiplication and subtraction: A functional magnetic resonance imaging study and correlation with a case of selective acalculia , 2000, Annals of neurology.

[66]  Sian L. Beilock,et al.  The relation between spatial skill and early number knowledge: the role of the linear number line. , 2012, Developmental psychology.

[67]  Justin Halberda,et al.  Number sense across the lifespan as revealed by a massive Internet-based sample , 2012, Proceedings of the National Academy of Sciences.

[68]  M. Hagger,et al.  Ego depletion and the strength model of self-control: a meta-analysis. , 2010, Psychological bulletin.

[69]  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.

[70]  Vincent Walsh A theory of magnitude: common cortical metrics of time, space and quantity , 2003, Trends in Cognitive Sciences.

[71]  Elizabeth M. Brannon,et al.  Malleability of the approximate number system: effects of feedback and training , 2012, Front. Hum. Neurosci..

[72]  高山 吉弘 Isolated acalculia due to left parietal lesion , 1994 .

[73]  S. Dehaene,et al.  The Number Sense: How the Mind Creates Mathematics. , 1998 .

[74]  S. Dehaene,et al.  Exact and Approximate Arithmetic in an Amazonian Indigene Group , 2004, Science.

[75]  C. Gilmore,et al.  Children's mapping between symbolic and nonsymbolic representations of number. , 2009, Journal of experimental child psychology.

[76]  S. Dehaene,et al.  A Magnitude Code Common to Numerosities and Number Symbols in Human Intraparietal Cortex , 2007, Neuron.

[77]  K. Wynn,et al.  Large-Number Addition and Subtraction by 9-Month-Old Infants , 2004, Psychological science.

[78]  M. Posner,et al.  Brain mechanisms of quantity are similar in 5-year-old children and adults. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[79]  L. Feigenson,et al.  Preschoolers' Precision of the Approximate Number System Predicts Later School Mathematics Performance , 2011, PloS one.

[80]  Avishai Henik,et al.  Color Congruity Effect: Where do Colors and Numbers Interact in Synesthesia? , 2006, Cortex.

[81]  H S Terrace,et al.  Ordering of the numerosities 1 to 9 by monkeys. , 1998, Science.

[82]  A. Henik,et al.  Is three greater than five: The relation between physical and semantic size in comparison tasks , 1982, Memory & cognition.

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

[84]  J. Cantlon,et al.  Shared System for Ordering Small and Large Numbers in Monkeys and Humans , 2006, Psychological science.

[85]  Sian L. Beilock,et al.  Numerical ordering ability mediates the relation between number-sense and arithmetic competence , 2011, Cognition.

[86]  R. Cohen Kadosh,et al.  When a line is a number: Color yields magnitude information in a digit-color synesthete , 2006, Neuroscience.

[87]  T. Verguts,et al.  Dissecting the symbolic distance effect: Comparison and priming effects in numerical and nonnumerical orders , 2008, Psychonomic bulletin & review.

[88]  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.

[89]  E. Spelke,et al.  Large number discrimination in 6-month-old infants , 2000, Cognition.

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