Impact of High Mathematics Education on the Number Sense

In adult number processing two mechanisms are commonly used: approximate estimation of quantity and exact calculation. While the former relies on the approximate number sense (ANS) which we share with animals and preverbal infants, the latter has been proposed to rely on an exact number system (ENS) which develops later in life following the acquisition of symbolic number knowledge. The current study investigated the influence of high level math education on the ANS and the ENS. Our results showed that the precision of non-symbolic quantity representation was not significantly altered by high level math education. However, performance in a symbolic number comparison task as well as the ability to map accurately between symbolic and non-symbolic quantities was significantly better the higher mathematics achievement. Our findings suggest that high level math education in adults shows little influence on their ANS, but it seems to be associated with a better anchored ENS and better mapping abilities between ENS and ANS.

[1]  M. Hauser,et al.  Spontaneous number discrimination of multi-format auditory stimuli in cotton-top tamarins (Saguinus oedipus) , 2002, Cognition.

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

[3]  Jessica Sullivan,et al.  Children's mappings of large number words to numerosities , 2009 .

[4]  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.

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

[6]  F. Campbell,et al.  The Magic Number 4 ± 0: A New Look at Visual Numerosity Judgements , 1976, Perception.

[7]  Paul B. Buckley,et al.  Comparisons of digits and dot patterns. , 1974, Journal of experimental psychology.

[8]  Michael Schneider,et al.  Mental number line, number line estimation, and mathematical achievement : Their interrelations in grades 5 and 6 , 2009 .

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

[10]  S. Dehaene.  Symbols and quantities in parietal cortex: elements of a mathematical theory of number representation and manipulation , 2007 .

[11]  Soon Chun Siong,et al.  Parametric effects of numerical distance on the intraparietal sulcus during passive viewing of rapid numerosity changes , 2006, Brain Research.

[12]  S. Dehaene,et al.  Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. , 1990, Journal of experimental psychology. Human perception and performance.

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

[14]  Manuela Piazza,et al.  How Humans Count: Numerosity and the Parietal Cortex , 2009, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.

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

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

[17]  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.

[18]  Avishai Henik,et al.  The development of internal representations of magnitude and their association with Arabic numerals. , 2002, Journal of experimental child psychology.

[19]  P. Haggard,et al.  Sensorimotor foundations of higher cognition , 1993 .

[20]  Gary J. Robertson,et al.  Wide‐Range Achievement Test , 2010 .

[21]  Elizabeth K. Warrington,et al.  Arithmetic Skills in Patients with Unilateral Cerebral Lesions , 1986, Cortex.

[22]  Stanislas Dehaene,et al.  Distinct Cerebral Pathways for Object Identity and Number in Human Infants , 2008, PLoS biology.

[23]  S. Dehaene.  Origins of Mathematical Intuitions , 2009, Annals of the New York Academy of Sciences.

[24]  Stanislas Dehaene,et al.  Development of Elementary Numerical Abilities: A Neuronal Model , 1993, Journal of Cognitive Neuroscience.

[25]  R. Siegler,et al.  The Development of Numerical Estimation , 2003, Psychological science.

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

[27]  Bert Reynvoet,et al.  Generating nonsymbolic number stimuli , 2011, Behavior research methods.

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

[29]  Christa Neuper,et al.  Intelligence and neural efficiency: further evidence of the influence of task content and sex on the brain-IQ relationship. , 2005, Brain research. Cognitive brain research.

[30]  Ann Dowker,et al.  The development of arithmetic concepts and skills: Constructing adaptive expertise , 2003 .

[31]  M. Passolunghi,et al.  The precursors of mathematics learning: Working memory, phonological ability and numerical competence. , 2007 .

[32]  Avishai Henik,et al.  Notation-Dependent and -Independent Representations of Numbers in the Parietal Lobes , 2007, Neuron.

[33]  M. Ashcraft,et al.  Cognitive processes of numerical estimation in children. , 2012, Journal of experimental child psychology.

[34]  Elizabeth M Brannon,et al.  A common representational system governed by Weber's law: nonverbal numerical similarity judgments in 6-year-olds and rhesus macaques. , 2006, Journal of experimental child psychology.

[35]  Richard J. Haier,et al.  Sex differences and lateralization in temporal lobe glucose metabolism during mathematical reasoning , 1995 .

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

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

[38]  Clarissa A. Thompson,et al.  Costs and benefits of representational change: effects of context on age and sex differences in symbolic magnitude estimation. , 2008, Journal of experimental child psychology.

[39]  Robert S. Siegler,et al.  Representational change and children’s numerical estimation , 2007, Cognitive Psychology.

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

[41]  Ann Dowker,et al.  YOUNG ADULTS’ STRATEGIC CHOICES IN SIMPLE ARITHMETIC: IMPLICATIONS FOR THE DEVELOPMENT OF MATHEMATICAL REPRESENTATIONS , 2013 .

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

[43]  E. J. Carter,et al.  Functional Imaging of Numerical Processing in Adults and 4-y-Old Children , 2006, PLoS biology.

[44]  R. Shalev,et al.  Developmental Dyscalculia , 2004, Journal of child neurology.

[45]  Justin Halberda,et al.  Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia). , 2011, Child development.

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

[47]  Philippe Pinel,et al.  Tuning Curves for Approximate Numerosity in the Human Intraparietal Sulcus , 2004, Neuron.

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

[49]  V Menon,et al.  Cerebral Cortex doi:10.1093/cercor/bhi055 Developmental Changes in Mental Arithmetic: Evidence for Increased Functional Specialization in the Left Inferior Parietal Cortex , 2005 .

[50]  Xavier Seron,et al.  Under- and over-estimation: a bi-directional mapping process between symbolic and non-symbolic representations of number? , 2011, Experimental psychology.

[51]  Julie L. Booth,et al.  Development of numerical estimation in young children. , 2004, Child development.

[52]  A. Neubauer,et al.  Intelligence and neural efficiency: The influence of task content and sex on the brain–IQ relationship , 2002 .

[53]  Glyn W. Humphreys,et al.  The magic number four and temporo-parietal damage: Neurological impairments in counting targets amongst distractors. , 1999 .

[54]  Lieven Verschaffel,et al.  A validation of eye movements as a measure of elementary school children's developing number sense , 2008 .

[55]  K. Fuson.  Children's Counting and Concepts of Number , 1987 .

[56]  G. Humphreys,et al.  Bilateral Field Advantage in Visual Enumeration , 2011, PLoS ONE.

[57]  Andreas Nieder,et al.  A parieto-frontal network for visual numerical information in the monkey. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[58]  Julie L. Booth,et al.  Developmental and individual differences in pure numerical estimation. , 2006, Developmental psychology.

[59]  Bahador Bahrami,et al.  Human Neuroscience , 2022 .

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

[61]  D. Ansari.  Effects of development and enculturation on number representation in the brain , 2008, Nature Reviews Neuroscience.

[62]  Avishai Henik,et al.  Automatic and intentional processing of numerical information , 1992 .

[63]  Xavier Seron,et al.  Numerical estimation in blind subjects: evidence of the impact of blindness and its following experience. , 2007, Journal of experimental psychology. Human perception and performance.

[64]  C. Gallistel,et al.  The Child's Understanding of Number , 1979 .

[65]  S. Carey.  The Origin of Concepts , 2000 .

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

[67]  Elizabeth S. Spelke,et al.  Core multiplication in childhood , 2010, Cognition.

[68]  Michael C. Frank,et al.  Number as a cognitive technology: Evidence from Pirahã language and cognition , 2008, Cognition.

[69]  M. Noël,et al.  Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs non-symbolic number magnitude processing , 2007, Cognition.

[70]  Susan Carey,et al.  Cognitive Foundations of Arithmetic: Evolution and Ontogenisis , 2001 .

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

[72]  Wim Fias,et al.  Representation of Number in Animals and Humans: A Neural Model , 2004, Journal of Cognitive Neuroscience.

[73]  A. Dowker.  Individual Differences in Arithmetic , 2012 .

[74]  Daniel Ansari,et al.  Neural correlates of symbolic number processing in children and adults , 2005, Neuroreport.

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

[76]  Derrick G. Watson,et al.  Effects of color heterogeneity on subitization , 2006, Perception & psychophysics.

[77]  Daniel Ansari,et al.  Age-related Changes in the Activation of the Intraparietal Sulcus during Nonsymbolic Magnitude Processing: An Event-related Functional Magnetic Resonance Imaging Study , 2006, Journal of Cognitive Neuroscience.

[78]  Katherine D. Kinzler,et al.  Core knowledge. , 2007, Developmental science.

[79]  Sylvie Droit-Volet,et al.  Time and number discrimination in a bisection task with a sequence of stimuli: a developmental approach. , 2003, Journal of experimental child psychology.

[80]  H S Terrace,et al.  Representation of the numerosities 1-9 by rhesus macaques (Macaca mulatta). , 2000, Journal of experimental psychology. Animal behavior processes.

[81]  P. Onghena,et al.  The relationship between the shape of the mental number line and familiarity with numbers in 5- to 9-year old children: evidence for a segmented linear model. , 2008, Journal of experimental child psychology.