Malleability of the approximate number system: effects of feedback and training

Prior research demonstrates that animals and humans share an approximate number system (ANS), characterized by ratio dependence and that the precision of this system increases substantially over human development. The goal of the present research was to investigate the malleability of the ANS (as measured by Weber fraction) in adult subjects in response to feedback and to explore the relationship between ANS acuity and acuity on another magnitude comparison task. We tested each of 20 subjects over six 1-h sessions. The main findings were that (a) Weber fractions rapidly decreased when trial-by-trial feedback was introduced in the second session and remained stable over continued training, (b) Weber fractions remained steady when trial-by-trial feedback was removed in session 6, (c)Weber fractions from the number comparison task were positively correlated with Weber fractions from a line length comparison task, (d) improvement in Weber fractions in response to feedback for the number task did not transfer to the line length task, (e) finally, the precision of the ANS was positively correlated with math, but not verbal, standardized aptitude scores. Potential neural correlates of the perceptual information and decision processes are considered, and predictions regarding the neural correlates of ANS malleability are discussed.

[1]  Kelly S. Mix,et al.  Multiple cues for quantification in infancy: is number one of them? , 2002, Psychological bulletin.

[2]  Andreas Nieder,et al.  Temporal and Spatial Enumeration Processes in the Primate Parietal Cortex , 2006, Science.

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

[4]  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.

[5]  Daniel Ansari,et al.  Challenging the reliability and validity of cognitive measures: the case of the numerical distance effect. , 2010, Acta psychologica.

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

[7]  Elizabeth S. Spelke,et al.  Discrimination of Large and Small Numerosities by Human Infants , 2004 .

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

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

[10]  N Ginsburg,et al.  Effect of Item Arrangement on Perceived Numerosity: Randomness vs Regularity , 1976, Perceptual and motor skills.

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

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

[13]  R. Church,et al.  A mode control model of counting and timing processes. , 1983, Journal of experimental psychology. Animal behavior processes.

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

[15]  Melissa E. Libertus,et al.  Stable individual differences in number discrimination in infancy. , 2010, Developmental science.

[16]  Midori Tokita,et al.  How might the discrepancy in the effects of perceptual variables on numerosity judgment be reconciled? , 2010, Attention, perception & psychophysics.

[17]  S. Dehaene,et al.  Interactions between number and space in parietal cortex , 2005, Nature Reviews Neuroscience.

[18]  Wim Fias,et al.  Symbolic and Nonsymbolic Pathways of Number Processing , 2008 .

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

[20]  Karen Wynn,et al.  Psychological foundations of number: numerical competence in human infants , 1998, Trends in Cognitive Sciences.

[21]  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.

[22]  Daniel Ansari,et al.  Common and segregated neural pathways for the processing of symbolic and nonsymbolic numerical magnitude: An fMRI study , 2010, NeuroImage.

[23]  H. Barth,et al.  Judgments of discrete and continuous quantity: An illusory Stroop effect , 2008, Cognition.

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

[25]  E. Brannon,et al.  Monotonic Coding of Numerosity in Macaque Lateral Intraparietal Area , 2007, PLoS biology.

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

[27]  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.

[28]  Michael W. L. Chee,et al.  Neural correlates of symbolic and non-symbolic arithmetic , 2005, Neuropsychologia.

[29]  Elizabeth M. Brannon,et al.  Beyond the number domain , 2009, Trends in Cognitive Sciences.

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

[31]  Andreas Nieder,et al.  Basic mathematical rules are encoded by primate prefrontal cortex neurons , 2010, Proceedings of the National Academy of Sciences.

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

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

[34]  E. Van den Bussche,et al.  The reliability of and the relation between non-symbolic numerical distance effects in comparison, same-different judgments and priming. , 2011, Acta psychologica.

[35]  Andreas Nieder,et al.  Semantic Associations between Signs and Numerical Categories in the Prefrontal Cortex , 2007, PLoS biology.

[36]  S. Dehaene,et al.  The mental representation of parity and number magnitude. , 1993 .

[37]  J. Piaget The Child's Conception of Number , 1953 .

[38]  John M. Pearson,et al.  A Physiologically-Inspired Model of Numerical Classification Based on Graded Stimulus Coding , 2009, Front. Behav. Neurosci..

[39]  Matthew Inglis,et al.  Measuring the Approximate Number System , 2011, Quarterly journal of experimental psychology.

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

[41]  Robert L. Goldstone Influences of categorization on perceptual discrimination. , 1994, Journal of experimental psychology. General.

[42]  David J. Freedman,et al.  Representation of the Quantity of Visual Items in the Primate Prefrontal Cortex , 2002, Science.

[43]  J. Tanji,et al.  Numerical representation for action in the parietal cortex of the monkey , 2002, Nature.

[44]  Rochel Gelman,et al.  Sometimes area counts more than number , 2006, Proceedings of the National Academy of Sciences.

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

[46]  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.

[47]  Valérie Dormal,et al.  A common right fronto‐parietal network for numerosity and duration processing: An fMRI study , 2012, Human brain mapping.

[48]  Elizabeth M Brannon,et al.  Spontaneous analog number representations in 3-year-old children. , 2010, Developmental science.

[49]  D. Scott Perceptual learning. , 1974, Queen's nursing journal.

[50]  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.

[51]  V. Dormal,et al.  Common and Specific Contributions of the Intraparietal Sulci to Numerosity and Length Processing , 2009, NeuroImage.

[52]  V. Walsh,et al.  The parietal cortex and the representation of time, space, number and other magnitudes , 2009, Philosophical Transactions of the Royal Society B: Biological Sciences.

[53]  B. Burns,et al.  Dimensional interactions and the structure of psychological space: The representation of hue, saturation, and brightness , 1988, Perception & psychophysics.

[54]  Lester E. Krueger,et al.  Perceived numerosity , 1972 .

[55]  K. Priftis,et al.  Brain damage: Neglect disrupts the mental number line , 2002, Nature.

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

[57]  Michael von Aster,et al.  Mental number line training in children with developmental dyscalculia , 2011, NeuroImage.

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

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