NUMBER COMPARISON AND NUMBER LINE ESTIMATION RELY ON DIFFERENT MECHANISMS

The performance in comparison and number line estimation is assumed to rely on the same underlying representation, similar to a compressed mental number line that becomes more linear with age. We tested this assumption explicitly by examining the relation between the linear/logarithmic fit in a non-symbolic number line estimation task and the size effect (SE) in a non-symbolic comparison task in first-, second-, and third graders. In two experiments, a correlation between the estimation pattern in number line estimation and the SE in comparison was absent. An ANOVA showed no difference between the groups of children with a linear or a logarithmic representation considering their SE in comparison. This suggests that different mechanisms underlie both basic number processing tasks.

[1]  Marco Zorzi,et al.  Numerical estimation in preschoolers. , 2010, Developmental psychology.

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

[3]  Daniel N. Allen,et al.  Test-Retest Reliability of Standard and Emotional Stroop Tasks , 2005, Assessment.

[4]  Wim Fias,et al.  Number Processing Pathways in Human Parietal Cortex , 2009, Cerebral cortex.

[5]  Lieven Verschaffel,et al.  Do numerical magnitude comparison skills predict individual differences in mathematical achievement , 2009 .

[6]  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.

[7]  Korbinian Moeller,et al.  A Unitary or Multiple Representations of Numerical Magnitude? – the Case of Structure in Symbolic and Non-Symbolic Quantities , 2012, Front. Psychology.

[8]  Kenneth A. Bollen,et al.  Regression Diagnostics , 1985 .

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

[10]  T. Verguts,et al.  The origins of the numerical distance effect: The same–different task , 2011 .

[11]  G. Orban,et al.  Processing of Abstract Ordinal Knowledge in the Horizontal Segment of the Intraparietal Sulcus , 2007, The Journal of Neuroscience.

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

[13]  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.

[14]  Juha Silvanto,et al.  Double Dissociation of Format-Dependent and Number-Specific Neurons in Human Parietal Cortex , 2010, Cerebral cortex.

[15]  E. Quertemont,et al.  How to Statistically Show the Absence of an Effect , 2011 .

[16]  W. Schwarz,et al.  On the temporal dynamics of digit comparison processes , 1998 .

[17]  Klaus Willmes,et al.  Decade breaks in the mental number line? Putting the tens and units back in different bins , 2001, Cognition.

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

[19]  M. Siegrist Reliability of the Stroop Test with Single-Stimulus Presentation , 1995, Perceptual and motor skills.

[20]  A. Petitto,et al.  Development of Numberline and Measurement Concepts , 1990 .

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

[22]  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.

[23]  Michaël A. Stevens,et al.  A model of exact small-number representation , 2005, Psychonomic bulletin & review.

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

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

[26]  Bert De Smedt,et al.  Numerical Magnitude Representations and Individual Differences in Children's Arithmetic Strategy Use , 2012 .

[27]  B. Reynvoet,et al.  Predictors for Mathematics Achievement? Evidence From a Longitudinal Study , 2012 .

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

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

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

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

[32]  B. Reynvoet,et al.  Children's representation of symbolic and nonsymbolic magnitude examined with the priming paradigm. , 2011, Journal of experimental child psychology.

[33]  Hilary C Barth,et al.  The development of numerical estimation: evidence against a representational shift. , 2011, Developmental science.

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

[35]  Matthew Inglis,et al.  Non-verbal number acuity correlates with symbolic mathematics achievement: But only in children , 2011, Psychonomic bulletin & review.

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

[37]  Elida V. Laski,et al.  Is 27 a big number? Correlational and causal connections among numerical categorization, number line estimation, and numerical magnitude comparison. , 2007, Child development.

[38]  Bert Reynvoet,et al.  Approximate number sense, symbolic number processing, or number-space mappings: what underlies mathematics achievement? , 2013, Journal of experimental child psychology.

[39]  C. Gallistel,et al.  Preverbal and verbal counting and computation , 1992, Cognition.

[40]  Mieke Vandewaetere,et al.  What can the same-different task tell us about the development of magnitude representations? , 2012, Acta psychologica.

[41]  M. Brysbaert,et al.  Combining speed and accuracy in cognitive psychology: Is the inverse efficiency score (IES) a better dependent variable than the mean reaction time (RT) and the percentage of errors (PE)? , 2011 .

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

[43]  Dénes Szűcs,et al.  Representational change and strategy use in children's number line estimation during the first years of primary school , 2012, Behavioral and Brain Functions.

[44]  Julie L. Booth,et al.  Numerical magnitude representations influence arithmetic learning. , 2008, Child development.

[45]  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.

[46]  David C. Burr,et al.  Linear mapping of numbers onto space requires attention , 2012, Cognition.