Examining the Presence and Determinants of Operational Momentum in Childhood

The operational momentum (OM) effect describes a systematic bias in estimating the outcomes of simple addition and subtraction problems. Outcomes of addition problems are overestimated while outcomes of subtraction problems are underestimated. The origin of OM remains debated. First, a flawed uncompression of numerical information during the course of mental arithmetic is supposed to cause OM due to linear arithmetic operations on a compressed magnitude code. Second, attentional shifts along the mental number line are thought to cause OM. A third hypothesis explains OM in 9-month olds by a cognitive heuristic of accepting more (less) than the original operand in addition (subtraction) problems. The current study attempts to disentangle these alternatives and systematically examines potential determinants of OM, such as reading fluency which has been found to modulate numerical–spatial associations. A group of 32 6- and 7-year-old children was tested in non-symbolic addition and subtraction problems, in which they had to choose the correct outcome from an array of several possible outcomes. Reading capacity was assessed for half of the children while attentional measures were assessed in the other half. Thirty-two adults were tested with the identical paradigm to validate its potential of revealing OM. Children (and adults) were readily able to solve the problems. We replicated previous findings of OM in the adults group. Using a Bayesian framework we observed an inverse OM effect in children, i.e., larger overestimations for subtraction compared to addition. A significant correlation between children’s level of attentional control and their propensity to exhibit OM was observed. The observed pattern of results, in particular the inverse OM in children is hard to reconcile with the previously proposed theoretical frameworks. The observed link between OM and the attentional system might be interpreted as evidence partially supporting the attentional shift hypothesis.

[1]  V. Michel,et al.  Recruitment of an Area Involved in Eye Movements During Mental Arithmetic , 2009, Science.

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

[3]  Stanislas Dehaene,et al.  Dynamic representations underlying symbolic and nonsymbolic calculation: Evidence from the operational momentum effect , 2009, Attention, perception & psychophysics.

[4]  M. Corbetta,et al.  The Reorienting System of the Human Brain: From Environment to Theory of Mind , 2008, Neuron.

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

[6]  Samuel Shaki,et al.  Reading habits for both words and numbers contribute to the SNARC effect , 2009, Psychonomic bulletin & review.

[7]  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.

[8]  Tom Verguts,et al.  Spatial Intuition in Elementary Arithmetic: A Neurocomputational Account , 2012, PloS one.

[9]  Yves Rossetti,et al.  Interference between number processing and line bisection: a methodology , 2005, Neuropsychologia.

[10]  Clarissa A. Thompson,et al.  Early development of spatial-numeric associations: evidence from spatial and quantitative performance of preschoolers. , 2010, Developmental science.

[11]  Melissa E. Libertus,et al.  Comment on "Log or Linear? Distinct Intuitions of the Number Scale in Western and Amazonian Indigene Cultures" , 2009, Science.

[12]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

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

[14]  永福 智志.  The Organization of Learning , 2005, Journal of Cognitive Neuroscience.

[15]  M. Carrasco.  Visual attention: The past 25 years , 2011, Vision Research.

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

[17]  Stanislas Dehaene,et al.  Moving along the Number Line: Operational Momentum in Nonsymbolic Arithmetic , 2006 .

[18]  M. H. Fischer,et al.  Number processing induces spatial performance biases , 2001, Neurology.

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

[20]  Simon Jackman,et al.  Bayesian Analysis for the Social Sciences , 2009 .

[21]  Michael D. Dodd,et al.  Perceiving numbers causes spatial shifts of attention , 2003, Nature Neuroscience.

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

[23]  E. Miller,et al.  Coding of Cognitive Magnitude Compressed Scaling of Numerical Information in the Primate Prefrontal Cortex , 2003, Neuron.

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

[25]  Koleen McCrink,et al.  Operational momentum in large-number addition and subtraction by 9-month-olds. , 2009, Journal of experimental child psychology.

[26]  Pieter Reitsma,et al.  Developing access to number magnitude: a study of the SNARC effect in 7- to 9-year-olds. , 2008, Journal of experimental child psychology.

[27]  D. Berch,et al.  Extracting parity and magnitude from Arabic numerals: developmental changes in number processing and mental representation. , 1999, Journal of experimental child psychology.

[28]  H. Huynh,et al.  Conditions under Which Mean Square Ratios in Repeated Measurements Designs Have Exact F-Distributions , 1970 .

[29]  W. Fias,et al.  The development of the SNARC effect: evidence for early verbal coding. , 2012, Journal of experimental child psychology.

[30]  R. Wilcox.  A Heteroscedastic ANOVA Procedure With Specified Power , 1987 .

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

[32]  Marco Zorzi,et al.  Emergence of a 'visual number sense' in hierarchical generative models , 2012, Nature Neuroscience.

[33]  W. Meck,et al.  Common Representations of Abstract Quantities , 2007 .

[34]  J. Kruschke.  Doing Bayesian Data Analysis: A Tutorial with R and BUGS , 2010 .

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

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

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

[38]  Marco Zorzi,et al.  Representation of numerical and non-numerical order in children , 2012, Cognition.

[39]  Stephan F. Taylor,et al.  Removing the effect of response time on brain activity reveals developmental differences in conflict processing in the posterior medial prefrontal cortex , 2012, NeuroImage.

[40]  C. Gallistel,et al.  Non-verbal numerical cognition: from reals to integers , 2000, Trends in Cognitive Sciences.

[41]  Peter Brugger,et al.  Stimulus-response compatibility in representational space , 1998, Neuropsychologia.

[42]  M. Corbetta,et al.  Quantitative analysis of attention and detection signals during visual search. , 2003, Journal of neurophysiology.

[43]  Martin H. Fischer,et al.  Mental movements without magnitude? A study of spatial biases in symbolic arithmetic , 2008, Cognition.

[44]  Kristina M. Visscher,et al.  A Core System for the Implementation of Task Sets , 2006, Neuron.

[45]  Wim Gevers,et al.  Look, no hands: A perceptual task shows that number magnitude induces shifts of attention , 2008, Psychonomic bulletin & review.

[46]  E. Schröger,et al.  The development of involuntary and voluntary attention from childhood to adulthood: A combined behavioral and event-related potential study , 2006, Clinical Neurophysiology.

[47]  Jin Fan,et al.  Development of attentional networks: An fMRI study with children and adults , 2005, NeuroImage.

[48]  E. Schröger,et al.  The cognitive control of distraction by novelty in children aged 7-8 and adults. , 2009, Psychophysiology.

[49]  Brian Butterworth,et al.  Mapping numerical magnitudes along the right lines: differentiating between scale and bias. , 2011, Journal of experimental psychology. General.

[50]  Karen Wynn,et al.  Addition and subtraction by human infants , 1992, Nature.

[51]  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.

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

[53]  Rand R. Wilcox,et al.  New monte carlo results on the robustness of the anova f, w and f statistics , 1986 .

[54]  Stanislas Dehaene,et al.  Number line compression and the illusory perception of random numbers. , 2010, Experimental psychology.

[55]  C R Gallistel,et al.  Numerical Subtraction in the Pigeon: Evidence for a Linear Subjective Number Scale , 2001, Psychological science.

[56]  Maciej Haman,et al.  The spatial-numerical congruity effect in preschoolers. , 2012, Journal of experimental child psychology.

[57]  Samuel Shaki,et al.  Direction counts: a comparative study of spatially directional counting biases in cultures with different reading directions. , 2012, Journal of experimental child psychology.