The role of executive functions in numerical magnitude skills

Abstract Executive functions (EF) are closely related to math performance. Little is known, however, about the role of EF in numerical magnitude skills (NS), although these skills are widely acknowledged to be important precursors of math learning. The current study focuses on the different roles of updating, shifting, and inhibition in NS. EF and NS were assessed in 47 five-year old children. Furthermore, 21 children were presented with six training sessions aimed at improving NS. Both pre-test and improvement scores were used to investigate the role of EF in NS. Bayesian analyses show that updating is a more important predictor of individual differences in NS than shifting and inhibition. Moreover, children with better updating skills showed more improvement in number line estimation after the training. It is argued that NS rely on the processing of multiple sources of information and, therefore, may be dependent on updating skills.

[1]  S. M. Carlson.  Developmentally Sensitive Measures of Executive Function in Preschool Children , 2005, Developmental neuropsychology.

[2]  Lieven Verschaffel,et al.  Working memory and individual differences in mathematics achievement: a longitudinal study from first grade to second grade. , 2009, Journal of experimental child psychology.

[3]  Sanne H. G. van der Ven,et al.  The development of executive functions and early mathematics: a dynamic relationship. , 2012, The British journal of educational psychology.

[4]  W. Fias,et al.  Number sense in children with visuospatial disabilities: Orientation of the mental number line , 2005 .

[5]  Herbert Hoijtink,et al.  Inequality constrained analysis of variance: a Bayesian approach. , 2005, Psychological methods.

[6]  C. Cornoldi,et al.  Working Memory Failures in Children with Arithmetical Difficulties , 2008, Child neuropsychology : a journal on normal and abnormal development in childhood and adolescence.

[7]  Clarissa A. Thompson,et al.  The trouble with transfer: insights from microgenetic changes in the representation of numerical magnitude. , 2008, Child development.

[8]  L. Pulkkinen,et al.  Dimensions of executive functioning: Evidence from children , 2003 .

[9]  S. Gathercole,et al.  Executive functions and achievements in school: Shifting, updating, inhibition, and working memory , 2006, Quarterly journal of experimental psychology.

[10]  Peter F. de Jong,et al.  Executive Functioning in Children, and Its Relations with Reasoning, Reading, and Arithmetic. , 2007 .

[11]  A. Diamond,et al.  The relationship between cognition and action: performance of children 3 1 2 –7 years old on a stroop- like day-night test , 1994, Cognition.

[12]  Mary K. Hoard,et al.  Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. , 2007, Child development.

[13]  W. Schneider,et al.  Exploring the impact of phonological awareness, visual-spatial working memory, and preschool quantity-number competencies on mathematics achievement in elementary school: findings from a 3-year longitudinal study. , 2009, Journal of experimental child psychology.

[14]  Geetha B. Ramani,et al.  Playing linear numerical board games promotes low-income children's numerical development. , 2008, Developmental science.

[15]  S. Wiebe,et al.  Short-Term Memory, Working Memory, and Executive Functioning in Preschoolers: Longitudinal Predictors of Mathematical Achievement at Age 7 Years , 2008, Developmental neuropsychology.

[16]  Jacob Cohen.  The earth is round (p < .05) , 1994 .

[17]  Claire Hughes,et al.  Executive function in preschoolers: Links with theory of mind and verbal ability , 1998 .

[18]  G. Scerif,et al.  Executive Functioning as a Predictor of Children's Mathematics Ability: Inhibition, Switching, and Working Memory , 2001, Developmental neuropsychology.

[19]  H. Hoijtink,et al.  Bayesian Evaluation of Informative Hypotheses. , 2008 .

[20]  E. Kroesbergen,et al.  Training working memory in kindergarten children: Effects on working memory and early numeracy , 2014, Child neuropsychology : a journal on normal and abnormal development in childhood and adolescence.

[21]  Michaela Swales,et al.  Frontal Lobe Deficits after Head Injury: Unity and Diversity of Function , 1997 .

[22]  T. Senn,et al.  The Contribution of Executive Functions to Emergent Mathematic Skills in Preschool Children , 2004, Developmental neuropsychology.

[23]  A. Baddeley.  Exploring the Central Executive , 1996 .

[24]  A. Baddeley.  The episodic buffer: a new component of working memory? , 2000, Trends in Cognitive Sciences.

[25]  M. J. Emerson,et al.  The Unity and Diversity of Executive Functions and Their Contributions to Complex “Frontal Lobe” Tasks: A Latent Variable Analysis , 2000, Cognitive Psychology.

[26]  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.

[27]  U. Andersson.  Working memory as a predictor of written arithmetical skills in children: the importance of central executive functions. , 2008, The British journal of educational psychology.

[28]  Joni Holmes,et al.  Adaptive training leads to sustained enhancement of poor working memory in children. , 2009, Developmental science.

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

[30]  David C. Geary,et al.  Development of Number Line Representations in Children With Mathematical Learning Disability , 2008, Developmental neuropsychology.

[31]  Julian Elliott,et al.  Attentional and Executive Function Behaviours in Children with Poor Working Memory. , 2008 .

[32]  Jan-Willem Romeijn,et al.  Evaluating expectations about negative emotional states of aggressive boys using Bayesian model selection. , 2011, Developmental psychology.

[33]  Geetha B. Ramani,et al.  Promoting broad and stable improvements in low-income children's numerical knowledge through playing number board games. , 2008, Child development.

[34]  Stanislas Dehaene,et al.  Précis of The Number Sense , 2001 .

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

[36]  Herbert Hoijtink,et al.  Moving Beyond Traditional Null Hypothesis Testing: Evaluating Expectations Directly , 2011, Front. Psychology.

[37]  E. Kroesbergen,et al.  Individual Differences in Early Numeracy , 2009 .

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

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

[40]  L. Thorell,et al.  Executive Functioning Deficits in Relation to Symptoms of ADHD and/or ODD in Preschool Children. , 2006 .

[41]  Evelyn H. Kroesbergen,et al.  Working memory and mathematics in primary school children: A meta-analysis , 2013 .

[42]  H. Hoijtink.  Informative Hypotheses: Theory and Practice for Behavioral and Social Scientists , 2011 .

[43]  Philip David Zelazo,et al.  The Dimensional Change Card Sort (DCCS): a method of assessing executive function in children , 2006, Nature Protocols.