Why Mental Arithmetic Counts: Brain Activation during Single Digit Arithmetic Predicts High School Math Scores

Do individual differences in the brain mechanisms for arithmetic underlie variability in high school mathematical competence? Using functional magnetic resonance imaging, we correlated brain responses to single digit calculation with standard scores on the Preliminary Scholastic Aptitude Test (PSAT) math subtest in high school seniors. PSAT math scores, while controlling for PSAT Critical Reading scores, correlated positively with calculation activation in the left supramarginal gyrus and bilateral anterior cingulate cortex, brain regions known to be engaged during arithmetic fact retrieval. At the same time, greater activation in the right intraparietal sulcus during calculation, a region established to be involved in numerical quantity processing, was related to lower PSAT math scores. These data reveal that the relative engagement of brain mechanisms associated with procedural versus memory-based calculation of single-digit arithmetic problems is related to high school level mathematical competence, highlighting the fundamental role that mental arithmetic fluency plays in the acquisition of higher-level mathematical competence.

[1]  Christa Neuper,et al.  Individual differences in mathematical competence predict parietal brain activation during mental calculation , 2007, NeuroImage.

[2]  Roi Cohen Kadosh,et al.  Are numbers special? An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation , 2008, Progress in Neurobiology.

[3]  Jerzy P. Szaflarski,et al.  Semantic association investigated with functional MRI and independent component analysis , 2011, Epilepsy & Behavior.

[4]  Jacquelynne S. Eccles,et al.  Course enrollment as self-regulatory behavior: Who takes optional high school math courses? , 1996 .

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

[6]  Michèle M. M. Mazzocco,et al.  Complexities in identifying and defining mathematics learning disability in the primary school-age years , 2003, Annals of dyslexia.

[7]  Gavin R. Price,et al.  Impaired parietal magnitude processing in developmental dyscalculia , 2007, Current Biology.

[8]  Margarete Delazer,et al.  Learning by strategies and learning by drill—evidence from an fMRI study , 2005, NeuroImage.

[9]  Rainer Goebel,et al.  Analysis of functional image analysis contest (FIAC) data with brainvoyager QX: From single‐subject to cortically aligned group general linear model analysis and self‐organizing group independent component analysis , 2006, Human brain mapping.

[10]  D. Geary Mathematical disabilities: cognitive, neuropsychological, and genetic components. , 1993, Psychological bulletin.

[11]  Daniel Ansari,et al.  The function of the left angular gyrus in mental arithmetic: Evidence from the associative confusion effect , 2013, Human brain mapping.

[12]  Herbert P. Ginsburg,et al.  Cognitive Analysis of Children's Mathematics Difficulties , 1984 .

[13]  J. Grafman,et al.  Visualizing Cortical Activation during Mental Calculation with Functional MRI , 1996, NeuroImage.

[14]  S. Dehaene,et al.  THREE PARIETAL CIRCUITS FOR NUMBER PROCESSING , 2003, Cognitive neuropsychology.

[15]  Martin Wiener,et al.  Fast Forward: Supramarginal Gyrus Stimulation Alters Time Measurement , 2010, Journal of Cognitive Neuroscience.

[16]  John Bynner,et al.  Does Numeracy Matter More , 2006 .

[17]  R. Turner,et al.  Event-Related fMRI: Characterizing Differential Responses , 1998, NeuroImage.

[18]  Steven E. Petersen,et al.  Manipulation of Length and Lexicality Localizes the Functional Neuroanatomy of Phonological Processing in Adult Readers , 2011, Journal of Cognitive Neuroscience.

[19]  Jonathan D. Cohen,et al.  Improved Assessment of Significant Activation in Functional Magnetic Resonance Imaging (fMRI): Use of a Cluster‐Size Threshold , 1995, Magnetic resonance in medicine.

[20]  Soohyun Cho,et al.  How does a child solve 7 + 8? Decoding brain activity patterns associated with counting and retrieval strategies. , 2011, Developmental science.

[21]  Snorre A. Ostad,et al.  Developmental Differences in Solving Simple Arithmetic Word Problems and Simple Number-fact Problems: A Comparison of Mathematically Normal and Mathematically Disabled Children , 1998 .

[22]  M. Mazzocco,et al.  Is it a Fact? Timed Arithmetic Performance of Children With Mathematical Learning Disabilities (MLD) Varies as a Function of How MLD is Defined , 2008, Developmental neuropsychology.

[23]  Jonathan D. Cohen,et al.  Conflict monitoring and anterior cingulate cortex: an update , 2004, Trends in Cognitive Sciences.

[24]  T. Carew,et al.  Neuroscience and Education: An Ideal Partnership for Producing Evidence-Based Solutions to Guide 21st Century Learning , 2010, Neuron.

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

[26]  G. Glover,et al.  Dissociating Prefrontal and Parietal Cortex Activation during Arithmetic Processing , 2000, NeuroImage.

[27]  E. Hanushek,et al.  The High Cost of Low Educational Performance: The Long-Run Economic Impact of Improving PISA Outcomes. , 2010 .

[28]  D. LeBihan,et al.  Modulation of Parietal Activation by Semantic Distance in a Number Comparison Task , 2001, NeuroImage.

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

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

[31]  Iroise Dumontheil,et al.  Brain activity during a visuospatial working memory task predicts arithmetical performance 2 years later. , 2012, Cerebral cortex.

[32]  Christa Neuper,et al.  To retrieve or to calculate? Left angular gyrus mediates the retrieval of arithmetic facts during problem solving , 2009, Neuropsychologia.

[33]  Is that a fact ? , 2001 .

[34]  Martin Wiener,et al.  Implicit timing activates the left inferior parietal cortex , 2010, Neuropsychologia.

[35]  Marie-Pascale Noël,et al.  Neural Correlates of Symbolic Number Comparison in Developmental Dyscalculia , 2010, Journal of Cognitive Neuroscience.

[36]  Bert De Smedt,et al.  Effects of problem size and arithmetic operation on brain activation during calculation in children with varying levels of arithmetical fluency , 2011, NeuroImage.

[37]  David C. Geary,et al.  Cognitive Addition : A Short Longitudinal Study of Strategy Choice and Speed-of-Processing Differences in Normal and Mathematically Disabled Children , 1991 .

[38]  M. Delazer,et al.  Learning complex arithmetic--an fMRI study. , 2003, Brain research. Cognitive brain research.

[39]  G. Duncan,et al.  School readiness and later achievement. , 2007, Developmental psychology.

[40]  Mark H. Ashcraft,et al.  The development of mental arithmetic: A chronometric approach☆ , 1982 .

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

[42]  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 .