Individual differences in solving arithmetic word problems

BackgroundWith the present functional magnetic resonance imaging (fMRI) study at 3 T, we investigated the neural correlates of visualization and verbalization during arithmetic word problem solving. In the domain of arithmetic, visualization might mean to visualize numbers and (intermediate) results while calculating, and verbalization might mean that numbers and (intermediate) results are verbally repeated during calculation. If the brain areas involved in number processing are domain-specific as assumed, that is, that the left angular gyrus (AG) shows an affinity to the verbal domain, and that the left and right intraparietal sulcus (IPS) shows an affinity to the visual domain, the activation of these areas should show a dependency on an individual’s cognitive style.Methods36 healthy young adults participated in the fMRI study. The participants habitual use of visualization and verbalization during solving arithmetic word problems was assessed with a short self-report assessment. During the fMRI measurement, arithmetic word problems that had to be solved by the participants were presented in an event-related design.ResultsWe found that visualizers showed greater brain activation in brain areas involved in visual processing, and that verbalizers showed greater brain activation within the left angular gyrus.ConclusionsOur results indicate that cognitive styles or preferences play an important role in understanding brain activation. Our results confirm, that strong visualizers use mental imagery more strongly than weak visualizers during calculation. Moreover, our results suggest that the left AG shows a specific affinity to the verbal domain and subserves number processing in a modality-specific way.

[1]  Guilherme Wood,et al.  On the Cognitive Link between Space and Number: A Meta-Analysis of the SNARC Effect , 2008 .

[2]  Marie-Pascale Noël,et al.  Arabic Number Reading Deficit - a Single-case Study Or When 236 Is Read (2306) and Judged Superior To 1258 , 1993 .

[3]  P. Holland,et al.  Discrete Multivariate Analysis. , 1976 .

[4]  Stanislas Dehaene,et al.  Cerebral Pathways for Calculation: Double Dissociation between Rote Verbal and Quantitative Knowledge of Arithmetic , 1997, Cortex.

[5]  J. M. Cortina,et al.  What Is Coefficient Alpha? An Examination of Theory and Applications , 1993 .

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

[7]  R. Dolan,et al.  Contrast polarity and face recognition in the human fusiform gyrus , 1999, Nature Neuroscience.

[8]  Karl J. Friston,et al.  How the brain learns to see objects and faces in an impoverished context , 1997, Nature.

[9]  Leslie G. Ungerleider.  Two cortical visual systems , 1982 .

[10]  Sharon L. Thompson-Schill,et al.  Color, Context, and Cognitive Style: Variations in Color Knowledge Retrieval as a Function of Task and Subject Variables , 2011, Journal of Cognitive Neuroscience.

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

[12]  D. Somers,et al.  Functional MRI reveals spatially specific attentional modulation in human primary visual cortex. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[13]  K. Uğurbil,et al.  Neural correlates of visual form and visual spatial processing , 1999, Human brain mapping.

[14]  Martin H. Fischer,et al.  A hierarchical view of grounded, embodied, and situated numerical cognition , 2012, Cognitive Processing.

[15]  S. Dehaene,et al.  Topographical Layout of Hand, Eye, Calculation, and Language-Related Areas in the Human Parietal Lobe , 2002, Neuron.

[16]  Rafael Malach,et al.  Object-processing neural efficiency differentiates object from spatial visualizers , 2008, Neuroreport.

[17]  T. Lehtimäki,et al.  Behavioral and Brain Functions , 2008 .

[18]  N. Kanwisher,et al.  Mental Imagery of Faces and Places Activates Corresponding Stimulus-Specific Brain Regions , 2000, Journal of Cognitive Neuroscience.

[19]  Thomas Lowrie,et al.  Relationship Between Visual and Nonvisual Solution Methods and Difficulty in Elementary Mathematics , 2001 .

[20]  J. Mazziotta,et al.  A Locus in Human Extrastriate Cortex for Visual Shape Analysis , 1997, Journal of Cognitive Neuroscience.

[21]  Gereon R Fink,et al.  ‘Where’ depends on ‘what’: A differential functional anatomy for position discrimination in one- versus two-dimensions , 2000, Neuropsychologia.

[22]  Christa Neuper,et al.  The Influence of verbalization on the pattern of cortical activation during mental arithmetic , 2011, Behavioral and Brain Functions.

[23]  Delinda van Garderen,et al.  Spatial Visualization, Visual Imagery, and Mathematical Problem Solving of Students With Varying Abilities , 2006, Journal of learning disabilities.

[24]  Jamie I. D. Campbell.  Architectures for numerical cognition , 1994, Cognition.

[25]  R. Peterson.  A Meta-analysis of Cronbach's Coefficient Alpha , 1994 .

[26]  Wim Fias,et al.  The representation of multiplication facts: developmental changes in the problem size, five, and tie effects. , 2006, Journal of experimental child psychology.

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

[28]  M. Torrens.  Co-Planar Stereotaxic Atlas of the Human Brain—3-Dimensional Proportional System: An Approach to Cerebral Imaging, J. Talairach, P. Tournoux. Georg Thieme Verlag, New York (1988), 122 pp., 130 figs. DM 268 , 1990 .

[29]  T. Allison,et al.  Face-Specific Processing in the Human Fusiform Gyrus , 1997, Journal of Cognitive Neuroscience.

[30]  D. Guehl,et al.  A functional magnetic resonance imaging study of mental subtraction in human subjects , 1999, Neuroscience Letters.

[31]  S. Kosslyn,et al.  The role of area 17 in visual imagery: convergent evidence from PET and rTMS. , 1999, Science.

[32]  B. Mesquita,et al.  Adjustment to Chronic Diseases and Terminal Illness Health Psychology : Psychological Adjustment to Chronic Disease , 2006 .

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

[34]  Margot J. Taylor,et al.  Is 2+2=4? Meta-analyses of brain areas needed for numbers and calculations , 2011, NeuroImage.

[35]  C. D. Frith,et al.  Abnormal monitoring of inner speech: a physiological basis for auditory hallucinations , 1995, The Lancet.

[36]  Klaus Willmes,et al.  Micro and Macro Pattern Analyses of fMRI Data Support Both Early and Late Interaction of Numerical and Spatial Information , 2011, Front. Hum. Neurosci..

[37]  E. Spelke,et al.  Sources of mathematical thinking: behavioral and brain-imaging evidence. , 1999, Science.

[38]  A. Engel,et al.  Neuronal Synchronization along the Dorsal Visual Pathway Reflects the Focus of Spatial Attention , 2008, Neuron.

[39]  Stanislas Dehaene,et al.  Cerebral networks for number processing: Evidence from a case of posterior callosal lesion , 1996 .

[40]  G. Fink,et al.  REVIEW: The functional organization of the intraparietal sulcus in humans and monkeys , 2005, Journal of anatomy.

[41]  S. Dehaene.  Varieties of numerical abilities , 1992, Cognition.

[42]  J. Jay Todd,et al.  Capacity limit of visual short-term memory in human posterior parietal cortex , 2004, Nature.

[43]  Alan Richardson,et al.  Verbalizer-visualizer: A cognitive style dimension. , 1977 .

[44]  Sharon L Thompson-Schill,et al.  The Neural Correlates of Visual and Verbal Cognitive Styles , 2009, The Journal of Neuroscience.

[45]  Leslie G. Ungerleider,et al.  Dissociation of object and spatial visual processing pathways in human extrastriate cortex. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[46]  Peter Thier,et al.  Dissociable Roles of the Superior Temporal Sulcus and the Intraparietal Sulcus in Joint Attention: A Functional Magnetic Resonance Imaging Study , 2008, Journal of Cognitive Neuroscience.

[47]  M. Hegarty,et al.  Types of visual–spatial representations and mathematical problem solving. , 1999 .

[48]  R. Marois,et al.  "What" and "where" in the intraparietal sulcus: an FMRI study of object identity and location in visual short-term memory. , 2010, Cerebral cortex.

[49]  Maria Kozhevnikov,et al.  The new object‐spatial‐verbal cognitive style model: Theory and measurement , 2009 .

[50]  Friedemann Pulvermüller,et al.  You can count on the motor cortex: Finger counting habits modulate motor cortex activation evoked by numbers , 2012, NeuroImage.

[51]  R. Riding,et al.  Cognitive Styles—an overview and integration , 1991 .

[52]  Jamie I. D. Campbell,et al.  An encoding-complex view of cognitive number processing: Comment on McCloskey, Sokol, and Goodman (1986). , 1988 .

[53]  M. McCloskey.  Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia , 1992, Cognition.

[54]  Chris Rorden,et al.  Spatial Normalization of Brain Images with Focal Lesions Using Cost Function Masking , 2001, NeuroImage.

[55]  R. Hari,et al.  Coinciding early activation of the human primary visual cortex and anteromedial cuneus , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[56]  A. Paivio.  Imagery and verbal processes , 1972 .

[57]  N. Kanwisher,et al.  The Fusiform Face Area: A Module in Human Extrastriate Cortex Specialized for Face Perception , 1997, The Journal of Neuroscience.

[58]  L. Cohen.  Number processing in pure alexia: The effect of hemispheric asymmetries and task demands , 1995 .

[59]  N. Kanwisher,et al.  Covert visual attention modulates face-specific activity in the human fusiform gyrus: fMRI study. , 1998, Journal of neurophysiology.

[60]  Stephen E. Fienberg,et al.  Discrete Multivariate Analysis: Theory and Practice , 1976 .

[61]  R. Weale.  Analysis of Visual Behaviour , 1983 .

[62]  D Le Bihan,et al.  Activation of human primary visual cortex during visual recall: a magnetic resonance imaging study. , 1993, Proceedings of the National Academy of Sciences of the United States of America.