Neural correlates of arithmetic calculation strategies

Recent research into math cognition has identified areas of the brain that are involved in number processing (Dehaene, Piazza, Pinel, & Cohen, 2003) and complex problem solving (Anderson, 2007). Much of this research assumes that participants use a single strategy; yet, behavioral research finds that people use a variety of strategies (LeFevre et al., 1996; Siegler, 1987; Siegler & Lemaire, 1997). In the present study, we examined cortical activation as a function of two different calculation strategies for mentally solving multidigit multiplication problems. The school strategy, equivalent to long multiplication, involves working from right to left. The expert strategy, used by “lightning” mental calculators (Staszewski, 1988), proceeds from left to right. The two strategies require essentially the same calculations, but have different working memory demands (the school strategy incurs greater demands). The school strategy produced significantly greater early activity in areas involved in attentional aspects of number processing (posterior superior parietal lobule, PSPL) and mental representation (posterior parietal cortex, PPC), but not in a numerical magnitude area (horizontal intraparietal sulcus, HIPS) or a semantic memory retrieval area (lateral inferior prefrontal cortex, LIPFC). An ACT-R model of the task successfully predicted BOLD responses in PPC and LIPFC, as well as in PSPL and HIPS.

[1]  John R. Anderson,et al.  Behavioral equivalence, but not neural equivalence—neural evidence of alternative strategies in mathematical thinking , 2004, Nature Neuroscience.

[2]  S. Petersen,et al.  Frontal cortex contributes to human memory formation , 1999, Nature Neuroscience.

[3]  Marsha C. Lovett,et al.  A source activation theory of working memory: cross-task prediction of performance in ACT-R , 2000, Cognitive Systems Research.

[4]  Cameron S. Carter,et al.  The Relationship of Three Cortical Regions to an Information-Processing Model , 2004, Journal of Cognitive Neuroscience.

[5]  John R Anderson,et al.  Predicting the practice effects on the blood oxygenation level-dependent (BOLD) function of fMRI in a symbolic manipulation task , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[6]  Florin Dolcos,et al.  Similarities and Differences in the Neural Correlates of Episodic Memory Retrieval and Working Memory , 2002, NeuroImage.

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

[8]  Jamie I. D. Campbell.  Handbook of mathematical cognition , 2004 .

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

[10]  E. Wagenmakers.  A practical solution to the pervasive problems ofp values , 2007, Psychonomic bulletin & review.

[11]  A. D. Fisk,et al.  An individual differences analysis of ability and strategy influences: age-related differences in associative learning. , 2000, Journal of experimental psychology. Learning, memory, and cognition.

[12]  A. Raftery.  Bayesian Model Selection in Social Research , 1995 .

[13]  Harry A. Whitaker,et al.  Acalculia: An historical review of localization , 1991, Brain and Cognition.

[14]  Elizabeth K. Warrington,et al.  Arithmetic Skills in Patients with Unilateral Cerebral Lesions , 1986, Cortex.

[15]  E K Warrington,et al.  The Fractionation of Arithmetical Skills: A Single Case Study , 1982, The Quarterly journal of experimental psychology. A, Human experimental psychology.

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

[17]  John R. Anderson,et al.  Using Brain Imaging to Guide the Development of a Cognitive Architecture , 2007, Integrated Models of Cognitive Systems.

[18]  J. Mazziotta,et al.  Rapid Automated Algorithm for Aligning and Reslicing PET Images , 1992, Journal of computer assisted tomography.

[19]  Jeffrey Bisanz,et al.  Multiple routes to solution of single-digit multiplication problems. , 1996 .

[20]  Erik D. Reichle,et al.  The Neural Bases of Strategy and Skill in Sentence–Picture Verification , 2000, Cognitive Psychology.

[21]  J. Mazziotta,et al.  Automated image registration , 1993 .

[22]  Lila Davachi,et al.  When Keeping in Mind Supports Later Bringing to Mind: Neural Markers of Phonological Rehearsal Predict Subsequent Remembering , 2001, Journal of Cognitive Neuroscience.

[23]  John R. Anderson,et al.  An information-processing model of the BOLD response in symbol manipulation tasks , 2003, Psychonomic bulletin & review.

[24]  Myeong-Ho Sohn,et al.  An information-processing model of three cortical regions: evidence in episodic memory retrieval , 2005, NeuroImage.

[25]  Peter A. Ornstein,et al.  Development of Memory Strategies: Analysis, Questions, and Issues , 1983 .

[26]  N. Kanwisher,et al.  The Generality of Parietal Involvement in Visual Attention , 1999, Neuron.

[27]  John R. Anderson,et al.  The role of examples and rules in the acquisition of a cognitive skill. , 1997, Journal of experimental psychology. Learning, memory, and cognition.

[28]  Trudy E. Kwong,et al.  Strategy development and learning to spell new words: generalization of a process. , 2005, Developmental psychology.

[29]  Frank E. Ritter,et al.  The Rise of Cognitive Architectures , 2007, Integrated Models of Cognitive Systems.

[30]  Anthony D Wagner,et al.  Assembling and encoding word representations: fMRI subsequent memory effects implicate a role for phonological control , 2003, Neuropsychologia.

[31]  Mauro Pesenti.  Calculation Abilities in Expert Calculators , 2004 .

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

[33]  Vinod Menon,et al.  Functional connectivity in the resting brain: A network analysis of the default mode hypothesis , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[34]  John R. Anderson,et al.  Using fMRI to Test Models of Complex Cognition , 2008, Cogn. Sci..

[35]  Michael McCloskey,et al.  Localizing Arithmetic Processes in the Brain: Evidence from a Transient Deficit During Cortical Stimulation , 1997, Journal of Cognitive Neuroscience.

[36]  Kyoung-Min Lee.  Cortical areas differentially involved in multiplication and subtraction: A functional magnetic resonance imaging study and correlation with a case of selective acalculia , 2000, Annals of neurology.

[37]  J. Staszewski.  Skilled memory and expert mental calculation. , 1988 .

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

[39]  Scott T. Grafton,et al.  Automated image registration: I. General methods and intrasubject, intramodality validation. , 1998, Journal of computer assisted tomography.

[40]  M. Just,et al.  Graded Functional Activation in the Visuospatial System with the Amount of Task Demand , 1999, Journal of Cognitive Neuroscience.

[41]  R. Siegler,et al.  Older and younger adults' strategy choices in multiplication: testing predictions of ASCM using the choice/no-choice method. , 1997, Journal of experimental psychology. General.

[42]  M. Alibali,et al.  Children's Thinking , 1986 .

[43]  Brian Butterworth,et al.  Selective Impairment in Manipulating Arabic Numerals , 1995, Cortex.

[44]  A. Wagner,et al.  Domain-general and domain-sensitive prefrontal mechanisms for recollecting events and detecting novelty. , 2005, Cerebral cortex.

[45]  R. Siegler.  The perils of averaging data over strategies: An example from children's addition. , 1987 .

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

[47]  S. Dehaene,et al.  Differential Contributions of the Left and Right Inferior Parietal Lobules to Number Processing , 1999, Journal of Cognitive Neuroscience.

[48]  G. Glover.  Deconvolution of Impulse Response in Event-Related BOLD fMRI1 , 1999, NeuroImage.

[49]  Lisa Cipolotti,et al.  Are multiplication facts implemented by the left supramarginal and angular gyri? , 2002, Neuropsychologia.

[50]  John R. Anderson,et al.  The roles of prefrontal and posterior parietal cortex in algebra problem solving: A case of using cognitive modeling to inform neuroimaging data , 2007, NeuroImage.

[51]  M. Petrides,et al.  Functional activation of the human brain during mental rotation , 1997, Neuropsychologia.

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

[53]  John R. Anderson,et al.  The change of the brain activation patterns as children learn algebra equation solving. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

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

[55]  G L Shulman,et al.  INAUGURAL ARTICLE by a Recently Elected Academy Member:A default mode of brain function , 2001 .

[56]  R W Cox,et al.  Software tools for analysis and visualization of fMRI data , 1997, NMR in biomedicine.

[57]  N. Kanwisher,et al.  Neuroimaging of cognitive functions in human parietal cortex , 2001, Current Opinion in Neurobiology.

[58]  M. Chi.  Trends in memory development research , 1983 .