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Michael L. Anderson - One of the best experts on this subject based on the ideXlab platform.
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CogSci - The Relation between Finger Gnosis and Mathematical Ability: Can we Attribute Function to Cortical Structure with Cross-Domain Modeling?
Cognitive Science, 2017Co-Authors: Marcie Penner-wilger, Michael L. AndersonAbstract:The Relation between Finger Gnosis and Mathematical Ability: Can we Attribute Function to Cortical Structure with Cross-Domain Modeling? Marcie Penner-Wilger (Marcie.Penner-Wilger@fandm.edu) Department of Psychology, Franklin & Marshall College, Lancaster, PA 17604 USA Michael L. Anderson (michael.anderson@fandm.edu) Department of Psychology, Franklin & Marshall College, Lancaster, PA 17604 USA Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742 USA anatomically distinct brain areas (Bergeron, 2008). As such, workings are neither consciously available nor describable with higher-level psychological vocabulary. Therefore, in contrast to the current practice in cognitive neuroscience, workings should be described using domain-independent vocabulary. Here, we adopt a vocabulary drawn from information processing theory, although certainly other possibilities (e.g. dynamic systems theory) may turn out to be more appropriate to the task (Anderson, 2007a). According to the Massive Redeployment Hypothesis (MRH; Anderson, 2010, 2007a,b) multiple workings, in concert, compose higher-level cognitive uses, and a typical brain area will contribute to many cognitive uses, across domains, but perform the same working across uses (Anderson, 2010). MRH straddles the middle ground between localization and holism in that, although parts of the brain are specialized (i.e., they always perform the same working), this specialization is at the lower-order level of cognitive workings (e.g., computations or transformations) rather than that of higher order cognitive uses. Anderson (2007a, p. 339) uses the analogy of “finding the right letter to go into a box on a (multidimensional) crossword puzzle” to describe the task of determining a shared cognitive working. Thus, knowing the many cognitive uses that a brain area supports will help to determine what that brain area does. Both Anderson (2010, 2007a,b) and Bergeron (2008) advocate for the determination of shared cognitive workings within and across domains as a method to advance our understanding of high-level cognition and to achieve the interdisciplinary goals of cognitive science. The methodology of looking across domain boundaries to determine the working of a brain area is not common in cognitive neuroscience; activations are generally attributed to processes specific to the domain under investigation (Cabeza & Nyberg, 2000). Cabeza and Nyberg conclude, in a review of 275 imaging studies, “it would be useful to systematically compare functional neuroimaging data in different cognitive domains and to develop general theories that account for the involvement of brain regions in a variety of cognitive tasks” (Cabeza & Nyberg, 2000, p. 31). One such working was proposed by Hubbard et al. (2005): a computational transformation for spatial updating implemented within the parietal sulcus. This cognitive working is also thought to play a role in another cognitive use: shifting attention along the mental number line. It is hypothesized that the SNARC effect— Abstract This paper details and applies a novel method for assigning function to local cortical structure. Imaging results from multiple cognitive domains were used to investigate what a shared neural substrate could be contributing to two apparently different domains: finger and number representation. We identified a region within the left precentral gyrus contributing to both tasks; identified, across several cognitive domains, other cognitive uses to which the ROI may have been put; and looked across these cognitive uses to ascertain the functional contribution of the ROI. The result of this process is a proposed local working—an array of pointers—that can be tested empirically and will allow for further elaboration of the redeployment view of the relation between finger and number representations. This work is significant for understanding the relationship between finger gnosis and math, and for introducing cross-domain modeling as a new empirical method. Keywords: number representation; finger representation; neural substrate; exaptation; function-structure mapping; localization; cross-domain modeling. The Redeployment View Finger gnosis or “finger sense” (indexed by the Ability to distinguish which fingers have been lightly touched without visual feedback) is related to math Ability (Fayol, Barrouillet, & Marinthe, 1998; Noel, 2005; Penner- Wilger et al., 2007). In Penner-Wilger and Anderson (2008) we elaborated a novel hypothesis regarding the observed predictive relation between finger gnosis and Mathematical Ability. In brief, we suggested that these two cognitive capacities have overlapping neural substrates, as the result of the re-use (“redeployment”) of part of the finger gnosis circuit for the purpose of representing number. On this redeployment view, the neural circuitry shared between finger gnosis and number representation forms one part of the functional complex necessary for number representation. Along with the neural circuit shared with finger gnosis, additional neural circuits (with additional abstract functional capacities) are expected to combine in support of the capacity for number representation. The crucial question that a shared neural circuit raises is: What is the shared circuit doing for the different functional complexes of which it is a part? What is the working of this circuit that allows it to support tasks in such apparently different cognitive domains? In the framework we adopt here, workings represent low-level operations that are performed by small,
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The relation between finger gnosis and Mathematical Ability: why redeployment of neural circuits best explains the finding.
Frontiers in Psychology, 2013Co-Authors: Marcie Penner-wilger, Michael L. AndersonAbstract:This paper elaborates a novel hypothesis regarding the observed predictive relation between finger gnosis and Mathematical Ability. In brief, we suggest that these two cognitive phenomena have overlapping neural substrates, as the result of the re-use (“redeployment”) of part of the finger gnosis circuit for the purpose of representing numbers. We offer some background on the relation and current explanations for it; an outline of our alternate hypothesis; some evidence supporting redeployment over current views; and a plan for further research.
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the relation between finger gnosis and Mathematical Ability can we attribute function to cortical structure with cross domain modeling
Cognitive Science, 2011Co-Authors: Marcie Pennerwilger, Michael L. AndersonAbstract:The Relation between Finger Gnosis and Mathematical Ability: Can we Attribute Function to Cortical Structure with Cross-Domain Modeling? Marcie Penner-Wilger (Marcie.Penner-Wilger@fandm.edu) Department of Psychology, Franklin & Marshall College, Lancaster, PA 17604 USA Michael L. Anderson (michael.anderson@fandm.edu) Department of Psychology, Franklin & Marshall College, Lancaster, PA 17604 USA Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742 USA anatomically distinct brain areas (Bergeron, 2008). As such, workings are neither consciously available nor describable with higher-level psychological vocabulary. Therefore, in contrast to the current practice in cognitive neuroscience, workings should be described using domain-independent vocabulary. Here, we adopt a vocabulary drawn from information processing theory, although certainly other possibilities (e.g. dynamic systems theory) may turn out to be more appropriate to the task (Anderson, 2007a). According to the Massive Redeployment Hypothesis (MRH; Anderson, 2010, 2007a,b) multiple workings, in concert, compose higher-level cognitive uses, and a typical brain area will contribute to many cognitive uses, across domains, but perform the same working across uses (Anderson, 2010). MRH straddles the middle ground between localization and holism in that, although parts of the brain are specialized (i.e., they always perform the same working), this specialization is at the lower-order level of cognitive workings (e.g., computations or transformations) rather than that of higher order cognitive uses. Anderson (2007a, p. 339) uses the analogy of “finding the right letter to go into a box on a (multidimensional) crossword puzzle” to describe the task of determining a shared cognitive working. Thus, knowing the many cognitive uses that a brain area supports will help to determine what that brain area does. Both Anderson (2010, 2007a,b) and Bergeron (2008) advocate for the determination of shared cognitive workings within and across domains as a method to advance our understanding of high-level cognition and to achieve the interdisciplinary goals of cognitive science. The methodology of looking across domain boundaries to determine the working of a brain area is not common in cognitive neuroscience; activations are generally attributed to processes specific to the domain under investigation (Cabeza & Nyberg, 2000). Cabeza and Nyberg conclude, in a review of 275 imaging studies, “it would be useful to systematically compare functional neuroimaging data in different cognitive domains and to develop general theories that account for the involvement of brain regions in a variety of cognitive tasks” (Cabeza & Nyberg, 2000, p. 31). One such working was proposed by Hubbard et al. (2005): a computational transformation for spatial updating implemented within the parietal sulcus. This cognitive working is also thought to play a role in another cognitive use: shifting attention along the mental number line. It is hypothesized that the SNARC effect— Abstract This paper details and applies a novel method for assigning function to local cortical structure. Imaging results from multiple cognitive domains were used to investigate what a shared neural substrate could be contributing to two apparently different domains: finger and number representation. We identified a region within the left precentral gyrus contributing to both tasks; identified, across several cognitive domains, other cognitive uses to which the ROI may have been put; and looked across these cognitive uses to ascertain the functional contribution of the ROI. The result of this process is a proposed local working—an array of pointers—that can be tested empirically and will allow for further elaboration of the redeployment view of the relation between finger and number representations. This work is significant for understanding the relationship between finger gnosis and math, and for introducing cross-domain modeling as a new empirical method. Keywords: number representation; finger representation; neural substrate; exaptation; function-structure mapping; localization; cross-domain modeling. The Redeployment View Finger gnosis or “finger sense” (indexed by the Ability to distinguish which fingers have been lightly touched without visual feedback) is related to math Ability (Fayol, Barrouillet, & Marinthe, 1998; Noel, 2005; Penner- Wilger et al., 2007). In Penner-Wilger and Anderson (2008) we elaborated a novel hypothesis regarding the observed predictive relation between finger gnosis and Mathematical Ability. In brief, we suggested that these two cognitive capacities have overlapping neural substrates, as the result of the re-use (“redeployment”) of part of the finger gnosis circuit for the purpose of representing number. On this redeployment view, the neural circuitry shared between finger gnosis and number representation forms one part of the functional complex necessary for number representation. Along with the neural circuit shared with finger gnosis, additional neural circuits (with additional abstract functional capacities) are expected to combine in support of the capacity for number representation. The crucial question that a shared neural circuit raises is: What is the shared circuit doing for the different functional complexes of which it is a part? What is the working of this circuit that allows it to support tasks in such apparently different cognitive domains? In the framework we adopt here, workings represent low-level operations that are performed by small,
Robert Plomin - One of the best experts on this subject based on the ideXlab platform.
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Gene-Environment Interaction in the Etiology of Mathematical Ability Using SNP Sets
Behavior genetics, 2010Co-Authors: Sophia J. Docherty, Yulia Kovas, Robert PlominAbstract:Mathematics Ability and disAbility is as heritable as other cognitive abilities and disabilities, however its genetic etiology has received relatively little attention. In our recent genome-wide association study of Mathematical Ability in 10-year-old children, 10 SNP associations were nominated from scans of pooled DNA and validated in an individually genotyped sample. In this paper, we use a ‘SNP set’ composite of these 10 SNPs to investigate gene-environment (GE) interaction, examining whether the association between the 10-SNP set and Mathematical Ability differs as a function of ten environmental measures in the home and school in a sample of 1888 children with complete data. We found two significant GE interactions for environmental measures in the home and the school both in the direction of the diathesis-stress type of GE interaction: The 10-SNP set was more strongly associated with Mathematical Ability in chaotic homes and when parents are negative.
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Generalist genes analysis of DNA markers associated with Mathematical Ability and disAbility reveals shared influence across ages and abilities
BMC medical genetics, 2010Co-Authors: Sophia J. Docherty, Yulia Kovas, Stephen A Petrill, Robert PlominAbstract:Background: The Generalist Genes Hypothesis is based upon quantitative genetic findings which indicate that many of the same genes influence diverse cognitive abilities and disabilities across age. In a recent genome-wide association study of Mathematical Ability in 10-year-old children, 43 SNP associations were nominated from scans of pooled DNA, 10 of which were validated in an individually genotyped sample. The 4927 children in this genotyped sample have also been studied at 7, 9 and 12 years of age on measures of Mathematical Ability, as well as on other cognitive and learning abilities. Results: Using these data we have explored the Generalist Genes Hypothesis by assessing the association of the available measures of Ability at age 10 and other ages with two composite 'SNP-set' scores, formed from the full set of 43 nominated SNPs and the sub-set of 10 SNPs that were previously found to be associated with Mathematical Ability at age 10. Both SNP sets yielded significant associations with Mathematical Ability at ages 7, 9 and 12, as well as with reading and general cognitive Ability at age 10. Conclusions: Although effect sizes are small, our results correspond with those of quantitative genetic research in supporting the Generalist Genes Hypothesis. SNP sets identified on the basis of their associations with Mathematical Ability at age 10 show associations with Mathematical Ability at earlier and later ages and show associations of similar magnitude with reading and general cognitive Ability. With small effect sizes expected in such complex traits, future studies may be able to capitalise on power by searching for 'generalist genes' using longitudinal and multivariate approaches.
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A genome-wide association study identifies multiple loci associated with mathematics Ability and disAbility
Genes brain and behavior, 2009Co-Authors: Sophia J. Docherty, Yulia Kovas, Stephen A Petrill, Oliver S. P. Davis, Emma L. Meaburn, Philip S. Dale, Leonard C. Schalkwyk, Robert PlominAbstract:Numeracy is as important as literacy and exhibits a similar frequency of disAbility. Although its etiology is relatively poorly understood, quantitative genetic research has demonstrated Mathematical Ability to be moderately heritable. In this first genome-wide association study (GWAS) of Mathematical Ability and disAbility, 10 out of 43 single nucleotide polymorphism (SNP) associations nominated from two high- vs. low-Ability (n = 600 10-year-olds each) scans of pooled DNA were validated (P < 0.05) in an individually genotyped sample of *2356 individuals spanning the entire distribution of Mathematical Ability, as assessed by teacher reports and online tests. Although the effects are of the modest sizes now expected for complex traits and require further replication, interesting candidate genes are implicated such as NRCAM which encodes a neuronal cell adhesion molecule. When combined into a set, the 10 SNPs account for 2.9% (F = 56.85; df = 1 and 1881; P = 7.277e–14) of the phenotypic variance. The association is linear across the distribution consistent with a quantitative trait locus (QTL) hypothesis; the third of children in our sample who harbour 10 or more of the 20 risk alleles identified are nearly twice as likely (OR = 1.96; df = 1; P = 3.696e–07) to be in the lowest performing 15% of the distribution. Our results correspond with those of quantitative genetic research in indicating that Mathematical Ability and disAbility are influenced by many genes generating small effects across the entire spectrum of Ability, implying that more highly powered studies will be needed to detect and replicate these QTL associations.
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Brain Correlates of Non-Symbolic Numerosity Estimation in Low and High Mathematical Ability Children
PloS one, 2009Co-Authors: Yulia Kovas, Vincent Giampietro, Essi Viding, Michael Brammer, Gareth J. Barker, Francesca Happé, Robert PlominAbstract:Previous studies have implicated several brain areas as subserving numerical approximation. Most studies have examined brain correlates of adult numerical approximation and have not considered individual differences in Mathematical Ability. The present study examined non-symbolic numerical approximation in two groups of 10-year-olds: Children with low and high Mathematical Ability. The aims of this study were to investigate the brain mechanisms associated with approximate numerosity in children and to assess whether individual differences in Mathematical Ability are associated with differential brain correlates during the approximation task. The results suggest that, similarly to adults, multiple and distributed brain areas are involved in approximation in children. Despite equal behavioral performance, there were differences in the brain activation patterns between low and high Mathematical Ability groups during the approximation task. This suggests that individual differences in Mathematical Ability are reflected in differential brain response during approximation.
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Mathematical Ability of 10 year old boys and girls genetic and environmental etiology of typical and low performance
Journal of Learning Disabilities, 2007Co-Authors: Yulia Kovas, Stephen A Petrill, Claire M A Haworth, Robert PlominAbstract:The genetic and environmental etiologies of 3 aspects of low Mathematical performance (math disAbility) and the full range of variAbility (math Ability) were compared for boys and girls in a sample of 5,348 children age 10 years (members of 2,674 pairs of same-sex and opposite-sex twins) from the United Kingdom (UK). The measures, which we developed for Web-based testing, included problems from 3 domains of mathematics taught as part of the UK National Curriculum. Using quantitative genetic model-fitting analyses, similar results were found for math disabilities and abilities for all 3 measures: Moderate genetic influence and environmental influence were mainly due to nonshared environmental factors that were unique to the individual, with little influence from shared environment. No sex differences were found in the etiologies of math abilities and disabilities. We conclude that low Mathematical performance is the quantitative extreme of the same genetic and environmental factors responsible for variation throughout the distribution.
Shijia Yan - One of the best experts on this subject based on the ideXlab platform.
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Children's Non-symbolic and Symbolic Numerical Representations and Their Associations With Mathematical Ability.
Frontiers in psychology, 2018Co-Authors: Meng Zhang, Yinghe Chen, Zhijun Deng, Xiaoshuang Zhu, Shijia YanAbstract:Most empirical evidence supports the view that non-symbolic and symbolic representations are foundations for advanced Mathematical Ability. However, the detailed development trajectories of these two types of representations in childhood are not very clear, nor are the different effects of non-symbolic and symbolic representations on the development of Mathematical Ability. We assessed 253 4- to 8-year-old children's non-symbolic and symbolic numerical representations, mapping skills, and Mathematical Ability, aiming to investigate the developmental trajectories and associations between these skills. Our results showed non-symbolic numerical representation emerged earlier than the symbolic one. Four-year-olds were capable of non-symbolic comparisons but not symbolic comparisons; five-year-olds performed better at non-symbolic comparisons than symbolic comparisons. This performance difference disappeared at age 6. Children at age 6 or older were able to map between symbolic and non-symbolic quantities. However, as children learn more about the symbolic representation system, their advantage in non-symbolic representation disappeared. Path analyses revealed that a direct effect of children's symbolic numerical skills on their math performance, and an indirect effect of non-symbolic numerical skills on math performance via symbolic skills. These results suggest that symbolic numerical skills are a predominant factor affecting math performance in early childhood. However, the influences of symbolic and non-symbolic numerical skills on Mathematical performance both declines with age.
Yulia Kovas - One of the best experts on this subject based on the ideXlab platform.
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Individual differences in Mathematical Ability: A behavioral genetic approach.
Development of Mathematical Cognition, 2015Co-Authors: Stephen A Petrill, Yulia KovasAbstract:This chapter examines mathematics and related cognitive and neurobiological characteristics from the perspectives of quantitativeand molecular genetics. After describing quantitativegenetic methods, weexamine the genetic and environmental etiology of mathematics performance and Mathematical cognition. Next, we examine the genetic and environmental etiology of the developmentof mathematics achievementas well as relationships among mathematics, Mathematical cognition and other academic features, in particular reading, motivation, and emotional characteristics. We conclude with a discussion of molecular genetics and neurobiological studies of mathematics within genetically informative designs.
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explaining individual differences in Mathematical Ability genes cultures personality and cognition
Personality and Individual Differences, 2014Co-Authors: Yulia Kovas, O E BogdanovaAbstract:Despite a growing body of educational, psychological, and genetic research into individual differences in Mathematical Ability, motivation, and achievement, many issues remain unresolved. This symposium presents different approaches to the study of variation in mathematics, addressing issues of genetic and cross-cultural differences (Talks 1 and 3); developmental issues (Talk 3); contribution of non-cognitive factors, such as emotional regulation and other regulatory processes, such as goal planning and modeling of goal achievement (Talks 2 and 4); and dimensional issues, such as whether factors underlying Mathematical giftedness are qualitatively different from those driving Mathematical variation in the normal range. We present findings from Russia, Kyrgyzia, and the UK, and discuss them in the context of existing literature and educational implications.
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Gene-Environment Interaction in the Etiology of Mathematical Ability Using SNP Sets
Behavior genetics, 2010Co-Authors: Sophia J. Docherty, Yulia Kovas, Robert PlominAbstract:Mathematics Ability and disAbility is as heritable as other cognitive abilities and disabilities, however its genetic etiology has received relatively little attention. In our recent genome-wide association study of Mathematical Ability in 10-year-old children, 10 SNP associations were nominated from scans of pooled DNA and validated in an individually genotyped sample. In this paper, we use a ‘SNP set’ composite of these 10 SNPs to investigate gene-environment (GE) interaction, examining whether the association between the 10-SNP set and Mathematical Ability differs as a function of ten environmental measures in the home and school in a sample of 1888 children with complete data. We found two significant GE interactions for environmental measures in the home and the school both in the direction of the diathesis-stress type of GE interaction: The 10-SNP set was more strongly associated with Mathematical Ability in chaotic homes and when parents are negative.
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Generalist genes analysis of DNA markers associated with Mathematical Ability and disAbility reveals shared influence across ages and abilities
BMC medical genetics, 2010Co-Authors: Sophia J. Docherty, Yulia Kovas, Stephen A Petrill, Robert PlominAbstract:Background: The Generalist Genes Hypothesis is based upon quantitative genetic findings which indicate that many of the same genes influence diverse cognitive abilities and disabilities across age. In a recent genome-wide association study of Mathematical Ability in 10-year-old children, 43 SNP associations were nominated from scans of pooled DNA, 10 of which were validated in an individually genotyped sample. The 4927 children in this genotyped sample have also been studied at 7, 9 and 12 years of age on measures of Mathematical Ability, as well as on other cognitive and learning abilities. Results: Using these data we have explored the Generalist Genes Hypothesis by assessing the association of the available measures of Ability at age 10 and other ages with two composite 'SNP-set' scores, formed from the full set of 43 nominated SNPs and the sub-set of 10 SNPs that were previously found to be associated with Mathematical Ability at age 10. Both SNP sets yielded significant associations with Mathematical Ability at ages 7, 9 and 12, as well as with reading and general cognitive Ability at age 10. Conclusions: Although effect sizes are small, our results correspond with those of quantitative genetic research in supporting the Generalist Genes Hypothesis. SNP sets identified on the basis of their associations with Mathematical Ability at age 10 show associations with Mathematical Ability at earlier and later ages and show associations of similar magnitude with reading and general cognitive Ability. With small effect sizes expected in such complex traits, future studies may be able to capitalise on power by searching for 'generalist genes' using longitudinal and multivariate approaches.
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A genome-wide association study identifies multiple loci associated with mathematics Ability and disAbility
Genes brain and behavior, 2009Co-Authors: Sophia J. Docherty, Yulia Kovas, Stephen A Petrill, Oliver S. P. Davis, Emma L. Meaburn, Philip S. Dale, Leonard C. Schalkwyk, Robert PlominAbstract:Numeracy is as important as literacy and exhibits a similar frequency of disAbility. Although its etiology is relatively poorly understood, quantitative genetic research has demonstrated Mathematical Ability to be moderately heritable. In this first genome-wide association study (GWAS) of Mathematical Ability and disAbility, 10 out of 43 single nucleotide polymorphism (SNP) associations nominated from two high- vs. low-Ability (n = 600 10-year-olds each) scans of pooled DNA were validated (P < 0.05) in an individually genotyped sample of *2356 individuals spanning the entire distribution of Mathematical Ability, as assessed by teacher reports and online tests. Although the effects are of the modest sizes now expected for complex traits and require further replication, interesting candidate genes are implicated such as NRCAM which encodes a neuronal cell adhesion molecule. When combined into a set, the 10 SNPs account for 2.9% (F = 56.85; df = 1 and 1881; P = 7.277e–14) of the phenotypic variance. The association is linear across the distribution consistent with a quantitative trait locus (QTL) hypothesis; the third of children in our sample who harbour 10 or more of the 20 risk alleles identified are nearly twice as likely (OR = 1.96; df = 1; P = 3.696e–07) to be in the lowest performing 15% of the distribution. Our results correspond with those of quantitative genetic research in indicating that Mathematical Ability and disAbility are influenced by many genes generating small effects across the entire spectrum of Ability, implying that more highly powered studies will be needed to detect and replicate these QTL associations.
Marcie Penner-wilger - One of the best experts on this subject based on the ideXlab platform.
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CogSci - The Relation between Finger Gnosis and Mathematical Ability: Can we Attribute Function to Cortical Structure with Cross-Domain Modeling?
Cognitive Science, 2017Co-Authors: Marcie Penner-wilger, Michael L. AndersonAbstract:The Relation between Finger Gnosis and Mathematical Ability: Can we Attribute Function to Cortical Structure with Cross-Domain Modeling? Marcie Penner-Wilger (Marcie.Penner-Wilger@fandm.edu) Department of Psychology, Franklin & Marshall College, Lancaster, PA 17604 USA Michael L. Anderson (michael.anderson@fandm.edu) Department of Psychology, Franklin & Marshall College, Lancaster, PA 17604 USA Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742 USA anatomically distinct brain areas (Bergeron, 2008). As such, workings are neither consciously available nor describable with higher-level psychological vocabulary. Therefore, in contrast to the current practice in cognitive neuroscience, workings should be described using domain-independent vocabulary. Here, we adopt a vocabulary drawn from information processing theory, although certainly other possibilities (e.g. dynamic systems theory) may turn out to be more appropriate to the task (Anderson, 2007a). According to the Massive Redeployment Hypothesis (MRH; Anderson, 2010, 2007a,b) multiple workings, in concert, compose higher-level cognitive uses, and a typical brain area will contribute to many cognitive uses, across domains, but perform the same working across uses (Anderson, 2010). MRH straddles the middle ground between localization and holism in that, although parts of the brain are specialized (i.e., they always perform the same working), this specialization is at the lower-order level of cognitive workings (e.g., computations or transformations) rather than that of higher order cognitive uses. Anderson (2007a, p. 339) uses the analogy of “finding the right letter to go into a box on a (multidimensional) crossword puzzle” to describe the task of determining a shared cognitive working. Thus, knowing the many cognitive uses that a brain area supports will help to determine what that brain area does. Both Anderson (2010, 2007a,b) and Bergeron (2008) advocate for the determination of shared cognitive workings within and across domains as a method to advance our understanding of high-level cognition and to achieve the interdisciplinary goals of cognitive science. The methodology of looking across domain boundaries to determine the working of a brain area is not common in cognitive neuroscience; activations are generally attributed to processes specific to the domain under investigation (Cabeza & Nyberg, 2000). Cabeza and Nyberg conclude, in a review of 275 imaging studies, “it would be useful to systematically compare functional neuroimaging data in different cognitive domains and to develop general theories that account for the involvement of brain regions in a variety of cognitive tasks” (Cabeza & Nyberg, 2000, p. 31). One such working was proposed by Hubbard et al. (2005): a computational transformation for spatial updating implemented within the parietal sulcus. This cognitive working is also thought to play a role in another cognitive use: shifting attention along the mental number line. It is hypothesized that the SNARC effect— Abstract This paper details and applies a novel method for assigning function to local cortical structure. Imaging results from multiple cognitive domains were used to investigate what a shared neural substrate could be contributing to two apparently different domains: finger and number representation. We identified a region within the left precentral gyrus contributing to both tasks; identified, across several cognitive domains, other cognitive uses to which the ROI may have been put; and looked across these cognitive uses to ascertain the functional contribution of the ROI. The result of this process is a proposed local working—an array of pointers—that can be tested empirically and will allow for further elaboration of the redeployment view of the relation between finger and number representations. This work is significant for understanding the relationship between finger gnosis and math, and for introducing cross-domain modeling as a new empirical method. Keywords: number representation; finger representation; neural substrate; exaptation; function-structure mapping; localization; cross-domain modeling. The Redeployment View Finger gnosis or “finger sense” (indexed by the Ability to distinguish which fingers have been lightly touched without visual feedback) is related to math Ability (Fayol, Barrouillet, & Marinthe, 1998; Noel, 2005; Penner- Wilger et al., 2007). In Penner-Wilger and Anderson (2008) we elaborated a novel hypothesis regarding the observed predictive relation between finger gnosis and Mathematical Ability. In brief, we suggested that these two cognitive capacities have overlapping neural substrates, as the result of the re-use (“redeployment”) of part of the finger gnosis circuit for the purpose of representing number. On this redeployment view, the neural circuitry shared between finger gnosis and number representation forms one part of the functional complex necessary for number representation. Along with the neural circuit shared with finger gnosis, additional neural circuits (with additional abstract functional capacities) are expected to combine in support of the capacity for number representation. The crucial question that a shared neural circuit raises is: What is the shared circuit doing for the different functional complexes of which it is a part? What is the working of this circuit that allows it to support tasks in such apparently different cognitive domains? In the framework we adopt here, workings represent low-level operations that are performed by small,
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The relation between finger gnosis and Mathematical Ability: why redeployment of neural circuits best explains the finding.
Frontiers in Psychology, 2013Co-Authors: Marcie Penner-wilger, Michael L. AndersonAbstract:This paper elaborates a novel hypothesis regarding the observed predictive relation between finger gnosis and Mathematical Ability. In brief, we suggest that these two cognitive phenomena have overlapping neural substrates, as the result of the re-use (“redeployment”) of part of the finger gnosis circuit for the purpose of representing numbers. We offer some background on the relation and current explanations for it; an outline of our alternate hypothesis; some evidence supporting redeployment over current views; and a plan for further research.