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Matsumoto D, Nakai T. Syntactic theory of mathematical expressions. Cogn Psychol 2023; 146:101606. [PMID: 37748253 DOI: 10.1016/j.cogpsych.2023.101606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2023] [Revised: 06/28/2023] [Accepted: 09/16/2023] [Indexed: 09/27/2023]
Abstract
Mathematical expressions consist of recursive combinations of numbers, variables, and operators. According to theoretical linguists, the syntactic mechanisms of natural language also provide a basis for mathematics. To date, however, no theoretically rigorous investigation has been conducted to support such arguments. Therefore, this study uses a methodology based on theoretical linguistics to analyze the syntactic properties of mathematical expressions. Through a review of recent behavioral and neuroimaging studies on mathematical syntax, we report several inconsistencies with theoretical linguistics, such as the use of ternary structures. To address these, we propose that a syntactic category called Applicative plays a central role in analyzing mathematical expressions with seemingly ternary structures by combining binary structures. Besides basic arithmetic expressions, we also examine algebraic equations and complex expressions such as integral and differential calculi. This study is the first attempt at building a comprehensive framework for analyzing the syntactic structures of mathematical expressions.
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Affiliation(s)
- Daiki Matsumoto
- Graduate School of Human and Environmental Studies, Kyoto University, Kyoto, Japan; Department of Humanities, Kanazawa Seiryo University, Kanazawa, Japan
| | - Tomoya Nakai
- Lyon Neuroscience Research Center (CRNL), (INSERM/CNRS/University of Lyon), Bron, France; Araya Inc., Tokyo, Japan; Advanced Comprehensive Research Organization, Teikyo University, Tokyo, Japan.
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2
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Amalric M, Cantlon JF. Common Neural Functions during Children's Learning from Naturalistic and Controlled Mathematics Paradigms. J Cogn Neurosci 2022; 34:1164-1182. [PMID: 35303098 DOI: 10.1162/jocn_a_01848] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
Two major goals of human neuroscience are to understand how the brain functions in the real world and to measure neural processes under conditions that are ecologically valid. A critical step toward these goals is understanding how brain activity during naturalistic tasks that mimic the real world relates to brain activity in more traditional laboratory tasks. In this study, we used intersubject correlations to locate reliable stimulus-driven cerebral processes among children and adults in a naturalistic video lesson and a laboratory forced-choice task that shared the same arithmetic concept. We show that relative to a control condition with grammatical content, naturalistic and laboratory arithmetic tasks evoked overlapping activation within brain regions previously associated with math semantics. The regions of specific functional overlap between the naturalistic mathematics lesson and laboratory mathematics task included bilateral intraparietal cortex, which confirms that this region processes mathematical content independently of differences in task mode. These findings suggest that regions of the intraparietal cortex process mathematical content when children are learning about mathematics in a naturalistic setting.
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Artemenko C, Coldea A, Soltanlou M, Dresler T, Nuerk HC, Ehlis AC. The neural circuits of number and letter copying: an fNIRS study. Exp Brain Res 2018; 236:1129-1138. [PMID: 29445828 DOI: 10.1007/s00221-018-5204-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2017] [Accepted: 02/10/2018] [Indexed: 11/30/2022]
Abstract
In our daily lives, we are constantly exposed to numbers and letters. However, it is still under debate how letters and numbers are processed in the brain, while information on this topic would allow for a more comprehensive understanding of, for example, known influences of language on numerical cognition or neural circuits shared by numerical cognition and language processing. Some findings provide evidence for a double dissociation between numbers and letters, with numbers being represented in the right and letters in the left hemisphere, while the opposing view suggests a shared neural network. Since processing may depend on the task, we address the reported inconsistencies in a very basic symbol copying task using functional near-infrared spectroscopy (fNIRS). fNIRS data revealed that both number and letter copying rely on the bilateral middle and left inferior frontal gyri. Only numbers elicited additional activation in the bilateral parietal cortex and in the left superior temporal gyrus. However, no cortical activation difference was observed between copying numbers and letters, and there was Bayesian evidence for common activation in the middle frontal gyri and superior parietal lobules. Therefore, we conclude that basic number and letter processing are based on a largely shared cortical network, at least in a simple task such as copying symbols. This suggests that copying can be used as a control condition for more complex tasks in neuroimaging studies without subtracting stimuli-specific activation.
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Affiliation(s)
- Christina Artemenko
- LEAD Graduate School & Research Network, University of Tübingen, Tübingen, Germany. .,Department of Psychology, University of Tübingen, Tübingen, Germany.
| | - Andra Coldea
- School of Psychology, University of Glasgow, Glasgow, UK
| | - Mojtaba Soltanlou
- Department of Psychology, University of Tübingen, Tübingen, Germany.,Graduate Training Centre of Neuroscience/IMPRS for Cognitive and Systems Neuroscience, Tübingen, Germany.,Leibniz-Institut für Wissensmedien, Tübingen, Germany
| | - Thomas Dresler
- LEAD Graduate School & Research Network, University of Tübingen, Tübingen, Germany.,Department of Psychiatry and Psychotherapy, University of Tübingen, Tübingen, Germany
| | - Hans-Christoph Nuerk
- LEAD Graduate School & Research Network, University of Tübingen, Tübingen, Germany.,Department of Psychology, University of Tübingen, Tübingen, Germany.,Leibniz-Institut für Wissensmedien, Tübingen, Germany
| | - Ann-Christine Ehlis
- LEAD Graduate School & Research Network, University of Tübingen, Tübingen, Germany.,Department of Psychiatry and Psychotherapy, University of Tübingen, Tübingen, Germany
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Peake C, Jiménez JE, Rodríguez C. Data-driven heterogeneity in mathematical learning disabilities based on the triple code model. RESEARCH IN DEVELOPMENTAL DISABILITIES 2017; 71:130-142. [PMID: 29035779 DOI: 10.1016/j.ridd.2017.10.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2016] [Revised: 09/29/2017] [Accepted: 10/04/2017] [Indexed: 06/07/2023]
Abstract
Many classifications of heterogeneity in mathematical learning disabilities (MLD) have been proposed over the past four decades, however no empirical research has been conducted until recently, and none of the classifications are derived from Triple Code Model (TCM) postulates. The TCM proposes MLD as a heterogeneous disorder, with two distinguishable profiles: a representational subtype and a verbal subtype. A sample of elementary school 3rd to 6th graders was divided into two age cohorts (3rd - 4th grades, and 5th - 6th grades). Using data-driven strategies, based on the cognitive classification variables predicted by the TCM, our sample of children with MLD clustered as expected: a group with representational deficits and a group with number-fact retrieval deficits. In the younger group, a spatial subtype also emerged, while in both cohorts a non-specific cluster was produced whose profile could not be explained by this theoretical approach.
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Affiliation(s)
- Christian Peake
- Faculty of Education, Universidad Católica de la Santísima Concepción, Concepción, Chile; Centro de Investigación en Educación y Desarrollo, CIEDE-UCSC, Concepción, Chile.
| | - Juan E Jiménez
- Department of Developmental Psychology and Education, University of La Laguna, Tenerife, Spain.
| | - Cristina Rodríguez
- Faculty of Education, Universidad Católica de la Santísima Concepción, Concepción, Chile; Department of Developmental Psychology and Education, University of La Laguna, Tenerife, Spain.
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Monfardini E, Reynaud AJ, Prado J, Meunier M. Social modulation of cognition: Lessons from rhesus macaques relevant to education. Neurosci Biobehav Rev 2017; 82:45-57. [DOI: 10.1016/j.neubiorev.2016.12.002] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2016] [Revised: 11/22/2016] [Accepted: 12/02/2016] [Indexed: 11/26/2022]
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Butterworth B. The implications for education of an innate numerosity-processing mechanism. Philos Trans R Soc Lond B Biol Sci 2017; 373:20170118. [PMID: 29292351 PMCID: PMC5784050 DOI: 10.1098/rstb.2017.0118] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 06/27/2017] [Indexed: 11/12/2022] Open
Abstract
One specific cause of low numeracy is a deficit in a mechanism for representing and processing numerosities that humans inherited and which is putatively shared with many other species. This deficit is evident at each of the four levels of explanation in the 'causal modelling' framework of Morton and Frith (Morton and Frith 1995 In Manual of developmental psychopathology, vol. 1 (eds D Cichetti, D Cohen), pp. 357-390). Very low numeracy can occur in cognitively able individuals with normal access to good education: it is linked to an easily measured deficit in basic numerosity processing; it has a distinctive neural signature; and twin studies suggest specific heritability, though the relevant genes have not yet been identified. Unfortunately, educators and policymakers seem largely unaware of this cause, but appropriate interventions could alleviate the suffering and handicap of those with low numeracy, and would be a major benefit to society.This article is part of a discussion meeting issue 'The origins of numerical abilities'.
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Affiliation(s)
- Brian Butterworth
- Institute of Cognitive Neuroscience, University College London, London WC1N 3AZ, UK
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