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Dowker A. The componential nature of arithmetical cognition: some important questions. Front Psychol 2023; 14:1188271. [PMID: 37780151 PMCID: PMC10536274 DOI: 10.3389/fpsyg.2023.1188271] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Accepted: 08/30/2023] [Indexed: 10/03/2023] Open
Abstract
Research on typically developing children and adults and people with developmental and acquired dyscalculia converges in indicating that arithmetical ability is not unitary but is made up of many different components. Categories of components include non-symbolic quantity representation and processing; symbolic quantity representation and processing; counting procedures and principles; arithmetic operations; arithmetical knowledge and understanding; multiple forms and applications of conceptual knowledge of arithmetic; and domain-general abilities such as attention, executive functions and working memory. There is much evidence that different components can and often do show considerable functional independence, not only in developmental and acquired dyscalculia, but in typically achieving children and adults. At the same time, it is possible to find complex interactions and bidirectional relationships between the different components, including between domain-specific and apparently domain-general abilities. There is a great deal that still needs to be discovered. In particular, we need to learn more about the origins in infancy of subitizing and approximate magnitude comparison, the extent to which these interact, the extent to which they may be further divisible, and the extent and ways in which they themselves may develop with age and the extent to which they may influence later-developing components. There also needs to be a lot more research on exactly how domain-general and domain-specific abilities contribute to mathematical development, and how they interact with one another.
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Affiliation(s)
- Ann Dowker
- Experimental Psychology, University of Oxford, Oxford, United Kingdom
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2
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Gosling E, Demeyere N, Dowker A. Numerical Cognition after Brain Injury: Is There a Relationship between Subitizing and Arithmetical Abilities? Brain Sci 2023; 13:381. [PMID: 36979191 PMCID: PMC10046770 DOI: 10.3390/brainsci13030381] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2022] [Revised: 02/12/2023] [Accepted: 02/15/2023] [Indexed: 02/24/2023] Open
Abstract
Subitizing is the ability to enumerate small quantities efficiently and automatically. Counting is a strategy adopted for larger numerosities resulting in a near linear increase in response time with each increase in quantity. Some developmental studies suggest that being able to subitize efficiently may be a predictor of later arithmetical ability. Being able to enumerate small quantities efficiently may be necessary for at least some aspects of arithmetical skill and understanding to develop. According to this view, arithmetic ability ultimately depends upon subitizing. If this were the case, when acquired brain injury results in impaired performance on subitizing tasks, mathematical performance may also be impaired. The following study tested eleven healthy control participants and nine chronic patients with acquired brain injury on tasks focused on visual enumeration, addition and multiplication to explore a potential relationship between subitizing ability and calculation performance. No overall correlations were found between subitizing and addition or multiplication speed. However, a very clear subitizing impairment was found in two patients who then demonstrated very different levels of preserved addition skills. The dissociations found and the large inter-individual variability supports a more componential view of arithmetical ability.
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Schindler M, Doderer JH, Simon AL, Schaffernicht E, Lilienthal AJ, Schäfer K. Small number enumeration processes of deaf or hard-of-hearing students: A study using eye tracking and artificial intelligence. Front Psychol 2022; 13:909775. [PMID: 36072043 PMCID: PMC9441847 DOI: 10.3389/fpsyg.2022.909775] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2022] [Accepted: 07/11/2022] [Indexed: 11/26/2022] Open
Abstract
Students who are deaf or hard-of-hearing (DHH) often show significant difficulties in learning mathematics. Previous studies have reported that students who are DHH lag several years behind in their mathematical development compared to hearing students. As possible reasons, limited learning opportunities due to a lesser incidental exposure to numerical ideas, delays in language and speech development, and further idiosyncratic difficulties of students who are DHH are discussed; however, early mathematical skills and their role in mathematical difficulties of students who are DHH are not explored sufficiently. In this study, we investigate whether students who are DHH differ from hearing students in their ability to enumerate small sets (1–9)—an ability that is associated with mathematical difficulties and their emergence. Based on a study with N = 63 who are DHH and N = 164 hearing students from third to fifth grade attempting 36 tasks, we used eye tracking, the recording of students' eye movements, to qualitatively investigate student enumeration processes. To reduce the effort of qualitative analysis of around 8,000 student enumeration processes (227 students x 36 tasks), we used Artificial Intelligence, in particular, a clustering algorithm, to identify student enumeration processes from the heatmaps of student gaze distributions. Based on the clustering, we found that gaze distributions of students who are DHH and students with normal hearing differed significantly on a group level, indicating differences in enumeration processes, with students who are DHH using advantageous processes (e.g., enumeration “at a glance”) more often than hearing students. The results indicate that students who are DHH do not lag behind in small number enumeration as compared to hearing students but, rather, appear to perform better than their hearing peers in small number enumeration processes, as well as when conceptual knowledge about the part-whole relationship is involved. Our study suggests that the mathematical difficulties of students who are DHH are not related to difficulties in the small number enumeration, which offers interesting perspectives for further research.
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Affiliation(s)
- Maike Schindler
- Department of Special Education and Rehabilitation, Faculty of Human Sciences, University of Cologne, Cologne, Germany
- *Correspondence: Maike Schindler
| | - Jan H. Doderer
- Department of Special Education and Rehabilitation, Faculty of Human Sciences, University of Cologne, Cologne, Germany
| | - Anna L. Simon
- Department of Special Education and Rehabilitation, Faculty of Human Sciences, University of Cologne, Cologne, Germany
| | | | | | - Karolin Schäfer
- Department of Special Education and Rehabilitation, Faculty of Human Sciences, University of Cologne, Cologne, Germany
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Chen J, Paul JM, Reeve R. Manipulation of Attention Affects Subitizing Performance: A Systematic Review and Meta-analysis. Neurosci Biobehav Rev 2022; 139:104753. [PMID: 35772633 DOI: 10.1016/j.neubiorev.2022.104753] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2022] [Revised: 06/07/2022] [Accepted: 06/22/2022] [Indexed: 11/18/2022]
Abstract
Subitizing is the fast and accurate enumeration of small sets. Whether attention is necessary for subitizing remains controversial considering (1) subitizing is claimed to be "pre-attentive", and (2) existing experimental methods and results are inconsistent. To determine whether manipulations to attention demonstratively affect subitizing, the current study comprises a systematic review and meta-analysis. Results from fourteen studies (22 experiments, 35 comparisons) suggest that changes to attentional demands interferes with enumeration of small sets; leading to slower response times, lower accuracy, and poorer Weber acuity (p <.010; p <.001; p <.001; respectively)-notwithstanding a potential publication bias. A unifying framework is proposed to explain the role of attention in visual enumeration, with progressively greater attentional involvement from estimation to subitizing to counting. Our findings suggest attention is integral for subitizing and highlights the need to emphasise attentional mechanisms into neurocognitive models of numerosity processing. We also discuss the possible role of attention in numerical processing difficulties (e.g., dyscalculia).
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Affiliation(s)
- Jian Chen
- Institute for Social Neuroscience, Melbourne, VIC, Australia; School of Psychological Sciences, The University of Melbourne, Melbourne, VIC, Australia.
| | - Jacob M Paul
- School of Psychological Sciences, The University of Melbourne, Melbourne, VIC, Australia
| | - Robert Reeve
- School of Psychological Sciences, The University of Melbourne, Melbourne, VIC, Australia
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Li D, Zhang X, Zhang L. What Skills Could Distinguish Developmental Dyscalculia and Typically Developing Children: Evidence From a 2-Year Longitudinal Screening. J Learn Disabil 2022:222194221099674. [PMID: 35674456 DOI: 10.1177/00222194221099674] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Developmental dyscalculia (DD) is a mathematics learning disorder that affects approximately 5% to 7% of the population. This study aimed to detect the underlying domain-specific and domain-general differences between DD and typically developing (TD) children. We recruited 9-year-old primary school children to form the DD group via a 2-year longitudinal screening process. In total, 75 DD children were screened from 1,657 children after the one-time screening, and 13 DD children were screened from 1,317 children through a consecutive 2-year longitudinal screening. In total, 13 experimental tasks were administered to assess their cognitive abilities to test the domain-specific magnitude representation hypothesis (including symbolic and nonsymbolic magnitude comparisons) and four alternative domain-general hypotheses (including working memory, executive function, attention, and visuospatial processing). The DD group had worse performance than the TD group on the number sense task, finger sense task, shifting task, and one-back task after both one-time and two-time screening. Logistic regressions further indicated the differences on the shifting task and the nonsymbolic magnitude comparison task could distinguish DD and TD children. Our findings suggest that domain-specific nonsymbolic magnitude representation and domain-general executive function both contribute to DD. Thus, both domain-specific and domain-general abilities will be necessary to investigate and to intervene in DD groups in the future.
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Affiliation(s)
- Danfeng Li
- Central University of Finance and Economics, Beijing, China
| | - Xuejing Zhang
- Central University of Finance and Economics, Beijing, China
| | - Li Zhang
- Central University of Finance and Economics, Beijing, China
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Levy S, Goldfarb L. The perception of subset quantity and items in an environment with distractors in a population with mathematical learning difficulties. Trends Neurosci Educ 2021; 25:100166. [PMID: 34844698 DOI: 10.1016/j.tine.2021.100166] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2021] [Revised: 11/03/2021] [Accepted: 11/04/2021] [Indexed: 11/30/2022]
Abstract
OBJECTIVE People often perceive a quantity of specific objects that appear as part of an overall group of items (a subset). This study investigates this type of perception among a population with mathematical leaning difficulties (MLD). METHOD Sixty-two participants (mean age: 26.82) reported the general and subset quantity of items using a subset quantity detection task or a conjunction visual search task. RESULTS MLD had difficulties perceiving both the general quantity presented and the subset quantity of items. They also had difficulties preforming a conjunction visual search task, even when the task did not involve numerical processing. CONCLUSIONS MLD has spatial difficulties in the form of visual search and subset quantity detection. The current study suggests that MLD might experience greater difficulties in daily tasks, which might be related to those tasks (e.g., detecting the amount of forks among other items of silverware on the table).
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Affiliation(s)
- Sharon Levy
- Edmond J. Safra Brain Research Center for the Study of Learning Disabilities, University of Haifa, Israel
| | - Liat Goldfarb
- Edmond J. Safra Brain Research Center for the Study of Learning Disabilities, University of Haifa, Israel.
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Saga M, Rkhaila A, Ounine K, Oubaha D. Developmental dyscalculia: the progress of cognitive modeling in the field of numerical cognition deficits for children. Appl Neuropsychol Child 2021; 11:904-914. [PMID: 34320331 DOI: 10.1080/21622965.2021.1955679] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
The study of dyscalculia requires an analysis of the current developed hypotheses which describe the cognitive mechanisms involved in this neurodevelopmental disorder. The objective of our review is to determine any progress in modeling developmental dyscalculia. The first hypothesis suggests that dyscalculia is the consequence of a specific deficit level number on the precise number system and the approximate system. Then, the second hypothesis states that developmental dyscalculia is linked to a failure to process non-symbolic representations of numbers. On the other hand, the third suggests that dyscalculia is caused by a lack of access to numerical quantities from symbols. However, the last hypothesis asserts that developmental dyscalculia is linked to general deficits. All these hypotheses are compatible with recent neuroimaging results and raise new horizons for experimentation, which will allow the development of precise diagnostic tools and the improvement of intervention strategies and the remediation of developmental dyscalculia.
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Affiliation(s)
- Mouhatti Saga
- Faculty of Sciences, Ibn Tofail University, Kenitra, Morocco
| | - Amine Rkhaila
- Faculty of Sciences, Ibn Tofail University, Kenitra, Morocco
| | - Khadija Ounine
- Faculty of Sciences, Ibn Tofail University, Kenitra, Morocco
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Decarli G, Paris E, Tencati C, Nardelli C, Vescovi M, Surian L, Piazza M. Impaired large numerosity estimation and intact subitizing in developmental dyscalculia. PLoS One 2020; 15:e0244578. [PMID: 33382740 PMCID: PMC7774972 DOI: 10.1371/journal.pone.0244578] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2020] [Accepted: 12/13/2020] [Indexed: 01/29/2023] Open
Abstract
It is believed that the approximate estimation of large sets and the exact quantification of small sets (subitizing) are supported by two different systems, the Approximate Number System (ANS) and Object Tracking System (OTS), respectively. It is a current matter of debate whether they are both impaired in developmental dyscalculia (DD), a specific learning disability in symbolic number processing and calculation. Here we tackled this question by asking 32 DD children and 32 controls to perform a series of tasks on visually presented sets, including exact enumeration of small sets as well as comparison of large, uncountable sets. In children with DD, we found poor sensitivity in processing large numerosities, but we failed to find impairments in the exact enumeration of sets within the subitizing range. We also observed deficits in visual short-term memory skills in children with dyscalculia that, however, did not account for their low ANS acuity. Taken together, these results point to a dissociation between quantification skills in dyscalculia, they highlight a link between DD and low ANS acuity and provide support for the notion that DD is a multifaceted disability that covers multiple cognitive skills.
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Affiliation(s)
- Gisella Decarli
- Department of Psychology and Cognitive Science, University of Trento, Rovereto, Italy
- Department of General Psychology, University of Padova, Padova, Italy
| | - Emanuela Paris
- Servizio di Logopedia, Azienda Pubblica di Servizi alla Persona “Beato de Tschiderer”, Trento, Italy
| | - Chiara Tencati
- Servizio di Logopedia, Azienda Pubblica di Servizi alla Persona “Beato de Tschiderer”, Trento, Italy
| | - Chiara Nardelli
- Department of Psychology and Cognitive Science, University of Trento, Rovereto, Italy
| | - Massimo Vescovi
- Center for Mind/Brain Sciences—CIMeC, University of Trento, Rovereto, Italy
| | - Luca Surian
- Department of Psychology and Cognitive Science, University of Trento, Rovereto, Italy
| | - Manuela Piazza
- Center for Mind/Brain Sciences—CIMeC, University of Trento, Rovereto, Italy
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Ranzato E, Tolmie A, Van Herwegen J. Perceptual subitizing and conceptual subitizing in Williams syndrome and Down syndrome: Insights from eye movements. Res Dev Disabil 2020; 106:103746. [PMID: 32829255 DOI: 10.1016/j.ridd.2020.103746] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2020] [Revised: 07/16/2020] [Accepted: 07/17/2020] [Indexed: 06/11/2023]
Abstract
BACKGROUND AND AIMS Mathematical difficulties in individuals with Williams Syndrome (WS) and in individuals with Down Syndrome (DS) are well-established. Perceptual subitizing and conceptual subitizing are domain-specific precursors of mathematical achievement in typically developing (TD) population. This study employed, for the first time, eye-tracking methodology to investigate subitizing abilities in WS and DS. METHODS AND PROCEDURES Twenty-five participants with WS and 24 participants with DS were compared to a younger group of TD children (n = 25) matched for mental age. Participants were asked to enumerate one to six dots arranged either in a dice or a random pattern. OUTCOMES AND RESULTS Accuracy rates and analyses of reaction time showed no significant differences between the clinical groups (WS and DS) and the control group, suggesting that all participants used the same processes to perform the enumeration task in the different experimental conditions. Analyses of the eye movements showed that both individuals with WS and individuals with DS were using inefficient scanning strategies when counting. Moreover, analyses of the eye movements showed significantly shorter fixation duration in participants with DS compared to the control group in all the experimental conditions. CONCLUSIONS AND IMPLICATIONS The current study provides evidence that individuals with WS and individuals with DS perform both perceptual subitizing and conceptual subitizing. Moreover, our results suggest a fixation instability in DS group that does not affect their performance when subitizing but might explain their low accuracy rates when counting. Findings are discussed in relation to previous studies and the impact for intervention programmes to improve counting and symbolic mathematical abilities in these populations.
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Affiliation(s)
- Erica Ranzato
- Department of Psychology and Human Development, UCL Institute of Education, 20 Bedford Way, Bloomsbury, London, UK.
| | - Andrew Tolmie
- Department of Psychology and Human Development, UCL Institute of Education, 20 Bedford Way, Bloomsbury, London, UK
| | - Jo Van Herwegen
- Department of Psychology and Human Development, UCL Institute of Education, 20 Bedford Way, Bloomsbury, London, UK
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Gomez A, Huron C. Subitizing and counting impairments in children with developmental coordination disorder. Res Dev Disabil 2020; 104:103717. [PMID: 32585441 DOI: 10.1016/j.ridd.2020.103717] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2020] [Revised: 06/03/2020] [Accepted: 06/10/2020] [Indexed: 06/11/2023]
Abstract
Developmental coordination disorder (DCD) interferes with academic achievement and daily life, and is associated with persistent academic difficulties, in particular within mathematical learning. In the present study, we aimed to study numerical cognition using an approach that taps very basic numerical processes such as subitizing and counting abilities in DCD. We used a counting task and a subitizing task in forty 7-10 years-old children with or without DCD. In both tasks, children were presented with arrays of one to eight dots and asked to name aloud the number of dots as accurately and quickly as possible. In the subitizing task, dots were presented during 250 ms whereas in the counting task they stayed on the screen until the participants gave a verbal response. The results showed that children with DCD were less accurate and slower in the two enumeration tasks (with and without a time limit), providing evidence that DCD impairs both counting and subitizing. These impairments might have a deleterious impact on the ability to improve the acuity of the Approximate Number System through counting, and thus could play a role in the underachievement of children with DCD in mathematics.
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Affiliation(s)
- Alice Gomez
- Institute of Cognitive Science Marc Jeannerod, CNRS, UMR 5229, Bron, France; Université Claude Bernard Lyon 1, Inspé, France; INSERM, U992, Cognitive Neuroimaging Unit, CEA/SAC/DSV/DRM/NeuroSpin, Bat 145, Point Courrier 156, F-91191 Gif/Yvette, France; CEA, DSV/I2BM, NeuroSpin Center, Bât 145, Point Courrier 156, F-91191 Gif/Yvette, France; Univ Paris-Sud, Cognitive Neuroimaging Unit, Bât 300, 91405 Orsay Cedex, France; INSERM U1284, France.
| | - Caroline Huron
- INSERM, U992, Cognitive Neuroimaging Unit, CEA/SAC/DSV/DRM/NeuroSpin, Bat 145, Point Courrier 156, F-91191 Gif/Yvette, France; CEA, DSV/I2BM, NeuroSpin Center, Bât 145, Point Courrier 156, F-91191 Gif/Yvette, France; Univ Paris-Sud, Cognitive Neuroimaging Unit, Bât 300, 91405 Orsay Cedex, France; Center for Research and Interdisciplinarity (CRI), France; Université de Paris, France; INSERM U1284, France
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Karagiannakis G, Noël MP. Mathematical Profile Test: A Preliminary Evaluation of an Online Assessment for Mathematics Skills of Children in Grades 1-6. Behav Sci (Basel) 2020; 10:E126. [PMID: 32759837 DOI: 10.3390/bs10080126] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2020] [Revised: 07/29/2020] [Accepted: 07/31/2020] [Indexed: 11/22/2022] Open
Abstract
The domain of numerical cognition still lacks an assessment tool that is theoretically driven and that covers a wide range of key numerical processes with the aim of identifying the learning profiles of children with difficulties in mathematics (MD) or dyscalculia. This paper is the first presentation of an online collectively administered tool developed to meet these goals. The Mathematical Profile Test (MathPro Test) includes 18 subtests that assess numerical skills related to the core number domain or to the visual-spatial, memory or reasoning domains. The specific aim of this paper is to present the preliminary evaluation both of the sensitivity and the psychometric characteristics of the individual measures of the MathPro Test, which was administered to 622 primary school children (grades 1–6) in Belgium. Performance on the subtests increased across all grades and varied along the level of difficulty of the items, supporting the sensitivity of the test. The MathPro Test also showed satisfactory internal consistency and significant and stable correlation with a standardized test in mathematics across all grades. In particular, the achievement in mathematics was strongly associated with the performance on the subtests assessing the reasoning and the visuospatial domains throughout all school grades, whereas associations with the core number and memory tasks were found mainly in the younger children. MD children performed significantly lower than their peers; these differences in performance on the MathPro subtests also varied according to the school grades, informing us about the developmental changes of the weaknesses of children with MD. These results suggest that the MathPro Test is a very promising tool for conducting large scale research and for clinicians to sketch out the mathematical profile of children with MD or dyscalculia.
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Cipora K, He Y, Nuerk HC. The spatial-numerical association of response codes effect and math skills: why related? Ann N Y Acad Sci 2020; 1477:5-19. [PMID: 32348577 DOI: 10.1111/nyas.14355] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2019] [Revised: 03/27/2020] [Accepted: 04/07/2020] [Indexed: 12/17/2022]
Abstract
Evidence from multiple studies conducted in the past few decades converges on the conclusion that numerical properties can be associated with specific directions in space. Such spatial-numerical associations (SNAs), as a signature of elementary number processing, seem to be a likely correlate of math skills. Nevertheless, almost three decades of research on the spatial-numerical association of response codes (SNARC) effect, the hallmark of SNAs, has not provided conclusive results on whether there is a relation with math skills. Here, going beyond reviewing the existing literature on the topic, we try to answer a more fundamental question about why the SNARC effect should (and should not) be related to math skills. We propose a multiroute model framework for a SNARC-math skills relationship. We conclude that the relationship is not straightforward and that several other factors should be considered, which under certain circumstances or in certain groups can cause effects of opposite directions. The model can account for conflicting results, and thus may be helpful for deriving predictions in future studies.
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Affiliation(s)
- Krzysztof Cipora
- Faculty of Science, Department of Psychology, University of Tübingen, Tübingen, Germany.,LEAD Graduate School & Research Network, University of Tübingen, Tübingen, Germany.,Centre for Mathematical Cognition, Loughborough University, Loughborough, United Kingdom
| | - Yunfeng He
- Faculty of Science, Department of Psychology, University of Tübingen, Tübingen, Germany.,Student Psychological Counseling Center, Liaoning University, Shenyang, China
| | - Hans-Christoph Nuerk
- Faculty of Science, Department of Psychology, University of Tübingen, Tübingen, Germany.,LEAD Graduate School & Research Network, University of Tübingen, Tübingen, Germany
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13
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Rotem A, Henik A. Multiplication facts and number sense in children with mathematics learning disabilities and typical achievers. Cognitive Development 2020. [DOI: 10.1016/j.cogdev.2020.100866] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Estévez-Pérez N, Castro-Cañizares D, Martínez-Montes E, Reigosa-Crespo V. Numerical processing profiles in children with varying degrees of arithmetical achievement. Acta Psychol (Amst) 2019; 198:102849. [PMID: 31220772 DOI: 10.1016/j.actpsy.2019.05.001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2018] [Revised: 04/23/2019] [Accepted: 05/06/2019] [Indexed: 11/21/2022] Open
Abstract
Recent studies show basic cognitive abilities such as the rapid and precise apprehension of small numerosities in object sets ("subitizing"), verbal counting and numerical magnitude comparison significantly influence the acquisition of arithmetic and continues to modulate more advanced stages of mathematical cognition. Additionally, children with low arithmetic achievement (LAA) and Developmental Dyscalculia (DD) exhibit significant deficits in these cognitive processes. Nevertheless, the different cognitive profiles of children with varying degrees of numerical and arithmetic processing deficits have not been sufficiently characterized, despite its potential relevance to the stimulation of numerical cognition and the design of appropriate intervention strategies. Here, the cognitive profiles of groups of typically developing children, children with low arithmetical achievement and DD, exhibiting typical and atypical subitizing ability were contrasted. The results suggest that relatively independent neurocognitive mechanisms may produce distinct profiles at the behavioral level and suggest children with low arithmetic performance exhibiting atypical subitizing abilities are not only significantly slower, but rely on compensatory mechanisms and strategies compared to typical subitizers. The role of subitizing as a correlate of arithmetic fluency is revised in the light of the present findings.
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Bloechle J, Huber S, Klein E, Bahnmueller J, Moeller K, Rennig J. Neuro-cognitive mechanisms of global Gestalt perception in visual quantification. Neuroimage 2018; 181:359-369. [DOI: 10.1016/j.neuroimage.2018.07.026] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2018] [Revised: 07/06/2018] [Accepted: 07/12/2018] [Indexed: 10/28/2022] Open
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Lambert K, Spinath B. Conservation Abilities, Visuospatial Skills, and Numerosity Processing Speed: Association With Math Achievement and Math Difficulties in Elementary School Children. J Learn Disabil 2018; 51:223-235. [PMID: 28118082 DOI: 10.1177/0022219417690354] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
The aim of the present study was to investigate the associations between elementary school children's mathematical achievement and their conservation abilities, visuospatial skills, and numerosity processing speed. We also assessed differences in these abilities between children with different types of learning problems. In Study 1 ( N = 229), we investigated second to fourth graders and in Study 2 ( N = 120), third and fourth graders. Analyses revealed significant contributions of numerosity processing speed and visuospatial skills to math achievement beyond IQ. Conservation abilities were predictive in Study 1 only. Children with math difficulties showed lower visuospatial skills and conservation abilities than children with typical achievement levels and children with reading and/or spelling difficulties, whereas children with combined difficulties explicitly showed low conservation abilities. These findings provide further evidence for the relations between children's math skills and their visuospatial skills, conservation abilities, and processing speed and contribute to the understanding of deficits that are specific to mathematical difficulties.
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Wilkey ED, Barone JC, Mazzocco MMM, Vogel SE, Price GR. The effect of visual parameters on neural activation during nonsymbolic number comparison and its relation to math competency. Neuroimage 2017; 159:430-42. [PMID: 28801254 DOI: 10.1016/j.neuroimage.2017.08.023] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2017] [Revised: 08/04/2017] [Accepted: 08/06/2017] [Indexed: 01/29/2023] Open
Abstract
Nonsymbolic numerical comparison task performance (whereby a participant judges which of two groups of objects is numerically larger) is thought to index the efficiency of neural systems supporting numerical magnitude perception, and performance on such tasks has been related to individual differences in math competency. However, a growing body of research suggests task performance is heavily influenced by visual parameters of the stimuli (e.g. surface area and dot size of object sets) such that the correlation with math is driven by performance on trials in which number is incongruent with visual cues. Almost nothing is currently known about whether the neural correlates of nonsymbolic magnitude comparison are also affected by visual congruency. To investigate this issue, we used functional magnetic resonance imaging (fMRI) to analyze neural activity during a nonsymbolic comparison task as a function of visual congruency in a sample of typically developing high school students (n = 36). Further, we investigated the relation to math competency as measured by the preliminary scholastic aptitude test (PSAT) in 10th grade. Our results indicate that neural activity was modulated by the ratio of the dot sets being compared in brain regions previously shown to exhibit an effect of ratio (i.e. left anterior cingulate, left precentral gyrus, left intraparietal sulcus, and right superior parietal lobe) when calculated from the average of congruent and incongruent trials, as it is in most studies, and that the effect of ratio within those regions did not differ as a function of congruency condition. However, there were significant differences in other regions in overall task-related activation, as opposed to the neural ratio effect, when congruent and incongruent conditions were contrasted at the whole-brain level. Math competency negatively correlated with ratio-dependent neural response in the left insula across congruency conditions and showed distinct correlations when split across conditions. There was a positive correlation between math competency in the right supramarginal gyrus during congruent trials and a negative correlation in the left angular gyrus during incongruent trials. Together, these findings support the idea that performance on the nonsymbolic comparison task relates to math competency and ratio-dependent neural activity does not differ by congruency condition. With regards to math competency, congruent and incongruent trials showed distinct relations between math competency and individual differences in ratio-dependent neural activity.
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Price GR, Wilkey ED, Yeo DJ. Eye-movement patterns during nonsymbolic and symbolic numerical magnitude comparison and their relation to math calculation skills. Acta Psychol (Amst) 2017; 176:47-57. [PMID: 28371671 DOI: 10.1016/j.actpsy.2017.03.012] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2016] [Revised: 03/24/2017] [Accepted: 03/24/2017] [Indexed: 01/29/2023] Open
Abstract
A growing body of research suggests that the processing of nonsymbolic (e.g. sets of dots) and symbolic (e.g. Arabic digits) numerical magnitudes serves as a foundation for the development of math competence. Performance on magnitude comparison tasks is thought to reflect the precision of a shared cognitive representation, as evidence by the presence of a numerical ratio effect for both formats. However, little is known regarding how visuo-perceptual processes are related to the numerical ratio effect, whether they are shared across numerical formats, and whether they relate to math competence independently of performance outcomes. The present study investigates these questions in a sample of typically developing adults. Our results reveal a pattern of associations between eye-movement measures, but not their ratio effects, across formats. This suggests that ratio-specific visuo-perceptual processing during magnitude processing is different across nonsymbolic and symbolic formats. Furthermore, eye movements are related to math performance only during symbolic comparison, supporting a growing body of literature suggesting symbolic number processing is more strongly related to math outcomes than nonsymbolic magnitude processing. Finally, eye-movement patterns, specifically fixation dwell time, continue to be negatively related to math performance after controlling for task performance (i.e. error rate and reaction time) and domain general cognitive abilities (IQ), suggesting that fluent visual processing of Arabic digits plays a unique and important role in linking symbolic number processing to formal math abilities.
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Affiliation(s)
- Gavin R Price
- Department of Psychology & Human Development, Peabody College, Vanderbilt University, 230 Appleton Place, Nashville, TN 37203, United States.
| | - Eric D Wilkey
- Department of Psychology & Human Development, Peabody College, Vanderbilt University, 230 Appleton Place, Nashville, TN 37203, United States
| | - Darren J Yeo
- Department of Psychology & Human Development, Peabody College, Vanderbilt University, 230 Appleton Place, Nashville, TN 37203, United States; Division of Psychology, School of Humanities and Social Sciences, Nanyang Technological University, 14 Nanyang Avenue, 637332, Singapore
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Träff U, Olsson L, Östergren R, Skagerlund K. Heterogeneity of Developmental Dyscalculia: Cases with Different Deficit Profiles. Front Psychol 2017; 7:2000. [PMID: 28101068 PMCID: PMC5209352 DOI: 10.3389/fpsyg.2016.02000] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2016] [Accepted: 12/12/2016] [Indexed: 11/30/2022] Open
Abstract
Developmental Dyscalculia (DD) has long been thought to be a monolithic learning disorder that can be attributed to a specific neurocognitive dysfunction. However, recent research has increasingly recognized the heterogeneity of DD, where DD can be differentiated into subtypes in which the underlying cognitive deficits and neural dysfunctions may differ. The aim was to further understand the heterogeneity of developmental dyscalculia (DD) from a cognitive psychological perspective. Utilizing four children (8–9 year-old) we administered a comprehensive cognitive test battery that shed light on the cognitive-behavioral profile of each child. The children were compared against norm groups of aged-matched peers. Performance was then contrasted against predominant hypotheses of DD, which would also give insight into candidate neurocognitive correlates. Despite showing similar mathematical deficits, these children showed remarkable interindividual variability regarding cognitive profile and deficits. Two cases were consistent with the approximate number system deficit account and also the general magnitude-processing deficit account. These cases showed indications of having domain-general deficits as well. One case had an access deficit in combination with a general cognitive deficit. One case suffered from general cognitive deficits only. The results showed that DD cannot be attributed to a single explanatory factor. These findings support a multiple deficits account of DD and suggest that some cases have multiple deficits, whereas other cases have a single deficit. We discuss a previously proposed distinction between primary DD and secondary DD, and suggest hypotheses of dysfunctional neurocognitive correlates responsible for the displayed deficits.
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Affiliation(s)
- Ulf Träff
- Behavioural Sciences and Learning, Linköping University Linköping, Sweden
| | - Linda Olsson
- Behavioural Sciences and Learning, Linköping University Linköping, Sweden
| | - Rickard Östergren
- Behavioural Sciences and Learning, Linköping University Linköping, Sweden
| | - Kenny Skagerlund
- Behavioural Sciences and Learning, Linköping University Linköping, Sweden
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Mock J, Huber S, Klein E, Moeller K. Insights into numerical cognition: considering eye-fixations in number processing and arithmetic. Psychological Research 2016; 80:334-59. [DOI: 10.1007/s00426-015-0739-9] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2015] [Accepted: 12/14/2015] [Indexed: 12/17/2022]
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Berteletti I, Prado J, Booth JR. Children with mathematical learning disability fail in recruiting verbal and numerical brain regions when solving simple multiplication problems. Cortex 2014; 57:143-55. [PMID: 24858066 DOI: 10.1016/j.cortex.2014.04.001] [Citation(s) in RCA: 45] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2013] [Revised: 02/10/2014] [Accepted: 04/01/2014] [Indexed: 10/25/2022]
Abstract
Greater skill in solving single-digit multiplication problems requires a progressive shift from a reliance on numerical to verbal mechanisms over development. Children with mathematical learning disability (MD), however, are thought to suffer from a specific impairment in numerical mechanisms. Here we tested the hypothesis that this impairment might prevent MD children from transitioning toward verbal mechanisms when solving single-digit multiplication problems. Brain activations during multiplication problems were compared in MD and typically developing (TD) children (3rd to 7th graders) in numerical and verbal regions which were individuated by independent localizer tasks. We used small (e.g., 2 × 3) and large (e.g., 7 × 9) problems as these problems likely differ in their reliance on verbal versus numerical mechanisms. Results indicate that MD children have reduced activations in both the verbal (i.e., left inferior frontal gyrus and left middle temporal to superior temporal gyri) and the numerical (i.e., right superior parietal lobule including intra-parietal sulcus) regions suggesting that both mechanisms are impaired. Moreover, the only reliable activation observed for MD children was in the numerical region when solving small problems. This suggests that MD children could effectively engage numerical mechanisms only for the easier problems. Conversely, TD children showed a modulation of activation with problem size in the verbal regions. This suggests that TD children were effectively engaging verbal mechanisms for the easier problems. Moreover, TD children with better language skills were more effective at engaging verbal mechanisms. In conclusion, results suggest that the numerical- and language-related processes involved in solving multiplication problems are impaired in MD children.
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Affiliation(s)
- Ilaria Berteletti
- Department of Communication Sciences and Disorders, Northwestern University, Evanston, IL, USA.
| | - Jérôme Prado
- Department of Communication Sciences and Disorders, Northwestern University, Evanston, IL, USA; Laboratoire Langage, Cerveau et Cognition (L2C2), Centre National de la Recherche Scientifique (CNRS), Bron, France
| | - James R Booth
- Department of Communication Sciences and Disorders, Northwestern University, Evanston, IL, USA
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Moll K, Göbel SM, Snowling MJ. Basic number processing in children with specific learning disorders: Comorbidity of reading and mathematics disorders. Child Neuropsychol 2014; 21:399-417. [PMID: 24697279 DOI: 10.1080/09297049.2014.899570] [Citation(s) in RCA: 45] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Ceulemans A, Titeca D, Loeys T, Hoppenbrouwers K, Rousseau S, Desoete A. Enumeration of small and large numerosities in adolescents with mathematical learning disorders. Res Dev Disabil 2014; 35:27-35. [PMID: 24216344 DOI: 10.1016/j.ridd.2013.10.018] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2013] [Revised: 10/13/2013] [Accepted: 10/14/2013] [Indexed: 06/02/2023]
Abstract
The accuracy and speed in an enumeration task were investigated in adolescents with typical and atypically poor development of arithmetic skills. The number naming performances on small and large non-symbolic numerosities of 18 adolescents with mathematical learning disorders (MLD) and 28 typically achieving age-matched (TA) adolescents were compared. A mixed logistic regression model showed that adolescents with MLD were not significantly less accurate on numbers within the subitizing range than control peers. Moreover, no significant differences in reaction times were found between both groups. Nevertheless, we found that within the control group adolescents with higher ability tended to respond faster when taking into account the whole range (1-9) of numerosities. This correlation was much weaker in the MLD group. When looking more closely at the data, however, it became clear that the correlation between accuracy and speed within the control group differed in direction dependent on the range (subitizing or counting) of the numerosities. As such, our findings did not support a limited capacity of subitizing in MLD. However, the data stressed a different correlation between speed and accuracy for both groups of adolescents and a different behavioral pattern depending on the numerosity range as well. Implications for the understanding and approach of MLD are considered.
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Affiliation(s)
- Annelies Ceulemans
- Department of Experimental Clinical and Health Psychology, Ghent University, Ghent, Belgium.
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Sella F, Lanfranchi S, Zorzi M. Enumeration skills in Down syndrome. Res Dev Disabil 2013; 34:3798-3806. [PMID: 24025435 DOI: 10.1016/j.ridd.2013.07.038] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2013] [Revised: 07/29/2013] [Accepted: 07/30/2013] [Indexed: 06/02/2023]
Abstract
Individuals with Down syndrome (DS) exhibit various math difficulties which can be ascribed both to global intelligence level and/or to their atypical cognitive profile. In this light, it is crucial to investigate whether DS display deficits in basic numerical skills. In the present study, individuals with DS and two groups of typically developing (TD) children matched for mental and chronological age completed two delayed match-to-sample tasks in order to evaluate the functioning of visual enumeration skills. Children with DS showed a specific deficit in the discrimination of small numerosities (within the subitizing range) with respect to both mental and chronological age matched TD children. In contrast, the discrimination of larger numerosities, though lower than that of chronological age matched controls, was comparable to that of mental age matched controls. Finally, counting was less fluent but the understanding of cardinality seemed to be preserved in DS. These results suggest a deficit of the object tracking system underlying the parallel individuation of small numerosities and a typical - but developmentally delayed - acuity of the approximate number system for discrimination of larger numerosities.
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Affiliation(s)
- Francesco Sella
- Department of Developmental Psychology and Socialization, University of Padova, Via Venezia 8, 35131 Padova, Italy.
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Andersson U, Östergren R. Number magnitude processing and basic cognitive functions in children with mathematical learning disabilities. Learning and Individual Differences 2012. [DOI: 10.1016/j.lindif.2012.05.004] [Citation(s) in RCA: 59] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Heine A, Wissmann J, Tamm S, De Smedt B, Schneider M, Stern E, Verschaffel L, Jacobs AM. An electrophysiological investigation of non-symbolic magnitude processing: numerical distance effects in children with and without mathematical learning disabilities. Cortex 2012; 49:2162-77. [PMID: 23287447 DOI: 10.1016/j.cortex.2012.11.009] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2011] [Revised: 02/22/2012] [Accepted: 11/22/2012] [Indexed: 11/28/2022]
Abstract
INTRODUCTION The aim of the present study was to probe electrophysiological effects of non-symbolic numerical processing in 20 children with mathematical learning disabilities (mean age = 99.2 months) compared to a group of 20 typically developing matched controls (mean age = 98.4 months). METHODS EEG data were obtained while children were tested with a standard non-symbolic numerical comparison paradigm that allowed us to investigate the effects of numerical distance manipulations for different set sizes, i.e., the classical subitizing, counting and estimation ranges. Effects of numerical distance manipulations on event-related potential (ERP) amplitudes as well as activation patterns of underlying current sources were analyzed. RESULTS In typically developing children, the amplitudes of a late parietal positive-going ERP component showed systematic numerical distance effects that did not depend on set size. For the group of children with mathematical learning disabilities, ERP distance effects were found only for stimuli within the subitizing range. Current source density analysis of distance-related group effects suggested that areas in right inferior parietal regions are involved in the generation of the parietal ERP amplitude differences. CONCLUSION Our results suggest that right inferior parietal regions are recruited differentially by controls compared to children with mathematical learning disabilities in response to non-symbolic numerical magnitude processing tasks, but only for stimuli with set sizes that exceed the subitizing range.
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Affiliation(s)
- Angela Heine
- Department of Psychology, Freie Universität Berlin, Germany.
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Ashkenazi S, Mark-Zigdon N, Henik A. Do subitizing deficits in developmental dyscalculia involve pattern recognition weakness? Dev Sci 2012; 16:35-46. [PMID: 23278925 DOI: 10.1111/j.1467-7687.2012.01190.x] [Citation(s) in RCA: 55] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2010] [Accepted: 06/25/2012] [Indexed: 11/26/2022]
Affiliation(s)
- Sarit Ashkenazi
- Department of Psychology and Zlotowski Center for Neuroscience; Ben-Gurion University of the Negev; Israel
| | - Nitza Mark-Zigdon
- Department of Psychology and Zlotowski Center for Neuroscience; Ben-Gurion University of the Negev; Israel
| | - Avishai Henik
- Department of Psychology and Zlotowski Center for Neuroscience; Ben-Gurion University of the Negev; Israel
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Abstract
Developmental dyscalculia (DD) is a congenital deficit that affects the ability to acquire arithmetical skills. Individuals with DD have problems learning standard number facts and procedures. Estimates of the prevalence rate of DD are similar to those of developmental dyslexia. Recent reports and discussions suggest that those with DD suffer from specific deficits (e.g., subitizing, comparative judgment). Accordingly, DD has been described as a domain-specific disorder that involves particular brain areas (e.g., intra-parietal sulcus). However, we and others have found that DD is characterized by additional deficiencies and may be affected by domain-general (e.g., attention) factors. Hence "pure DD" might be rather rare and not as pure as one would think. We suggest that the heterogeneity of symptoms that commonly characterize learning disabilities needs to be taken into account in future research and treatment.
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Affiliation(s)
- Avishai Henik
- Department of Psychology, Ben-Gurion University of the Negev, Beer-Sheva, Israel.
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Heine A, Tamm S, Wissmann J, Jacobs AM. Electrophysiological correlates of non-symbolic numerical magnitude processing in children: joining the dots. Neuropsychologia 2011; 49:3238-46. [PMID: 21821057 DOI: 10.1016/j.neuropsychologia.2011.07.028] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2011] [Accepted: 07/22/2011] [Indexed: 10/17/2022]
Abstract
Whether and in what way enumeration processes differ for small and large sets of objects is still a matter of debate. In order to shed light on this issue, EEG data were obtained from 60 normally developing elementary school children. Adopting a standard non-symbolic numerical comparison paradigm allowed us to manipulate numerical distance between stimulus arrays for different quantity ranges, i.e. the subitizing, counting and estimation ranges. In line with the existing literature, the amplitudes of parietal positive going ERP components showed systematic effects of numerical distance, which did not depend on set size. In contrast to the similarities in surface distribution of electrophysiological activity across all number ranges, applying source localization we found distance related current density effects in inferior parietal processing systems to be similar for all numerical ranges, there was, however, considerable variation in the involvement of medial parietal and lateral occipital regions. The precuneus, which is known to be involved in visual imagery, showed distance effects exclusively for numerical comparisons on large set sizes. In contrast, the processing of small quantities and stimulus arrays arranged into canonical patterns relied on lateral occipital areas that are linked to higher-level shape recognition. These findings suggest, on the one hand, that for explicit numerical decisions an involvement of domain-specific resources does not depend on quantity features of the visual input. On the other hand, it seems that the recruitment of mediating perceptual systems differs between the apprehension of small quantities and the enumeration of large sets of objects.
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Affiliation(s)
- Angela Heine
- Department of Psychology, Freie Universität Berlin, Berlin, Germany.
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Abstract
Dargestellt werden potentielle kognitive und neuronale Verursachungsfaktoren der Dyskalkulie. Ergebnisse zu approximativen Mengenrepräsentationen, basalen visuellen Mechanismen der Mengenwahrnehmung (Subitizing), symbolischen Mengenrepräsentationen und arithmetischen Prozessen werden skizziert und diskutiert. Die berichteten Befunde legen nahe, dass verschiedene Ursachen für das Zustandekommen einer Dyskalkulie verantwortlich sein können, denen spezifische Störungen auf neuronaler Ebene zugrunde liegen könnten. Individuelle Störungsprofile sollten daher stärkere Beachtung finden, um in der Zukunft individuelle Förderansätze entwickeln zu können.
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Affiliation(s)
- Jan Lonnemann
- Deutsches Institut für Internationale Pädagogische Forschung (DIPF) und Center for Individual Development and Adaptive Education of Children at Risk (IDeA) Frankfurt am Main
- Goethe-Universität Frankfurt am Main
- geteilte Erstautorenschaft
| | - Janosch Linkersdörfer
- Deutsches Institut für Internationale Pädagogische Forschung (DIPF) und Center for Individual Development and Adaptive Education of Children at Risk (IDeA) Frankfurt am Main
- Goethe-Universität Frankfurt am Main
- geteilte Erstautorenschaft
| | - Marcus Hasselhorn
- Deutsches Institut für Internationale Pädagogische Forschung (DIPF) und Center for Individual Development and Adaptive Education of Children at Risk (IDeA) Frankfurt am Main
- Goethe-Universität Frankfurt am Main
| | - Sven Lindberg
- Deutsches Institut für Internationale Pädagogische Forschung (DIPF) und Center for Individual Development and Adaptive Education of Children at Risk (IDeA) Frankfurt am Main
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Desoete A, Ceulemans A, De Weerdt F, Pieters S. Can we predict mathematical learning disabilities from symbolic and non-symbolic comparison tasks in kindergarten? Findings from a longitudinal study. British Journal of Educational Psychology 2010; 82:64-81. [PMID: 21199482 DOI: 10.1348/2044-8279.002002] [Citation(s) in RCA: 181] [Impact Index Per Article: 12.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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