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Ruiz C, Kohnen S, Muñez D, Bull R. The development of number line estimation in children at risk of mathematics learning difficulties: A longitudinal study. J Exp Child Psychol 2024; 243:105916. [PMID: 38613903 DOI: 10.1016/j.jecp.2024.105916] [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: 08/23/2023] [Revised: 03/04/2024] [Accepted: 03/11/2024] [Indexed: 04/15/2024]
Abstract
Children with mathematics learning difficulties (MLD) show poorer performance on the number line task, but how performance on this task relates to other mathematical skills is unclear. This study examined the association between performance on the number line task and mathematical skills during the first 2 years of school for children at risk of MLD. Children (N = 100; Mage = 83.63 months) were assessed on four occasions on the number line task and other mathematical skills (math fluency, numerical operations, and mathematical reasoning). Estimation patterns were analyzed based on the representational shift and proportional judgment accounts separately. More consistent longitudinal trends and stronger evidence for differences in mathematical skills based on estimation patterns were found within the representational shift account. Latent growth curve models showed accuracy on the number line task as a predictor of growth in some mathematical skills assessed. We discuss impacts of methodological limitations on the study of estimation patterns.
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Affiliation(s)
- Carola Ruiz
- School of Education, Centre for Research in Numeracy Development and Learning, Macquarie University, Sydney, NSW 2109, Australia; Departamento de Neurociencia y Aprendizaje, Universidad Católica del Uruguay, 11600 Montevideo, Departamento de Montevideo, Uruguay.
| | - Saskia Kohnen
- School of Psychological Sciences, Centre for Research in Numeracy Development and Learning, Centre for Reading, Macquarie University, Sydney, NSW 2109, Australia; Australian Centre for the Advancement of Literacy, Australian Catholic University
| | - David Muñez
- Centre for Research in Child Development, National Institute of Education, Nanyang Technological University, Singapore 639798, Singapore
| | - Rebecca Bull
- School of Education, Centre for Research in Numeracy Development and Learning, Macquarie University, Sydney, NSW 2109, Australia
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2
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Ma M, Likhanov M, Zhou X. Number sense-arithmetic link in Grade 1 and Grade 2: A case of fluency. BRITISH JOURNAL OF EDUCATIONAL PSYCHOLOGY 2024. [PMID: 38802998 DOI: 10.1111/bjep.12693] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Revised: 05/10/2024] [Accepted: 05/13/2024] [Indexed: 05/29/2024]
Abstract
BACKGROUND Recent research suggested fluent processing as an explanation on why number sense contributes to simple arithmetic tasks-'Fluency hypothesis'. AIMS The current study investigates whether number sense contributes to such arithmetic tasks when other cognitive factors are controlled for (including those that mediate the link); and whether this contribution varies as a function of participants' individual maths fluency levels. SAMPLE Four hundred and thirty-seven Chinese schoolchildren (186 females; Mage = 83.49 months) completed a range of cognitive measures in Grade 1 (no previous classroom training) and in Grade 2 (a year later). METHODS Number sense, arithmetic (addition and subtraction), spatial ability, visuo-spatial working memory, perception, reaction time, character reading and general intelligence were measured. RESULTS Our data showed that the link between number sense and arithmetic was weaker in Grade 1 (Beta = .15 for addition and .06 (ns) for subtraction) compared to Grade 2 (.23-.28), but still persisted in children with no previous maths training. Further, math's performance in Grade 1 did not affect the link between number sense and maths performance in Grade 2. CONCLUSION Our data extended previous findings by showing that number sense is linked with simple maths task performance even after controlling for multiple cognitive factors. Our results brought some evidence that number sense-arithmetic link is somewhat sensitive to previous formal maths education. Further research is needed, as the differences in effects between grades were quite small, and arithmetic in Grade 1 did not moderate the link at question in Grade 2.
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Affiliation(s)
- Mei Ma
- State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China
| | - Maxim Likhanov
- State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China
| | - Xinlin Zhou
- State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China
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3
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Aragón E, Cerda G, Pérez C, Aguilar M, Navarro JI. Socio-Economic and Cultural Context in the Development of Early Mathematical Competencies: A Comparative Study of Specific Educational Contexts in Chile and Spain. Psychol Rep 2023; 126:2904-2923. [PMID: 35485168 DOI: 10.1177/00332941221097950] [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] [Indexed: 11/15/2022]
Abstract
This research presents the findings of a comparative study of mathematical competence among 130 students (M = 54.08 months; SD = 2.57) from vulnerable school contexts in Chile and the Spanish public school system. The study analyses a set of general and specific domain precursors for which evidence of socioeconomic background exists. Using multivariate regression and discriminant analysis techniques, we calculated similarities and differences between groups by comparing these precursors. Significant differences were found between the Spanish and Chilean groups (p < .05); however, no differences were observed in non-symbolic comparison and receptive vocabulary. Possible reasons for the existence and extent of these differences are discussed in terms of socio-cultural and educational contexts.
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Affiliation(s)
| | - Gamal Cerda
- Department of Research Methodology and Educational Informatics, University of Concepción, Concepción, Chile
| | - Carlos Pérez
- Institute of Social Sciences, University of O'Higgins, Rancagua, Chile
| | - Manuel Aguilar
- Department of Psychology, University of Cadiz, Cádiz, Spain
| | - José I Navarro
- Department of Psychology, University of Cadiz, Cádiz, Spain
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4
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Decarli G, Zingaro D, Surian L, Piazza M. Number sense at 12 months predicts 4-year-olds' maths skills. Dev Sci 2023; 26:e13386. [PMID: 36869432 DOI: 10.1111/desc.13386] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2022] [Revised: 11/17/2022] [Accepted: 01/27/2023] [Indexed: 03/05/2023]
Abstract
Preverbal infants spontaneously represent the number of objects in collections. Is this 'sense of number' (also referred to as Approximate Number System, ANS) part of the cognitive foundations of mathematical skills? Multiple studies reported a correlation between the ANS and mathematical achievement in children. However, some have suggested that such correlation might be mediated by general-purpose inhibitory skills. We addressed the question using a longitudinal approach: we tested the ANS of 60 12 months old infants and, when they were 4 years old (final N = 40), their symbolic math achievement as well as general intelligence and inhibitory skills. Results showed that the ANS at 12 months is a specific predictor of later maths skills independent from general intelligence or inhibitory skills. The correlation between ANS and maths persists when both abilities are measured at four years. These results confirm that the ANS has an early, specific and longstanding relation with mathematical abilities in childhood. RESEARCH HIGHLIGHTS: In the literature there is a lively debate about the correlation between the ANS and maths skills. We longitudinally tested a sample of 60 preverbal infants at 12 months and rested them at 4 years (final sample of 40 infants). The ANS tested at 12 months predicted later symbolic mathematical skills at 4 years, even when controlling for inhibition, general intelligence and perceptual skills. The ANS tested at 4 years remained linked with symbolic maths skills, confirming this early and longstanding relation in childhood.
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Affiliation(s)
- Gisella Decarli
- Department of Psychology and Cognitive Science, University of Trento, Trento, Italy
| | | | - Luca Surian
- Department of Psychology and Cognitive Science, University of Trento, Trento, Italy
| | - Manuela Piazza
- Center for Mind/Brain Sciences, University of Trento, Italy
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5
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Liu K, Huang X, Yang X. Visual perception and linguistic abilities, not quantitative knowledge, count in geometric knowledge of kindergarten children. Cogn Process 2023; 24:563-574. [PMID: 37428367 DOI: 10.1007/s10339-023-01145-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2022] [Accepted: 06/06/2023] [Indexed: 07/11/2023]
Abstract
Geometric knowledge is one of the important mathematical skills acquired by children at a young age and is a major area of future mathematical learning; however, there is no direct research on the factors influencing kindergarteners' early geometric knowledge. The pathways model to mathematics was modified to examine the cognitive mechanisms underlying geometric knowledge in Chinese kindergarten children aged 5-7 (n = 99). Quantitative knowledge, visual-spatial processing, and linguistic abilities were stepped into hierarchical multiple regression models. The results revealed that after age, sex, and nonverbal intelligence were statistically controlled, visual perception, phonological awareness, and rapid automatized naming in linguistic abilities significantly predicted the variation in geometric knowledge. For quantitative knowledge, neither dot comparison nor number comparison test could be a significant precursor of geometry skills. The findings indicate that visual perception and linguistic abilities, not quantitative knowledge, account for the geometric knowledge of kindergarten children.
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Affiliation(s)
- Kaichun Liu
- Beijing Key Laboratory of Applied Experimental Psychology, National Demonstration Center for Experimental Psychology Education (Beijing Normal University), Beijing Normal University, Beijing, 100875, China
| | - Xiaohan Huang
- Beijing Key Laboratory of Applied Experimental Psychology, National Demonstration Center for Experimental Psychology Education (Beijing Normal University), Beijing Normal University, Beijing, 100875, China
| | - Xiujie Yang
- Beijing Key Laboratory of Applied Experimental Psychology, National Demonstration Center for Experimental Psychology Education (Beijing Normal University), Beijing Normal University, Beijing, 100875, China.
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6
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Brumm L, Rathgeb-Schnierer E. The relationship between accuracy in numerosity estimation, math achievement, and math interest in primary school students. Front Psychol 2023; 14:1146458. [PMID: 37492447 PMCID: PMC10363689 DOI: 10.3389/fpsyg.2023.1146458] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2023] [Accepted: 06/23/2023] [Indexed: 07/27/2023] Open
Abstract
Estimation is a primary activity in everyday life, so getting it "right" in primary school provides a foundational basis in mathematical reasoning. This study focuses on numerosity estimation in primary mathematics, which is one of four types of estimation reported in literature. In numerosity estimation, a non-numerical quantitative representation is typically translated into a number. While it is assumed that fostering numerosity estimation has a great impact on the development of mathematical skills, research indicates that math achievement is influenced by non-cognitive aspects such as students' math interests. So, math interest could also influence the accuracy in numerosity estimation. In this study, we investigate the relationship between accuracy in numerosity estimation, math achievement, and math interest in third-grade students. For capturing accuracy in numerosity estimation in a standardized way, we developed an online numerosity estimation test. For assessing the construct of math interest, we used an existing questionnaire. Math achievement was assessed by a standardized math test that includes two subtests focusing on arithmetic and application tasks. The sample was comprised of 185 third-grade students. We analyzed the data using correlation and multiple linear regression analysis. The results showed a significant positive correlation between math interest and math achievement. However, no relationship was found between accuracy in numerosity estimation and math interest nor between accuracy in numerosity estimation and math achievement. These partly unexpected findings suggest further studies dedicated to numerosity estimation and its relationship to other constructs.
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Affiliation(s)
- Leonie Brumm
- Department of Mathematics and Natural Science, University of Kassel, Kassel, Germany
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7
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Meloni C, Delogu F, Fanari R. Symbolic and non-symbolic predictors of number line task in Italian kindergarteners. Front Psychol 2023; 14:1137607. [PMID: 37205065 PMCID: PMC10185831 DOI: 10.3389/fpsyg.2023.1137607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2023] [Accepted: 04/07/2023] [Indexed: 05/21/2023] Open
Abstract
The number line estimation task (NLE) is often used as a predictor for broader measures of mathematical achievement. In spite of its popularity, it is still not clear whether the task is based on symbolic or non-symbolic numerical competence. In particular, there is only a very limited amount of studies investigating the relationship between NLE performance and symbolic vs. non-symbolic math skills in children who have not yet begun formal schooling. This study investigates the strength of the association between NLE performance and symbolic and non-symbolic tasks in young kindergarteners. Ninety two 5-year-old children completed the NLE task (range 0-100) and a battery of early numerical competence tests including symbolic-lexical tasks, symbolic semantic tasks, and non-symbolic semantic tasks. The relationship between symbolic and non-symbolic early numerical competence and NLE performance was analyzed using a regression model based on the Bayesian Information Criterion (BIC). Results show that only symbolic semantic tasks are significant predictors of NLE performance. These results suggest that symbolic numerical knowledge is involved in number line processing among young children, whilst non-symbolic knowledge is not. This finding brings new data to the debate on the relationship between non-symbolic numeral knowledge and symbolic number processing and supports the evidence of a primary role of symbolic number processing already in young kindergarteners.
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Affiliation(s)
- Carla Meloni
- Department of Pedagogy, Psychology, Philosophy, Faculty of Humanities, University of Cagliari, Cagliari, Italy
| | - Franco Delogu
- Department of Humanities, Social Sciences and Communication, Lawrence Technological University, Southfield, MI, United States
| | - Rachele Fanari
- Department of Pedagogy, Psychology, Philosophy, Faculty of Humanities, University of Cagliari, Cagliari, Italy
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8
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Xu X, Chen C, Wang L, Zhao M, Xin Z, Liu H. Longitudinal relationship between number line estimation and other mathematical abilities in Chinese preschool children. J Exp Child Psychol 2023; 228:105619. [PMID: 36592578 DOI: 10.1016/j.jecp.2022.105619] [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: 02/17/2022] [Revised: 12/11/2022] [Accepted: 12/15/2022] [Indexed: 01/02/2023]
Abstract
Many cross-sectional studies have shown that number line estimation is associated with other mathematical skills, but there has been limited longitudinal research. To systematically examine such associations longitudinally at the earliest stage of mathematical learning, the current study tested 40 Chinese preschoolers (mean age = 4.97 years, SD = 0.18) and followed them up 8 months later. For both waves of data collection, children were administered six tasks: number line estimation, dot counting, comparison of two dot arrays, comparison of triple dot arrays, symbolic number comparison, and simple addition. Results of two-wave cross-lagged panel analysis showed that (a) dot counting and non-symbolic numerical comparison at Time 1 had significant longitudinal associations with number line estimation at Time 2, (b) number line estimation had bidirectional associations with symbolic number comparison, and (c) number line estimation at Time 1 had a marginally significant longitudinal association with simple addition at Time 2. These results extend the small but accumulating literature on the longitudinal relations between number line estimation and other mathematical skills and specify the important role of number line estimation in the early development of mathematical skills.
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Affiliation(s)
- Xiaohui Xu
- School of Preschool Education, Capital Normal University, Beijing 100048, China
| | - Chuansheng Chen
- Department of Psychological Science, University of California, Irvine, Irvine, CA 92697, USA
| | - Lan Wang
- School of Education, Capital Normal University, Beijing 100048, China
| | - Mengmeng Zhao
- School of Education, Capital Normal University, Beijing 100048, China
| | - Zhiyong Xin
- School of Sociology and Psychology, Central University of Finance and Economics, Beijing 100081, China
| | - Hongyun Liu
- Faculty of Psychology, Beijing Normal University, Beijing 100875, China.
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9
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Leonard SJ, Roche C, Durkan A, Gomides M, Santos FH. Children grow upwards, and so does the number line: Evidence from a directional number line paradigm. PROGRESS IN BRAIN RESEARCH 2023; 279:37-56. [PMID: 37661162 DOI: 10.1016/bs.pbr.2023.03.002] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/05/2023]
Abstract
Technological advancements give researchers the opportunity to explore the internal metric that allows to mentally place numbers in a spatial and ordered way to establish relationships between quantities. In this study, we implement the cMNL, an embodied number line paradigm to investigate the configuration of children's number space mappings under multiple conditions. A sample of 185 primary school children aged 8-10years old completed digitally an embodied number line task encompassing directionality and modality as variables. Contrary to the premise of a fixed internal number line moving from left to right in many Western scripts, our results suggest that children's number-space mapping is more robust along a vertical axis. In addition, children's embodied number line estimation differed depending on input modality. The findings provide insight into the variability in children's number line estimation, and the usability of digital assessment in understanding the mechanisms of the developing number-space system.
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Affiliation(s)
- Sophie J Leonard
- UCD School of Psychology, University College Dublin, Dublin, Ireland
| | - Ciara Roche
- UCD School of Psychology, University College Dublin, Dublin, Ireland
| | - Aoife Durkan
- UCD School of Psychology, University College Dublin, Dublin, Ireland
| | - Mariuche Gomides
- UCD School of Psychology, University College Dublin, Dublin, Ireland
| | - Flavia H Santos
- UCD School of Psychology, University College Dublin, Dublin, Ireland.
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10
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Lin P, Zhou X, Zang S, Zhu Y, Zhang L, Bai Y, Wang H. Early neural markers for individual difference in mathematical achievement determined from rational number processing. Neuropsychologia 2023; 181:108493. [PMID: 36707024 DOI: 10.1016/j.neuropsychologia.2023.108493] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2022] [Revised: 01/19/2023] [Accepted: 01/23/2023] [Indexed: 01/26/2023]
Abstract
The neural markers for individual differences in mathematical achievement have been studied extensively using magnetic resonance imaging; however, high temporal resolution electrophysiological evidence for individual differences in mathematical achievement require further elucidation. This study evaluated the event-related potential (ERP) when 48 college students with high or low mathematical achievement (HA vs. LA) matched non-symbolic and symbolic rational numbers. Behavioral results indicated that HA students had better performance in the discretized non-symbolic matching, although the two groups showed similar performances in the continuous matching. ERP data revealed that even before non-symbolic stimulus presentation, HA students had greater Bereitschaftspotential (BP) amplitudes over posterior central electrodes. After the presentation of non-symbolic numbers, HA students had larger N1 amplitudes at 160 ms post-stimulus, over left-lateralized parieto-occipital electrodes. After the presentation of symbolic numbers, HA students displayed more profound P1 amplitudes at 100 ms post-stimulus, over left parietal electrodes. Furthermore, larger BP and N1 amplitudes were associated with the shorter reaction times, and larger P1 amplitudes corresponded to lower error rates. The BP effect could indicate preparation processing, and early left-lateralized N1 and P1 effects could reflect the non-symbolic and symbolic number processing along the dorsal neural pathways. These results suggest that the left-lateralized P1 and N1 components elicited by matching non-symbolic and symbolic rational numbers can be considered as neurocognitive markers for individual differences in mathematical achievement.
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Affiliation(s)
- Pingting Lin
- School of Biological Science and Medical Engineering, Southeast University, Nanjing, 210096, Jiangsu, PR China; Key Laboratory of Child Development and Learning Science (Southeast University), Ministry of Education, Nanjing, 210096, Jiangsu, PR China; Research Center for Learning Science, Southeast University, Nanjing, 210096, Jiangsu, PR China
| | - Xinlin Zhou
- State Key Laboratory of Cognitive Neuroscience and Learning, IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, 100875, PR China
| | - Shiyi Zang
- School of Biological Science and Medical Engineering, Southeast University, Nanjing, 210096, Jiangsu, PR China; Key Laboratory of Child Development and Learning Science (Southeast University), Ministry of Education, Nanjing, 210096, Jiangsu, PR China; Research Center for Learning Science, Southeast University, Nanjing, 210096, Jiangsu, PR China
| | - Yanmei Zhu
- School for Early-Childhood Education, Nanjing Xiaozhuang University, Nanjing, 211171, Jiangsu, PR China
| | - Li Zhang
- School for Early-Childhood Education, Nanjing Xiaozhuang University, Nanjing, 211171, Jiangsu, PR China
| | - Yi Bai
- School of Biological Science and Medical Engineering, Southeast University, Nanjing, 210096, Jiangsu, PR China; Key Laboratory of Child Development and Learning Science (Southeast University), Ministry of Education, Nanjing, 210096, Jiangsu, PR China; Research Center for Learning Science, Southeast University, Nanjing, 210096, Jiangsu, PR China
| | - Haixian Wang
- School of Biological Science and Medical Engineering, Southeast University, Nanjing, 210096, Jiangsu, PR China; Key Laboratory of Child Development and Learning Science (Southeast University), Ministry of Education, Nanjing, 210096, Jiangsu, PR China; Research Center for Learning Science, Southeast University, Nanjing, 210096, Jiangsu, PR China.
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Malykh S, Tarasov S, Baeva I, Nikulchev E, Kolyasnikov P, Ilin D, Marnevskaia I, Malykh A, Ismatullina V, Kuzmina Y. Large-scale study of the precision of the approximate number system: Differences between formats, heterogeneity and congruency effects. Heliyon 2023; 9:e14912. [PMID: 37064479 PMCID: PMC10102223 DOI: 10.1016/j.heliyon.2023.e14912] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2022] [Revised: 03/16/2023] [Accepted: 03/21/2023] [Indexed: 03/30/2023] Open
Abstract
The study used a large sample of elementary schoolchildren in Russia (N = 3,448, 51.6% were girls, with a mean age of 8.70 years, ranging 6-11 years) to investigate the congruency, format and heterogeneity effects in a nonsymbolic comparison test and between-individual differences in these effects with generalized linear mixed effects models (GLMMs). The participants were asked to compare two arrays of figures of different colours in spatially separated or spatially intermixed formats. In addition, the figures could be similar or different for the two arrays. The results revealed that congruency (difference between congruent and incongruent items), format (difference between mixed and separated formats) and heterogeneity (difference between homogeneous and heterogeneous conditions) interacted. The heterogeneity effect was higher in the separated format, while the format effect was higher for the homogeneous condition. The separated format produced a greater congruency effect than the mixed format. In addition, the congruency effect was lower in the heterogeneous condition than in the homogeneous condition. Analysis of between-individual differences revealed that there was significant between-individual variance in the format and congruency effects. Analysis of between-grade differences revealed that accuracy improved from grade 1 to grade 4 only for congruent trials in separated formats. Consequently, the congruency effect increased in separated/homogeneous and separated/heterogeneous conditions. In general, the study demonstrated that the test format and heterogeneity affected accuracy and that this effect varied for congruent and incongruent items.
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Affiliation(s)
- S. Malykh
- Department of Psychology, Lomonosov Moscow State University, Moscow, Russia
- Russian Academy of Education, Moscow, Russia
- Corresponding author. Department of Psychology, Lomonosov Moscow State University, Moscow, Russia.
| | - S. Tarasov
- The Herzen State Pedagogical University of Russia, St. Petersburg, Russia
| | - I. Baeva
- The Herzen State Pedagogical University of Russia, St. Petersburg, Russia
| | - E. Nikulchev
- MIREA—Russian Technological University, Moscow, Russia
| | | | - D. Ilin
- MIREA—Russian Technological University, Moscow, Russia
| | - I. Marnevskaia
- Psychological Institute of Russian Academy of Education, Moscow, Russia
| | - A. Malykh
- Psychological Institute of Russian Academy of Education, Moscow, Russia
| | - V. Ismatullina
- Psychological Institute of Russian Academy of Education, Moscow, Russia
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12
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How many seconds was that? Teaching children about time does not refine their ability to track durations. Cognition 2023; 235:105410. [PMID: 36848703 DOI: 10.1016/j.cognition.2023.105410] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2022] [Revised: 01/09/2023] [Accepted: 02/13/2023] [Indexed: 02/27/2023]
Abstract
Over development, children acquire symbols to represent abstract concepts such as time and number. Despite the importance of quantity symbols, it is unknown how acquiring these symbols impacts one's ability to perceive quantities (i.e., nonsymbolic representations). While it has been proposed that learning symbols shapes nonsymbolic quantitative abilities (i.e., the refinement hypothesis), this hypothesis has been understudied, especially in the domain of time. Moreover, the majority of research in support of this hypothesis has been correlational in nature, and thus, experimental manipulations are critical for determining whether this relation is causal. In the present study, kindergarteners and first graders (N = 154) who have yet to learn about temporal symbols in school completed a temporal estimation task during which they were either (1) trained on temporal symbols and effective timing strategies ("2 s" and counting on the beat), (2) trained on temporal symbols only ("2 s"), or (3) participated in a control training. Children's nonsymbolic and symbolic timing abilities were assessed before and after training. Results revealed a correlation between children's nonsymbolic and symbolic timing abilities at pre-test (when controlling for age), indicating this relation exists prior to formal classroom instruction on temporal symbols. Notably, we found no support for the refinement hypothesis, as learning temporal symbols did not impact children's nonsymbolic timing abilities. Implications and future directions are discussed.
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Rodríguez C, Ferreira RA. To what extent is dot comparison an appropriate measure of approximate number system? Front Psychol 2023; 13:1065600. [PMID: 36704683 PMCID: PMC9873381 DOI: 10.3389/fpsyg.2022.1065600] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2022] [Accepted: 12/12/2022] [Indexed: 01/12/2023] Open
Abstract
Introduction Number sense has been systematically measured using dot comparison tasks. However, recent studies have reported that performance on dot comparison might be influenced inhibitory control and visual properties of dot arrays. In the present study, we analysed the influence of continuous magnitude, inhibitory control, and numerical ratio on the dot comparison performance of preschool children. Methods Participants were 517 preschool children from 13 different schools in Chile. Children completed a dot comparison and two inhibitory control tasks. Gebuis and Reynvoet method was used to create well-controlled dot arrays for use in the dot comparison task. A logistic mixed effects model was conducted to predict participants' dot comparison accuracy. Continuous magnitude and ratio were entered as level-1 predictors and inhibitory control as level-2 predictors. Results The results showed that all predictors made a significant contribution to dot comparison accuracy. Furthermore, a significant double interaction (inhibitory control x continuous magnitude) and a triple interaction (inhibitory control x continuous magnitude x ratio) showed that the contribution of inhibitory control skills in dot comparison accuracy depends on the continuous properties of dot arrays and ratio. Discussion These findings suggest that preschool children rely more on continuous magnitudes than numerosity in dot comparison tasks. They also indicate that the greater children's inhibitory control, the more able they are to respond based on numerosity in fully incongruent trials, particularly when ratio is low (easiest items). Taken together, the above findings support the competing processes account provided that both ANS and inhibitory control skills influence performance on dot comparison tasks.
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Affiliation(s)
- Cristina Rodríguez
- Millennium Nucleus for the Science of Learning (MiNSoL), Talca, Chile,Facultad de Ciencias de la Educación, Universidad Católica del Maule, Talca, Chile,*Correspondence: Cristina Rodríguez,
| | - Roberto A. Ferreira
- Millennium Nucleus for the Science of Learning (MiNSoL), Talca, Chile,Facultad de Ciencias de la Educación, Universidad Católica del Maule, Talca, Chile
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14
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Fang S, Zhou X. Form perception speed is critical for the relationship between non-verbal number sense and arithmetic fluency. INTELLIGENCE 2022. [DOI: 10.1016/j.intell.2022.101704] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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15
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Haman M, Patro K. More linear than log? Non-symbolic number-line estimation in 3- to 5-year-old children. Front Psychol 2022; 13:1003696. [PMID: 36389566 PMCID: PMC9659870 DOI: 10.3389/fpsyg.2022.1003696] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2022] [Accepted: 10/03/2022] [Indexed: 11/04/2022] Open
Abstract
The number-line estimation task has become one of the most important methods in numerical cognition research. Originally applied as a direct measure of spatial number representation, it became also informative regarding various other aspects of number processing and associated strategies. However, most of this work and associated conclusions concerns processing numbers in a symbolic format, by school children and older subjects. Symbolic number system is formally taught and trained at school, and its basic mathematical properties (e.g., equidistance, ordinality) can easily be transferred into a spatial format of an oriented number line. This triggers the question on basic characteristics of number line estimation before children get fully familiar with the symbolic number system, i.e., when they mostly rely on approximate system for non-symbolic quantities. In our three studies, we examine therefore how preschool children (3–5-years old) estimate position of non-symbolic quantities on a line, and how this estimation is related to the developing symbolic number knowledge and cultural (left-to-right) directionality. The children were tested with the Give-a-number task, then they performed a computerized number-line task. In Experiment 1, lines bounded with sets of 1 and 20 elements going left-to-right or right-to-left were used. Even in the least numerically competent group, the linear model better fit the estimates than the logarithmic or cyclic power models. The line direction was irrelevant. In Experiment 2, a 1–9 left-to-right oriented line was used. Advantage of linear model was found at group level, and variance of estimates correlated with tested numerosities. In Experiment 3, a position-to-number procedure again revealed the advantage of the linear model, although the strategy of selecting an option more similar to the closer end of the line was prevalent. The precision of estimation increased with the mastery of counting principles in all three experiments. These results contradict the hypothesis of the log-to-linear shift in development of basic numerical representation, rather supporting the linear model with scalar variance. However, the important question remains whether the number-line task captures the nature of the basic numerical representation, or rather the strategies of mapping that representation to an external space.
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Affiliation(s)
- Maciej Haman
- Faculty of Psychology, University of Warsaw, Warsaw, Poland
- *Correspondence: Maciej Haman,
| | - Katarzyna Patro
- Faculty of Psychology, University of Warsaw, Warsaw, Poland
- Department of Psychology, University of Tuebingen, Tübingen, Germany
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16
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Zhang Y, An N, Chen J, Zhou X, Cui Z. Numerosity sense correlates with fluent mathematical abilities. Acta Psychol (Amst) 2022; 228:103655. [DOI: 10.1016/j.actpsy.2022.103655] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2021] [Revised: 05/11/2022] [Accepted: 06/20/2022] [Indexed: 01/29/2023] Open
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17
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Zhang Y, Ma Y, Zhou X. The association between non-symbolic number comparison and mathematical abilities depends on fluency. Cogn Process 2022; 23:423-439. [PMID: 35704131 DOI: 10.1007/s10339-022-01098-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2021] [Accepted: 05/19/2022] [Indexed: 11/03/2022]
Abstract
Numerous studies have explored the correlation between non-symbolic number comparison and mathematical abilities in children, but the results have been inconsistent. The underlying mental processing featuring fluency may affect the correlation. The current study tested the fluency hypothesis that non-symbolic number comparison is associated with mathematical fluency in the development of mathematical ability. Non-symbolic number comparison, arithmetic computation, mathematical reasoning, non-symbolic number estimation, symbolic number comparison, and a series of basic cognitive processing tasks, including mental rotation, non-verbal matrix reasoning, and choice reaction time, were administered to 1072 first- to fourth-grade children. The results show that non-symbolic number comparison (measured via numerosity comparison) was the only independent predictor of arithmetic computation in higher grades, even after controlled for age, gender, basic cognitive processing, non-symbolic number estimation (measured via numerosity estimation), and symbolic number comparison (measured via digit comparison). However, it did not correlate with mathematical reasoning in any grade. These findings support the fluency hypothesis for developmental correlation between non-symbolic number comparison and mathematical abilities. That is, non-symbolic number comparison correlates with mathematical ability featuring fluency.
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Affiliation(s)
- Yiyun Zhang
- School of Psychology, Liaoning Normal University, Liaoning, China.,State Key Laboratory of Cognitive Neuroscience and Learning and IDG, McGovern Institute for Brain Research, Beijing Normal University, Beijing, 100875, China
| | - Yuanyuan Ma
- School of Psychology, Liaoning Normal University, Liaoning, China
| | - Xinlin Zhou
- State Key Laboratory of Cognitive Neuroscience and Learning and IDG, McGovern Institute for Brain Research, Beijing Normal University, Beijing, 100875, China. .,Research Associationion for Brain and Mathematical Learning, Beijing Normal University, Beijing, China.
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18
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Predicting Math Ability Using Working Memory, Number Sense, and Neurophysiology in Children and Adults. Brain Sci 2022; 12:brainsci12050550. [PMID: 35624937 PMCID: PMC9139259 DOI: 10.3390/brainsci12050550] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2022] [Revised: 04/21/2022] [Accepted: 04/22/2022] [Indexed: 11/16/2022] Open
Abstract
Previous work has shown relations between domain-general processes, domain-specific processes, and mathematical ability. However, the underlying neurophysiological effects of mathematical ability are less clear. Recent evidence highlighted the potential role of beta oscillations in mathematical ability. Here we investigate whether domain-general (working memory) and domain-specific (number sense) processes mediate the relation between resting-state beta oscillations and mathematical ability, and how this may differ as a function of development (children vs. adults). We compared a traditional analysis method normally used in EEG studies with a more recently developed parameterization method that separates periodic from aperiodic activity. Regardless of methods chosen, we found no support for mediation of working memory and number sense, neither for children nor for adults. However, we found subtle differences between the methods. Additionally, we showed that the traditional EEG analysis method conflates periodic activity with aperiodic activity; in addition, the latter is strongly related to mathematical ability and this relation differs between children and adults. At the cognitive level, our findings do not support previous suggestions of a mediation of working memory and number sense. At the neurophysiological level our findings suggest that aperiodic, rather than periodic, activity is linked to mathematical ability as a function of development.
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19
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Ching BHH, Kong KHC. Understanding additive composition is important for symbolic numerical magnitude processing. COGNITIVE DEVELOPMENT 2022. [DOI: 10.1016/j.cogdev.2022.101170] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
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20
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Haberstroh S, Schulte-Körne G. The Cognitive Profile of Math Difficulties: A Meta-Analysis Based on Clinical Criteria. Front Psychol 2022; 13:842391. [PMID: 35360597 PMCID: PMC8962618 DOI: 10.3389/fpsyg.2022.842391] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2021] [Accepted: 02/16/2022] [Indexed: 12/03/2022] Open
Abstract
Math difficulties (MD) manifest across various domain-specific and domain-general abilities. However, the existing cognitive profile of MD is incomplete and thus not applicable in typical settings such as schools or clinics. So far, no review has applied inclusion criteria according to DSM or ICD, summarized domain-specific abilities or examined the validity of response time scores for MD identification. Based upon stringent clinical criteria, the current meta-analysis included 34 studies which compared cognitive performances of a group with MD (n = 680) and a group without MD (n = 1565). Criteria according to DSM and ICD were applied to identify MD (percentile rank ≤ 16, age range 8–12 years, no comorbidities/low IQ). Effect sizes for 22 abilities were estimated and separated by their level and type of scoring (AC = accuracy, RT = response time). A cognitive profile of MD was identified, characterized by distinct weaknesses in: (a) computation (calculation [AC], fact retrieval [AC]), (b) number sense (quantity processing [AC], quantity-number linking [RT], numerical relations [AC]), and (c) visual-spatial short-term storage [AC]. No particular strength was found. Severity of MD, group differences in reading performance and IQ did not significantly moderate the results. Further analyses revealed that (a) effects are larger when dealing with numbers or number words than with quantities, (b) MD is not accompanied by any weakness in abilities typically assigned to reading, and (c) weaknesses in visual-spatial short-term storage emphasize the notion that number and space are interlinked. The need for high-quality studies investigating domain-general abilities is discussed.
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21
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Zhang D, Zhou L, Yang A, Li S, Chang C, Liu J, Zhou K. A connectome-based neuromarker of nonverbal number acuity and arithmetic skills. Cereb Cortex 2022; 33:881-894. [PMID: 35254408 PMCID: PMC9890459 DOI: 10.1093/cercor/bhac108] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2021] [Revised: 02/15/2022] [Accepted: 02/16/2022] [Indexed: 02/04/2023] Open
Abstract
The approximate number system (ANS) is vital for survival and reproduction in animals and is crucial for constructing abstract mathematical abilities in humans. Most previous neuroimaging studies focused on identifying discrete brain regions responsible for the ANS and characterizing their functions in numerosity perception. However, a neuromarker to characterize an individual's ANS acuity is lacking, especially one based on whole-brain functional connectivity (FC). Here, based on the resting-state functional magnetic resonance imaging (rs-fMRI) data obtained from a large sample, we identified a distributed brain network (i.e. a numerosity network) using a connectome-based predictive modeling (CPM) analysis. The summed FC strength within the numerosity network reliably predicted individual differences in ANS acuity regarding behavior, as measured using a nonsymbolic number-comparison task. Furthermore, in an independent dataset of the Human Connectome Project (HCP), we found that the summed FC strength within the numerosity network also specifically predicted individual differences in arithmetic skills, but not domain-general cognitive abilities. Therefore, our findings revealed that the identified numerosity network could serve as an applicable neuroimaging-based biomarker of nonverbal number acuity and arithmetic skills.
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Affiliation(s)
- Dai Zhang
- Beijing Key Laboratory of Applied Experimental Psychology, School of Psychology, Beijing Normal University, No. 19, Xinjiekouwai Street, Haidian District, Beijing 100875, China,Guangdong Key Laboratory for Biomedical Measurements and Ultrasound Imaging, School of Biomedical Engineering, Shenzhen University Health Science Center, No. 1066, Xueyuan Street, Nanshan District, Shenzhen 518060, China
| | - Liqin Zhou
- Beijing Key Laboratory of Applied Experimental Psychology, School of Psychology, Beijing Normal University, No. 19, Xinjiekouwai Street, Haidian District, Beijing 100875, China
| | - Anmin Yang
- Beijing Key Laboratory of Applied Experimental Psychology, School of Psychology, Beijing Normal University, No. 19, Xinjiekouwai Street, Haidian District, Beijing 100875, China
| | - Shanshan Li
- Beijing Key Laboratory of Applied Experimental Psychology, School of Psychology, Beijing Normal University, No. 19, Xinjiekouwai Street, Haidian District, Beijing 100875, China
| | - Chunqi Chang
- Guangdong Key Laboratory for Biomedical Measurements and Ultrasound Imaging, School of Biomedical Engineering, Shenzhen University Health Science Center, No. 1066, Xueyuan Street, Nanshan District, Shenzhen 518060, China
| | - Jia Liu
- Department of Psychology & Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, No. 30, Shuangqing Street, Haidian District, Beijing 100084, China
| | - Ke Zhou
- Corresponding author: Beijing Key Laboratory of Applied Experimental Psychology, School of Psychology, Beijing Normal University, No. 19, Xinjiekouwai Street, Haidian District, Beijing 100875, China.
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22
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Revisiting the Relationship Between Number-Line Estimation and Basic Addition and Subtraction in Elementary School Children and Adults. JOURNAL OF COGNITIVE EDUCATION AND PSYCHOLOGY 2021. [DOI: 10.1891/jcep-d-20-00001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Abstract
This study aims to examine the differences in numerosity estimation on a right-to-left number line between second- to fourth-grade students and undergraduate students, together with whether number-line estimation is related to basic arithmetic tasks (addition and subtraction). Hence, 53 Arabic-speaking children and 63 Arabic-speaking adults performed a paper-based number-line estimation task and also an arithmetic task. Number-line estimation was represented either by the percentage of absolute errors in positing the quantities on the line, by the accuracy, or by the r score for linearity of representation. The results show that, although children's addition (but not subtraction) performance resembles that of adults, the correlations vary between number line and arithmetic scores. Addition scores are positively correlated with error percentages in the children's number-line tasks, while subtraction is negatively correlated with adults' error percentages. These differences are assumed to be attributed to various uses of recall and procedural strategies.
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23
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He X, Zhou X, Zhao J, Zhang Y. Visual Perception Supports Adults in Numerosity Processing and Arithmetical Performance. Front Psychol 2021; 12:722261. [PMID: 34744887 PMCID: PMC8570262 DOI: 10.3389/fpsyg.2021.722261] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2021] [Accepted: 09/24/2021] [Indexed: 11/20/2022] Open
Abstract
Previous studies have found a correlation between numerosity processing and arithmetical performance. Visual perception has already been indicated as the shared cognitive mechanism between these two; however, these studies mostly focused on children. It is not clear whether the association between numerosity processing and arithmetical performance still existed following the development of individual arithmetical performance. Consequently, the underlying role of visual perception in numerosity processing and arithmetical performance has not been sufficiently studied in adults. For this study, researchers selected a total of 205 adult participants with an average age of 22years. The adults were administered arithmetic tests, numerosity comparison, and visual figure matching. Mental rotation, choice reaction time, and nonverbal intelligence were used as cognitive covariates. Results showed that numerosity comparison of adults correlated with their arithmetical performance, even after controlling for age and gender differences as well as general cognitive processing. However, after controlled for visual figure matching, the well-established association between numerosity comparison and arithmetic performance disappeared. These results supported the visual perception hypothesis, that visual perception measured by visual figure matching can account for the correlation between numerosity comparison and arithmetic performance. This indicated that even for adult populations, visual perceptual ability was the underlying component of numerosity processing and arithmetic performance.
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Affiliation(s)
- Xinyao He
- School of Psychology, Liaoning Normal University, Liaoning, China
| | - Xinlin Zhou
- State Key Laboratory of Cognitive Neuroscience and Learning, Siegler Center for Innovative Learning, Advanced Innovation Center for Future Education, Beijing Normal University, Beijing, China
| | - Jin Zhao
- Dalian Institute of Science and Technology, Liaoning, China
| | - Yiyun Zhang
- School of Psychology, Liaoning Normal University, Liaoning, China
- State Key Laboratory of Cognitive Neuroscience and Learning, Siegler Center for Innovative Learning, Advanced Innovation Center for Future Education, Beijing Normal University, Beijing, China
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24
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Numerical estimation strategies are correlated with math ability in school-aged children. COGNITIVE DEVELOPMENT 2021. [DOI: 10.1016/j.cogdev.2021.101089] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
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25
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Longitudinal relations between the approximate number system and symbolic number skills in preschool children. J Exp Child Psychol 2021; 212:105254. [PMID: 34352660 DOI: 10.1016/j.jecp.2021.105254] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2021] [Revised: 07/05/2021] [Accepted: 07/07/2021] [Indexed: 01/29/2023]
Abstract
This study examined the longitudinal relation between the approximate number system (ANS) and two symbolic number skills, namely word problem-solving skill and number line skill, in a sample of 138 Chinese 4- to 6-year-old children. The ANS and symbolic number skills were measured first in the second year of preschool (Time 1 [T1], mean age = 4.98 years; SD = 0.33) and then in the third year of preschool (Time 2 [T2]). Cross-lagged analyses indicated that word problem-solving skill at T1 predicted ANS acuity at T2 but not vice versa. In addition, there were bidirectional relations between children's word problem-solving skill and number line estimation skill. The observed longitudinal relations were robust to the control of child's sex, age, maternal education, receptive vocabulary, spatial visualization, and working memory except for the relation between T1 word problem-solving skill and T2 number line estimation skill, which was explained by child's age.
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26
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Nelwan M, Friso-van den Bos I, Vissers C, Kroesbergen E. The relation between working memory, number sense, and mathematics throughout primary education in children with and without mathematical difficulties. Child Neuropsychol 2021; 28:143-170. [PMID: 34340649 DOI: 10.1080/09297049.2021.1959905] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Abstract
Number sense and working memory contribute to mathematical development throughout primary school. However, it is still unclear how the contributions of each of these predictors may change across development and whether the cognitive contribution is the same for children with and without mathematical difficulties. The aim of the two studies in this paper was to shed light on these topics. In a cross-sectional design, a typically developing group of children (study 1; N = 459, Grades 1-4) and a group with mathematical difficulties (study 2; N = 61, Grades 4-6) completed a battery of number sense and working memory tests, as well as a measure of arithmetic competence. Results of study 1 indicated that number sense was important in first grade, while working memory gained importance in second grade, before predictive value of both predictors waned. Number sense and working memory supported mathematics development independently from one another from Grade 1. Analysis of task demands showed that typically developing children rely on comprehension and visualization of quantity-to-number associations in early development. Later in development, pupils rely on comparing larger numerals and working memory until automatization. Children with mathematical difficulties were less able to employ number sense during mathematical operations, and thus might remain dependent on their working memory resources during arithmetic tasks. This suggests that children with mathematical difficulties need aid to employ working memory for mathematics from an early age to be able to automatize mathematical abilities later in development.
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Affiliation(s)
- Michel Nelwan
- Department of Child Psychiatry, Erasmus MC -Sophia Children's Hospital, Rotterdam, The Netherlands.,Behavioural Science Institute, Radboud University, Nijmegen, The Netherlands
| | | | - Constance Vissers
- Behavioural Science Institute, Radboud University, Nijmegen, The Netherlands.,Kentalis Academy, Royal Dutch Kentalis, Sint-Michielsgestel, The Netherlands
| | - Evelyn Kroesbergen
- Behavioural Science Institute, Radboud University, Nijmegen, The Netherlands
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27
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Silver AM, Elliott L, Braham EJ, Bachman HJ, Votruba-Drzal E, Tamis-LeMonda CS, Cabrera N, Libertus ME. Measuring Emerging Number Knowledge in Toddlers. Front Psychol 2021; 12:703598. [PMID: 34354646 PMCID: PMC8329077 DOI: 10.3389/fpsyg.2021.703598] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Accepted: 06/29/2021] [Indexed: 12/02/2022] Open
Abstract
Recent evidence suggests that infants and toddlers may recognize counting as numerically relevant long before they are able to count or understand the cardinal meaning of number words. The Give-N task, which asks children to produce sets of objects in different quantities, is commonly used to test children’s cardinal number knowledge and understanding of exact number words but does not capture children’s preliminary understanding of number words and is difficult to administer remotely. Here, we asked whether toddlers correctly map number words to the referred quantities in a two-alternative forced choice Point-to-X task (e.g., “Which has three?”). Two- to three-year-old toddlers (N = 100) completed a Give-N task and a Point-to-X task through in-person testing or online via videoconferencing software. Across number-word trials in Point-to-X, toddlers pointed to the correct image more often than predicted by chance, indicating that they had some understanding of the prompted number word that allowed them to rule out incorrect responses, despite limited understanding of exact cardinal values. No differences in Point-to-X performance were seen for children tested in-person versus remotely. Children with better understanding of exact number words as indicated on the Give-N task also answered more trials correctly in Point-to-X. Critically, in-depth analyses of Point-to-X performance for children who were identified as 1- or 2-knowers on Give-N showed that 1-knowers do not show a preliminary understanding of numbers above their knower-level, whereas 2-knowers do. As researchers move to administering assessments remotely, the Point-to-X task promises to be an easy-to-administer alternative to Give-N for measuring children’s emerging number knowledge and capturing nuances in children’s number-word knowledge that Give-N may miss.
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Affiliation(s)
- Alex M Silver
- Department of Psychology, Learning Research and Development Center, University of Pittsburgh, Pittsburgh, PA, United States
| | - Leanne Elliott
- Department of Psychology, Learning Research and Development Center, University of Pittsburgh, Pittsburgh, PA, United States
| | - Emily J Braham
- Department of Psychology, Learning Research and Development Center, University of Pittsburgh, Pittsburgh, PA, United States
| | - Heather J Bachman
- Department of Health and Human Development, School of Education, University of Pittsburgh, Pittsburgh, PA, United States
| | - Elizabeth Votruba-Drzal
- Department of Psychology, Learning Research and Development Center, University of Pittsburgh, Pittsburgh, PA, United States
| | - Catherine S Tamis-LeMonda
- Department of Applied Psychology, Steinhardt School of Culture, Education and Human Development, New York University, New York, NY, United States
| | - Natasha Cabrera
- Department of Human Development and Quantitative Methodology, University of Maryland, College Park, MD, United States
| | - Melissa E Libertus
- Department of Psychology, Learning Research and Development Center, University of Pittsburgh, Pittsburgh, PA, United States
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28
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Wang J, Liu RD, Star J, Zhen R, Liu Y, Hong W. Do Students Respond Faster to Inequalities with a Greater than Sign or to Inequalities with a Less than Sign: Spatial-Numerical Association in Inequalities. JOURNAL OF COGNITION AND DEVELOPMENT 2021. [DOI: 10.1080/15248372.2021.1916499] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
| | | | | | - Rui Zhen
- Hangzhou Normal University, China
| | | | - Wei Hong
- Beijing Normal University, China
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29
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Chen L, Wang Y, Wen H. Numerical Magnitude Processing in Deaf Adolescents and Its Contribution to Arithmetical Ability. Front Psychol 2021; 12:584183. [PMID: 33841229 PMCID: PMC8026863 DOI: 10.3389/fpsyg.2021.584183] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2020] [Accepted: 03/02/2021] [Indexed: 11/13/2022] Open
Abstract
Although most deaf individuals could use sign language or sign/spoken language mix, hearing loss would still affect their language acquisition. Compensatory plasticity holds that the lack of auditory stimulation experienced by deaf individuals, such as congenital deafness, can be met by enhancements in visual cognition. And the studies of hearing individuals have showed that visual form perception is the cognitive mechanism that could explain the association between numerical magnitude processing and arithmetic computation. Therefore, we examined numerical magnitude processing and its contribution to arithmetical ability in deaf adolescents, and explored the differences between the congenital and acquired deafness. 112 deaf adolescents (58 congenital deafness) and 58 hearing adolescents performed a series of cognitive and mathematical tests, and it was found there was no significant differences between the congenital group and the hearing group, but congenital group outperformed acquired group in numerical magnitude processing (reaction time) and arithmetic computation. It was also found there was a close association between numerical magnitude processing and arithmetic computation in all deaf adolescents, and after controlling for the demographic variables (age, gender, onset of hearing loss) and general cognitive abilities (non-verbal IQ, processing speed, reading comprehension), numerical magnitude processing could predict arithmetic computation in all deaf adolescents but not in congenital group. The role of numerical magnitude processing (symbolic and non-symbolic) in deaf adolescents' mathematical performance should be paid attention in the training of arithmetical ability.
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Affiliation(s)
- Lilan Chen
- School of Psychology, Hainan Normal University, Haikou, China
| | - Yan Wang
- Faculty of Education, Beijing Normal University, Beijing, China
| | - Hongbo Wen
- Collaborative Innovation Center of Assessment Toward Basic Education Quality, Beijing Normal University, Beijing, China
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30
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Long-term relevance and interrelation of symbolic and non-symbolic abilities in mathematical-numerical development: Evidence from large-scale assessment data. COGNITIVE DEVELOPMENT 2021. [DOI: 10.1016/j.cogdev.2021.101008] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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31
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Huijsmans MDE, Kleemans T, Kroesbergen EH. How Cognitive Strengths Compensate Weaknesses Related to Specific Learning Difficulties in Fourth-Grade Children. Front Psychol 2021; 12:552458. [PMID: 33716844 PMCID: PMC7945979 DOI: 10.3389/fpsyg.2021.552458] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2020] [Accepted: 01/26/2021] [Indexed: 11/21/2022] Open
Abstract
The goal of the present study was to investigate whether children's cognitive strengths can compensate the accompanied weaknesses related to their specific learning difficulties. A Bayesian multigroup mediation SEM analysis in 281 fourth-grade children identified a cognitive compensatory mechanism in children with mathematical learning difficulties (n = 36): Children with weak number sense, but strong rapid naming performed slightly better on mathematics compared to peers with weak rapid naming. In contrast, a compensatory mechanism was not identified for children with a comorbid mathematical and reading difficulty (n = 16). One explanation for the latter finding could relate to the lack of ability to compensate, because of the difficulties these children experience in both academic domains. These findings lead to a new direction in research on learning difficulties in mathematics and/or reading by suggesting that children with a learning disability each have a unique profile of interrelated cognitive strengths and weaknesses. Children might compensate with these strengths for their weaknesses, which could lead to (small) learning gains in the affected domain.
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32
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Gasteiger H, Moeller K. Fostering early numerical competencies by playing conventional board games. J Exp Child Psychol 2021; 204:105060. [PMID: 33401161 DOI: 10.1016/j.jecp.2020.105060] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2018] [Revised: 10/23/2020] [Accepted: 11/12/2020] [Indexed: 10/22/2022]
Abstract
Recent evidence indicates that playing numerical board games is beneficial for the numerical development of preschoolers. However, board games used in these studies were often specifically developed for training numerical skills. Therefore, we examined whether similar beneficial effects could be observed for playing conventional board games such as Parcheesi. In an intervention study with seven 30-min training sessions over a period of 4 weeks, we observed that 4- to 6-year-old children (Mage = 4 years 11 months) who played conventional board games with traditional number dice (with dot faces numbered from one to six) benefitted more from the board games than children who played board games with color or non-numerical symbol dice. Pretest-posttest comparisons indicated differential effects on counting skills and the ability to recognize and use structures. Beyond these immediate training effects observed in posttest, the differential beneficial effects of playing board games using traditional dot dice on recognizing and using structures was still present in a follow-up test 1 year after the intervention. Thus, playing conventional board games using traditional number dice seems to be an effective low-threshold intervention to foster early numerical competencies.
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Affiliation(s)
- Hedwig Gasteiger
- Department of Mathematics, Osnabrück University, 49076 Osnabrück, Germany; Center for Early Childhood Development and Educational Research (CEDER), Osnabrück University, 49074 Osnabrück, Germany.
| | - Korbinian Moeller
- Centre for Mathematical Cognition, Loughborough University, Loughborough LE11 3TU, UK; Leibniz-Institut für Wissensmedien, 72076 Tübingen, Germany; Department of Psychology, University of Tübingen, 72074 Tübingen, Germany; LEAD Graduate School and Research Network, University of Tübingen, 72074 Tübingen, Germany
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33
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van ‘t Noordende JE, Kroesbergen EH, Leseman PPM, Volman M(CJM. The Role of Non-symbolic and Symbolic Skills in the Development of Early Numerical Cognition from Preschool to Kindergarten Age. JOURNAL OF COGNITION AND DEVELOPMENT 2020. [DOI: 10.1080/15248372.2020.1858835] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
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34
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Li M, Cheng D, Lu Y, Zhou X. Neural association between non-verbal number sense and arithmetic fluency. Hum Brain Mapp 2020; 41:5128-5140. [PMID: 32937010 PMCID: PMC7670642 DOI: 10.1002/hbm.25179] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2020] [Revised: 06/18/2020] [Accepted: 08/04/2020] [Indexed: 11/29/2022] Open
Abstract
Non‐verbal number sense has been shown to significantly correlate with arithmetic fluency. Accumulated behavioral evidence indicates that the cognitive mechanism relies on visual perception. However, few studies have investigated the neural mechanism underlying this association. Following the visual perception account, we hypothesized that there would be a neural association in occipital areas of the brain between non‐verbal number sense, arithmetic fluency, and visual perception. We analyzed event‐related potentials that are sensitive to neural responses while participants performed five cognitive tasks: simple addition, simple subtraction, numerosity comparison, figure matching, and character rhyming. The single‐trial ERP‐behavior correlation approach was used to enhance the statistical power. The results showed that the N1 component significantly correlated with reaction time at occipital electrodes on all tasks except for character rhyming. The N1 component for arithmetic fluency (simple addition and subtraction) and character rhyming correlated with the reaction time for numerosity comparison and figure matching. The results suggest that there are neural associations between arithmetic fluency, non‐verbal number sense, and visual perception in the occipital cortex, and that visual perception is the shared mechanism for both non‐verbal number sense and arithmetic fluency.
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Affiliation(s)
- Mengyi Li
- State Key Laboratory of Cognitive Neuroscience and Learning, IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China.,Advanced Innovation Center for Future Education, Beijing Normal University, Beijing, China.,Siegler Center for Innovative Learning, Beijing Normal University, Beijing, China
| | - Dazhi Cheng
- State Key Laboratory of Cognitive Neuroscience and Learning, IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China.,Advanced Innovation Center for Future Education, Beijing Normal University, Beijing, China.,Department of Pediatric Neurology, Capital Institute of Pediatrics, Beijing, China
| | - Yujie Lu
- State Key Laboratory of Cognitive Neuroscience and Learning, IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China.,Advanced Innovation Center for Future Education, Beijing Normal University, Beijing, China.,Siegler Center for Innovative Learning, Beijing Normal University, Beijing, China
| | - Xinlin Zhou
- State Key Laboratory of Cognitive Neuroscience and Learning, IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China.,Advanced Innovation Center for Future Education, Beijing Normal University, Beijing, China.,Siegler Center for Innovative Learning, Beijing Normal University, Beijing, China
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35
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Georges C, Guillaume M, Schiltz C. A robust electrophysiological marker of spontaneous numerical discrimination. Sci Rep 2020; 10:18376. [PMID: 33110202 PMCID: PMC7591903 DOI: 10.1038/s41598-020-75307-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2020] [Accepted: 10/12/2020] [Indexed: 01/29/2023] Open
Abstract
Humans have a Number Sense that enables them to represent and manipulate numerical quantities. Behavioral data suggest that the acuity of numerical discrimination is predictively associated with math ability-especially in children-but some authors argued that its assessment is problematic. In the present study, we used frequency-tagged electroencephalography to objectively measure spontaneous numerical discrimination during passive viewing of dot or picture arrays in healthy adults. During 1-min sequences, we introduced periodic numerosity changes and we progressively increased the magnitude of such changes every ten seconds. We found significant brain synchronization to the periodic numerosity changes from the 1.2 ratio over medial occipital regions, and amplitude strength increased with the numerical ratio. Brain responses were reliable across both stimulus formats. Interestingly, electrophysiological responses also mirrored performances on a number comparison task and seemed to be linked to math fluency. In sum, we present a neural marker of numerical acuity that is passively evaluated in short sequences, independent of stimulus format and that reflects behavioural performances on explicit number comparison tasks.
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Affiliation(s)
- Carrie Georges
- Department of Behavioural and Cognitive Sciences (DBCS), Faculty of Humanities, Education and Social Sciences (FHSE), Institute of Cognitive Science and Assessment (COSA), University of Luxembourg, Campus Belval, Maison des Sciences Humaines, Porte des Sciences 11, 4366, Esch-sur-Alzette, Luxembourg.
| | - Mathieu Guillaume
- Center for Research in Cognitive Neuroscience (CRCN), Université Libre de Bruxelles, Avenue Franklin Roosevelt 50 (CP 191), 1050, Brussels, Belgium
| | - Christine Schiltz
- Department of Behavioural and Cognitive Sciences (DBCS), Faculty of Humanities, Education and Social Sciences (FHSE), Institute of Cognitive Science and Assessment (COSA), University of Luxembourg, Campus Belval, Maison des Sciences Humaines, Porte des Sciences 11, 4366, Esch-sur-Alzette, Luxembourg
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36
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Mutaf-Yıldız B, Sasanguie D, De Smedt B, Reynvoet B. Probing the Relationship Between Home Numeracy and Children's Mathematical Skills: A Systematic Review. Front Psychol 2020; 11:2074. [PMID: 33071838 PMCID: PMC7530373 DOI: 10.3389/fpsyg.2020.02074] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2020] [Accepted: 07/27/2020] [Indexed: 11/18/2022] Open
Abstract
The concept of home numeracy has been defined as parent–child interactions with numerical content. This concept started to receive increasing attention since the last decade. Most of the studies indicated that the more parents and their children engage in numerical experiences, the better children perform in mathematical tasks. However, there are also contrasting results indicating that home numeracy does not play a role or that there is a negative association between the parent–child interactions and children's mathematics performance. To shed light on these discrepancies, a systematic review searching for available articles examining the relationship between home numeracy and mathematical skills was conducted. Thirty-seven articles were retained and a p-curve analysis showed a true positive association between home numeracy and children's mathematical skills. A more qualitative investigation of the articles revealed five common findings: (1) Advanced home numeracy interactions but not basic ones are associated with children's mathematical skills. (2) Most participants in the studies were mothers, however, when both parents participated and were compared, only mothers' reports of formal home numeracy activities (i.e., explicit numeracy teaching) were linked to children's mathematical skill. (3) Formal home numeracy activities have been investigated more commonly than informal home numeracy activities (i.e., implicit numeracy teaching). (4) The number of studies that have used questionnaires to assess home numeracy is larger compared with the ones that have used observations. (5) The majority of the studies measured children's mathematical skills with comprehensive tests that index mathematical ability with one composite score rather than with specific numerical tasks. These five common findings might explain the contradictory results regarding the relationship between home numeracy and mathematical skills. Therefore, more research is necessary to draw quantitative conclusions about these five points.
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Affiliation(s)
- Belde Mutaf-Yıldız
- Brain and Cognition, Faculty of Psychology and Educational Sciences, KU Leuven, Leuven, Belgium
| | | | - Bert De Smedt
- Parenting and Special Education, Faculty of Psychology and Educational Sciences, KU Leuven, Leuven, Belgium
| | - Bert Reynvoet
- Faculty of Psychology and Educational Sciences, KU Leuven Kulak, Kortrijk, Belgium
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37
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Maldonado Moscoso PA, Castaldi E, Burr DC, Arrighi R, Anobile G. Grouping strategies in number estimation extend the subitizing range. Sci Rep 2020; 10:14979. [PMID: 32917941 PMCID: PMC7486368 DOI: 10.1038/s41598-020-71871-5] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2020] [Accepted: 08/17/2020] [Indexed: 01/29/2023] Open
Abstract
When asked to estimate the number of items in a visual array, educated adults and children are more precise and rapid if the items are clustered into small subgroups rather than randomly distributed. This phenomenon, termed "groupitizing", is thought to rely on the recruitment of the subitizing system (dedicated to the perception of very small numbers), with the aid of simple arithmetical calculations. The aim of current study is to verify whether the advantage for clustered stimuli does rely on subitizing, by manipulating attention, known to strongly affect attention. Participants estimated the numerosity of grouped or ungrouped arrays in condition of full attention or while attention was diverted with a dual-task. Depriving visual attention strongly decreased estimation precision of grouped but not of ungrouped arrays, as well as increasing the tendency for numerosity estimation to regress towards the mean. Additional explorative analyses suggested that calculation skills correlated with the estimation precision of grouped, but not of ungrouped, arrays. The results suggest that groupitizing is an attention-based process that leverages on the subitizing system. They also suggest that measuring numerosity estimation thresholds with grouped stimuli may be a sensitive correlate of math abilities.
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Affiliation(s)
- Paula A Maldonado Moscoso
- Department of Neuroscience, Psychology, Pharmacology and Child Health, University of Florence, Florence, Italy
- Institut für Psychologie, Universität Regensburg, Regensburg, Germany
| | - Elisa Castaldi
- Department of Neuroscience, Psychology, Pharmacology and Child Health, University of Florence, Florence, Italy.
- Department of Translational Research and New Technologies in Medicine and Surgery, University of Pisa, Pisa, Italy.
| | - David C Burr
- Department of Neuroscience, Psychology, Pharmacology and Child Health, University of Florence, Florence, Italy
| | - Roberto Arrighi
- Department of Neuroscience, Psychology, Pharmacology and Child Health, University of Florence, Florence, Italy
| | - Giovanni Anobile
- Department of Neuroscience, Psychology, Pharmacology and Child Health, University of Florence, Florence, Italy
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38
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Aragón E, Cerda G, Aguilar M, Mera C, Navarro JI. Modulation of general and specific cognitive precursors to early mathematical competencies in preschool children. EUROPEAN JOURNAL OF PSYCHOLOGY OF EDUCATION 2020. [DOI: 10.1007/s10212-020-00483-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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39
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Szczygieł M. When does math anxiety in parents and teachers predict math anxiety and math achievement in elementary school children? The role of gender and grade year. SOCIAL PSYCHOLOGY OF EDUCATION 2020. [DOI: 10.1007/s11218-020-09570-2] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Abstract
AbstractThe study investigated the relationship between math anxiety in parents and teachers and math anxiety and math achievement in first- to third-grade children. The results indicate that math anxiety in fathers (but not mothers and teachers) is associated with math anxiety in first-grade children and third-grade girls. Math anxiety in mothers and teachers (but not fathers) explains the level of math achievement in third-grade children. The research results indicate the importance of adults in shaping pupils’ math anxiety and math achievement, but these relationships vary depending on gender and the grade year. The obtained outcomes generally suggest that adults’ math anxiety is not a social source of children’s math anxiety, but it can be considered a source of low math achievement among children in the final grade of early school education.
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40
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Kang I, Ratcliff R. Modeling the interaction of numerosity and perceptual variables with the diffusion model. Cogn Psychol 2020; 120:101288. [PMID: 32325289 DOI: 10.1016/j.cogpsych.2020.101288] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2020] [Accepted: 02/25/2020] [Indexed: 10/24/2022]
Abstract
Ratcliff and McKoon (2018) proposed integrated diffusion models for numerosity judgments in which a numerosity representation provides evidence used to drive the decision process. We extend this modeling framework to examine the interaction of non-numeric perceptual variables with numerosity by assuming that drift rate and non-decision time are functions of those variables. Four experiments were conducted with two different types of stimuli: a single array of intermingled blue and yellow dots in which both numerosity and dot area vary over trials and two side-by-side arrays of dots in which numerosity, dot area, and convex hull vary over trials. The tasks were to decide whether there were more blue or yellow dots (two experiments), more dots on which side, or which dots have a larger total area. Development of models started from the principled models in Ratcliff and McKoon (2018) and became somewhat ad hoc as we attempted to capture unexpected patterns induced by the conflict between numerosity and perceptual variables. In the three tasks involving numerosity judgments, the effects of the non-numeric variables were moderated by the number of dots. Under a high conflict, judgments were dominated by perceptual variables and produced an unexpected shift in the leading edge of the reaction time (RT) distributions. Although the resulting models were able to predict most of the accuracy and RT patterns, the models were not able to completely capture this shift in the RT distributions. However, when subjects judged area, numerosity affected perceptual judgments but there was no leading edge effect. Based on the results, it appears that the integrated diffusion models provide an effective framework to study the role of numerical and perceptual variables in numerosity tasks and their context-dependency.
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Affiliation(s)
- Inhan Kang
- The Ohio State University, 291 Psychology Building, 1835 Neil Avenue, Columbus, OH 43210, United States.
| | - Roger Ratcliff
- The Ohio State University, 291 Psychology Building, 1835 Neil Avenue, Columbus, OH 43210, United States.
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41
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Are the acuities of magnitude representations of different types and ranges of numbers related? Testing the core assumption of the integrated theory of numerical development. COGNITIVE DEVELOPMENT 2020. [DOI: 10.1016/j.cogdev.2020.100888] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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42
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Wei W, Li Y, Su HY. Predicting the growth patterns in early mathematics achievement from cognitive and environmental factors among Chinese kindergarten children. LEARNING AND INDIVIDUAL DIFFERENCES 2020. [DOI: 10.1016/j.lindif.2020.101841] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
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43
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Zhang T, Chen C, Chen C, Wei W. Gender differences in the development of semantic and spatial processing of numbers. BRITISH JOURNAL OF DEVELOPMENTAL PSYCHOLOGY 2020; 38:391-414. [PMID: 32212402 DOI: 10.1111/bjdp.12329] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2018] [Revised: 02/19/2020] [Indexed: 01/29/2023]
Abstract
This study recruited kindergarteners and first graders to investigate gender and grade differences in semantic and spatial processing of number magnitude. Results based on the Bayesian statistics showed that (1) there was extreme evidence in favour of grade differences in both semantic processing and spatial processing; (2) there were no gender differences in semantic processing; and (3) boys developed earlier than girls in spatial processing of numbers, especially for the more difficult task. These results are discussed in terms of gender differences in cognitive mechanisms underlying semantic and spatial processing of number magnitude.
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Affiliation(s)
- Tingyan Zhang
- Department of Psychology and Behavioral Sciences, Zhejiang University, Hang Zhou, China
| | - Chuansheng Chen
- Department of Psychology and Social Behavior, University of California, Irvine, California
| | - Chen Chen
- Department of Psychology and Behavioral Sciences, Zhejiang University, Hang Zhou, China
| | - Wei Wei
- Department of Psychology and Behavioral Sciences, Zhejiang University, Hang Zhou, China
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44
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Caviola S, Colling LJ, Mammarella IC, Szűcs D. Predictors of mathematics in primary school: Magnitude comparison, verbal and spatial working memory measures. Dev Sci 2020; 23:e12957. [DOI: 10.1111/desc.12957] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2019] [Revised: 11/15/2019] [Accepted: 02/10/2020] [Indexed: 11/28/2022]
Affiliation(s)
- Sara Caviola
- School of Psychology University of Leeds Leeds UK
- Department of Psychology Centre for Neuroscience in Education University of Cambridge Cambridge UK
| | - Lincoln J. Colling
- Department of Psychology Centre for Neuroscience in Education University of Cambridge Cambridge UK
- School of Psychology University of Sussex Brighton UK
| | | | - Dénes Szűcs
- Department of Psychology Centre for Neuroscience in Education University of Cambridge Cambridge UK
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45
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Ratcliff R, McKoon G. Decision making in numeracy tasks with spatially continuous scales. Cogn Psychol 2020; 116:101259. [PMID: 31838271 PMCID: PMC6953628 DOI: 10.1016/j.cogpsych.2019.101259] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2019] [Revised: 11/26/2019] [Accepted: 11/26/2019] [Indexed: 10/25/2022]
Abstract
A diffusion model of decision making on continuous response scales is applied to three numeracy tasks. The goal is to explain the distributions of responses on the continuous response scale and the time taken to make decisions. In the model, information from a stimulus is spatially continuously distributed, the response is made by accumulating information to a criterion, which is a 1D line, and the noise in the accumulation process is continuous Gaussian process noise over spatial position. The model is fit to the data from three experiments. In one experiment, a one or two digit number is displayed and the task is to point to its location on a number line ranging from 1 to 100. This task is used extensively in research in education but there has been no model for it that accounts for both decision times and decision choices. In the second task, an array of dots is displayed and the task is to point to the position of the number of dots on an arc ranging from 11 to 90. In a third task, an array of dots is displayed and the task is to speak aloud the number of dots. The model we propose accounts for both accuracy and response time variables, including the full distributions of response times. It also provides estimates of the acuity of decisions (standard deviations in the evidence distributions) and it shows how representations of numeracy information are task-dependent. We discuss how our model relates to research on numeracy and the neuroscience of numeracy, and how it can produce more comprehensive measures of individual differences in numeracy skills in tasks with continuous response scales than have hitherto been available.
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46
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Tikhomirova T, Kuzmina Y, Lysenkova I, Malykh S. The Relationship Between Non-symbolic and Symbolic Numerosity Representations in Elementary School: The Role of Intelligence. Front Psychol 2019; 10:2724. [PMID: 31866910 PMCID: PMC6906201 DOI: 10.3389/fpsyg.2019.02724] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2019] [Accepted: 11/18/2019] [Indexed: 01/29/2023] Open
Abstract
This study aimed to estimate the extent to which the development of symbolic numerosity representations relies on pre-existing non-symbolic numerosity representations that refer to the Approximate Number System. To achieve this aim, we estimated the longitudinal relationships between accuracy in the Number Line (NL) test and “blue–yellow dots” test across elementary school children. Data from a four-wave longitudinal study involving schoolchildren in grades 1–4 in Russia and Kyrgyzstan (N = 490, mean age 7.65 years in grade 1) were analyzed. We applied structural equation modeling and tested several competing models. The results revealed that at the start of schooling, the accuracy in the NL test predicted subsequent accuracy in the “blue–yellow dots” test, whereas subsequently, non-symbolic representation in grades 2 and 3 predicted subsequent symbolic representation. These results indicate that the effect of non-symbolic representation on symbolic representation emerges after a child masters the basics of symbolic number knowledge, such as counting in the range of twenty and simple arithmetic. We also examined the extent to which the relationships between non-symbolic and symbolic representations might be explained by fluid intelligence, which was measured by Raven’s Standard Progressive Matrices test. The results revealed that the effect of symbolic representation on non-symbolic representation was explained by fluid intelligence, whereas at the end of elementary school, non-symbolic representation predicted subsequent symbolic representation independently of fluid intelligence.
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Affiliation(s)
- Tatiana Tikhomirova
- Department of Psychology, Lomonosov Moscow State University, Moscow, Russia.,Psychological Institute of Russian Academy of Education, Moscow, Russia
| | - Yulia Kuzmina
- Department of Psychology, Lomonosov Moscow State University, Moscow, Russia.,Psychological Institute of Russian Academy of Education, Moscow, Russia
| | - Irina Lysenkova
- Department of Psychology, Kyrgyz-Russian Slavic University, Bishkek, Kyrgyzstan
| | - Sergey Malykh
- Department of Psychology, Lomonosov Moscow State University, Moscow, Russia.,Psychological Institute of Russian Academy of Education, Moscow, Russia
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47
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Carey S, Barner D. Ontogenetic Origins of Human Integer Representations. Trends Cogn Sci 2019; 23:823-835. [PMID: 31439418 DOI: 10.1016/j.tics.2019.07.004] [Citation(s) in RCA: 53] [Impact Index Per Article: 10.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2019] [Revised: 07/15/2019] [Accepted: 07/16/2019] [Indexed: 11/30/2022]
Abstract
Do children learn number words by associating them with perceptual magnitudes? Recent studies argue that approximate numerical magnitudes play a foundational role in the development of integer concepts. Against this, we argue that approximate number representations fail both empirically and in principle to provide the content required of integer concepts. Instead, we suggest that children's understanding of integer concepts proceeds in two phases. In the first phase, children learn small exact number word meanings by associating words with small sets. In the second phase, children learn the meanings of larger number words by mastering the logic of exact counting algorithms, which implement the successor function and Hume's principle (that one-to-one correspondence guarantees exact equality). In neither phase do approximate number representations play a foundational role.
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Affiliation(s)
- Susan Carey
- Department of Psychology, Harvard University, Cambridge, MA 02138, USA.
| | - David Barner
- Department of Psychology, University of California, San Diego, La Jolla, CA 92093, USA; University of California, San Diego, La Jolla, CA 92093, USA
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48
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Lane C, Van Herwegen J, Freeth M. Exploring the approximate number system in Sotos syndrome: insights from a dot comparison task. JOURNAL OF INTELLECTUAL DISABILITY RESEARCH : JIDR 2019; 63:917-925. [PMID: 30734385 DOI: 10.1111/jir.12604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2018] [Revised: 12/19/2018] [Accepted: 01/14/2019] [Indexed: 06/09/2023]
Abstract
BACKGROUND Sotos syndrome is a congenital overgrowth condition associated with intellectual disability and an uneven cognitive profile. Previous research has established that individuals with Sotos syndrome have relatively poor mathematical ability, but domain-specific numeracy skills have not been explored within this population. This study investigated the approximate number system (ANS) in Sotos syndrome. METHOD A dot comparison task was administered to 20 participants with Sotos syndrome (mean age in years = 18.43, SD = 9.29). Performance was compared to a chronological agematched typically developing control group (n = 25) and a mental age-matched Williams syndrome group (n = 24). RESULTS The Sotos group did not display an ANS deficit overall when compared to chronological agematched control participants. However, for trials where the size of the individual dots and the envelope area were negatively correlated with the total number of dots (incongruent trials), the Sotos group were less accurate than the typically developing group but more accurate than the Williams syndrome group, suggesting an inhibitory control deficit. Better accuracy on incongruent trials, but not congruent trials, was associated with higher quantitative reasoning ability for participants with Sotos syndrome. CONCLUSION Overall, the findings suggest that ANS acuity is not impaired in Sotos syndrome but that numerical difficulties may be associated with an inhibitory control deficit for individuals with Sotos syndrome.
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Affiliation(s)
- C Lane
- Department of Psychology, The University of Sheffield, Sheffield, UK
| | - J Van Herwegen
- Department of Psychology and Human Development, UCL Institute of Education, London, UK
| | - M Freeth
- Department of Psychology, The University of Sheffield, Sheffield, UK
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49
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Zhang Y, Liu T, Chen C, Zhou X. Visual form perception supports approximate number system acuity and arithmetic fluency. LEARNING AND INDIVIDUAL DIFFERENCES 2019. [DOI: 10.1016/j.lindif.2019.02.008] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
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50
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Cueli M, Areces D, McCaskey U, Álvarez-García D, González-Castro P. Mathematics Competence Level: The Contribution of Non-symbolic and Spatial Magnitude Comparison Skills. Front Psychol 2019; 10:465. [PMID: 30890988 PMCID: PMC6411688 DOI: 10.3389/fpsyg.2019.00465] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2018] [Accepted: 02/15/2019] [Indexed: 11/13/2022] Open
Abstract
Magnitude comparison skills have been related to mathematics competence, although results in this area vary. The current study aimed to describe the performance of 75 children (aged 4-5 years) in two comparison tasks; and examine the strength of the relationship between each of the two tasks and mathematics competence level (MCL). Participants were assessed with the Early Numeracy Test which provides a global MCL score. Magnitude comparison skills were assessed with two tasks: a non-symbolic number comparison task and a spatial comparison task. Results of the Pearson correlation analysis showed a relationship between the two tasks with better performance in the spatial comparison task. Regression analysis with the stepwise method showed that only the non-symbolic number comparison task had a significant value in the prediction of the MCL pointing to the need to take these kinds of tasks into account in the first years of school.
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Affiliation(s)
- Marisol Cueli
- Department of Psychology, University of Oviedo, Oviedo, Spain
| | - Débora Areces
- Department of Psychology, University of Oviedo, Oviedo, Spain
| | - Ursina McCaskey
- Center for MR-Research, University Children's Hospital Zurich, Zurich, Switzerland.,Children's Research Center, University Children's Hospital Zurich, Zurich, Switzerland
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