1
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Chan JYC, Mazzocco MMM. New measures of number line estimation performance reveal children's ordinal understanding of numbers. J Exp Child Psychol 2024; 245:105965. [PMID: 38823358 DOI: 10.1016/j.jecp.2024.105965] [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: 08/06/2023] [Revised: 04/17/2024] [Accepted: 04/18/2024] [Indexed: 06/03/2024]
Abstract
Children's performance on the number line estimation task, often measured by the percentage of absolute error, predicts their later mathematics achievement. This task may also reveal (a) children's ordinal understanding of the target numbers in relation to each other and the benchmarks (e.g., endpoints, midpoint) and (b) the ordinal skills that are a necessary precursor to children's ability to understand the interval nature of a number line as measured by percentage of absolute error. Using data from 104 U.S. kindergartners, we measured whether children's estimates were correctly sequenced across trials and correctly positioned relative to given benchmarks within trials at two time points. For both time points, we found that each ordinal error measure revealed a distinct pattern of data distribution, providing opportunities to tap into different aspects of children's ordinal understanding. Furthermore, children who made fewer ordinal errors scored higher on the Test of Early Mathematics Ability and showed greater improvement on their interval understanding of numbers as reflected by a larger reduction of percentage of absolute error from Time 1 to Time 2. The findings suggest that our number line measures reveal individual differences in children's ordinal understanding of numbers, and that such understanding may be a precursor to their interval understanding and later mathematics performance.
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Affiliation(s)
- Jenny Yun-Chen Chan
- Institute of Child Development, University of Minnesota-Twin Cities, Minneapolis, MN 55455, USA; Early Childhood Education, The Education University of Hong Kong, Tai Po, New Territories, Hong Kong Special Administrative Region.
| | - Michèle M M Mazzocco
- Institute of Child Development, University of Minnesota-Twin Cities, Minneapolis, MN 55455, USA
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2
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Kaicher CM, Conti JJ, Dedhe AM, Aulet LS, Cantlon JF. Is core knowledge a natural subdivision of infant cognition? Behav Brain Sci 2024; 47:e133. [PMID: 38934427 DOI: 10.1017/s0140525x23003229] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/28/2024]
Abstract
We examine Spelke's core knowledge taxonomy and test its boundaries. We ask whether Spelke's core knowledge is a distinct type of cognition in the sense that the cognitive processes it includes and excludes are biologically and mechanically coherent.
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Affiliation(s)
- Caroline M Kaicher
- Department of Psychology, Carnegie Mellon University, Pittsburgh, PA, USA ; ; ; ; https://www.cmu.edu/dietrich/psychology/kidneurolab/
| | - Julia J Conti
- Department of Psychology, Carnegie Mellon University, Pittsburgh, PA, USA ; ; ; ; https://www.cmu.edu/dietrich/psychology/kidneurolab/
| | - Abhishek M Dedhe
- Department of Psychology, Carnegie Mellon University, Pittsburgh, PA, USA ; ; ; ; https://www.cmu.edu/dietrich/psychology/kidneurolab/
| | - Lauren S Aulet
- Department of Psychology, Carnegie Mellon University, Pittsburgh, PA, USA ; ; ; ; https://www.cmu.edu/dietrich/psychology/kidneurolab/
| | - Jessica F Cantlon
- Department of Psychology, Carnegie Mellon University, Pittsburgh, PA, USA ; ; ; ; https://www.cmu.edu/dietrich/psychology/kidneurolab/
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3
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Castaldi E, Tinelli F, Filippo G, Bartoli M, Anobile G. Auditory time perception impairment in children with developmental dyscalculia. RESEARCH IN DEVELOPMENTAL DISABILITIES 2024; 149:104733. [PMID: 38663331 PMCID: PMC11155440 DOI: 10.1016/j.ridd.2024.104733] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2023] [Revised: 02/19/2024] [Accepted: 04/09/2024] [Indexed: 05/21/2024]
Abstract
Developmental dyscalculia (DD) is a specific learning disability which prevents children from acquiring adequate numerical and arithmetical competences. We investigated whether difficulties in children with DD spread beyond the numerical domain and impact also their ability to perceive time. A group of 37 children/adolescent with and without DD were tested with an auditory categorization task measuring time perception thresholds in the sub-second (0.25-1 s) and supra-second (0.75-3 s) ranges. Results showed that auditory time perception was strongly impaired in children with DD at both time scales. The impairment remained even when age, non-verbal reasoning, and gender were regressed out. Overall, our results show that the difficulties of DD can affect magnitudes other than numerical and contribute to the increasing evidence that frames dyscalculia as a disorder affecting multiple neurocognitive and perceptual systems.
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Affiliation(s)
- Elisa Castaldi
- Department of Neuroscience, Psychology, Pharmacology, and Child Health, University of Florence, Florence, Italy.
| | - Francesca Tinelli
- Department of Developmental Neuroscience, IRCCS Fondazione Stella Maris, Pisa, Italy
| | - Gasperini Filippo
- Department of Developmental Neuroscience, IRCCS Fondazione Stella Maris, Pisa, Italy
| | - Mariaelisa Bartoli
- Department of Developmental Neuroscience, IRCCS Fondazione Stella Maris, Pisa, Italy
| | - Giovanni Anobile
- Department of Neuroscience, Psychology, Pharmacology, and Child Health, University of Florence, Florence, Italy
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4
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Tang Y, Qian P, Yan L. Developmental changes of the impact of visual cues on ANS acuity across grades 1-5: Different patterns of visual cues on numerosity processing. Iperception 2024; 15:20416695241259160. [PMID: 38846636 PMCID: PMC11155340 DOI: 10.1177/20416695241259160] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2023] [Accepted: 05/18/2024] [Indexed: 06/09/2024] Open
Abstract
Numerous studies have consistently demonstrated the presence of the approximate number system (ANS) throughout development. Research has also revealed that visual cues may influence the ANS acuity, which may change with age. However, most studies have drawn conclusions based on performance differences between incongruent and congruent trials, which may be confounded by an individual's ability to inhibit interference. Therefore, to examine the developmental changes of the impact of visual cues on ANS acuity, we utilized congruent trials with varying visual cues. Our sample comprised Chinese children from grade one to grade five. We manipulated the salience of numerical cues (numerical ratio) and visual cues (dot size) in a non-symbolic numerosity comparison task. The results revealed a discernible leap in development from first to third grade and first to fifth grade; however, this upward trajectory did not persist into the transition from third to fifth grade, where no appreciable advancement was observed. Moreover, we observed different effects of visual cues on the dot-comparison task depending on the numerical cues and age. Specifically, visual cues (i.e., dot size) only facilitated ANS acuity in older school-aged children when numerical cues were weakened. The results indicate the presence of two distinct magnitude representational systems-one for the numerical dimension and another for the non-numerical dimension-during development.
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Affiliation(s)
- Yike Tang
- Zhejiang Sci-Tech University, Hangzhou, China
| | - Ping Qian
- Zhejiang Sci-Tech University, Hangzhou, China
| | - Linlin Yan
- Zhejiang Sci-Tech University, Hangzhou, China
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5
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Li X, Li J, Zhao S, Liao Y, Zhu L, Mou Y. Magnitude representation of preschool children with autism spectrum condition. AUTISM : THE INTERNATIONAL JOURNAL OF RESEARCH AND PRACTICE 2024; 28:866-880. [PMID: 37522624 DOI: 10.1177/13623613231185408] [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: 08/01/2023]
Abstract
LAY ABSTRACT The mathematical abilities of children with autism spectrum condition have been understudied. Magnitude representation (e.g. presenting the number of a collection of objects) is a fundamental numerical ability presented since early infancy and is correlated with children's later learning of formal mathematics. It remains unclear about whether children with autism spectrum condition differ from their peers without autism spectrum condition in precision of magnitude representations. This study compared preschool children with and without autism spectrum condition in their precision of magnitude representation with an approximate number comparison task, in which children compared two sets of dots without counting and chose the set with more dots. Children with autism spectrum condition exhibited the lower numerical comparison accuracy (i.e. the weaker magnitude representation) than their peers without autism spectrum condition. This difference existed even when multiple general cognitive abilities (working memory, inhibitory control, and nonverbal intelligence) and language abilities were statistically controlled. Moreover, the individual difference of the numerical comparison accuracy was larger in children with autism spectrum condition than without autism spectrum condition. These findings suggest that children with autism spectrum condition are at risk of weaker magnitude representation from an early age, emphasizing the need for specialized mathematics education or interventions to support their learning. In addition, the large variance in the precision of their magnitude representation suggests that individualized mathematics interventions are needed for children with autism spectrum condition.
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Affiliation(s)
- Xueyan Li
- Department of Psychology, Sun Yat-sen University, Guangzhou, China
| | - Jiaxi Li
- Department of Psychology, The University of Hong Kong, Hong Kong, China
| | - Sijia Zhao
- Department of Psychology, Sun Yat-sen University, Guangzhou, China
| | - Yini Liao
- Department of Psychology, Sun Yat-sen University, Guangzhou, China
| | - Liqi Zhu
- CAS Key Laboratory of Behavioral Science, Institute of Psychology, Chinese Academy of Sciences, Beijing, China
- Department of Psychology, University of Chinese Academy of Sciences, Beijing, China
| | - Yi Mou
- Department of Psychology, Sun Yat-sen University, Guangzhou, China
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6
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Santacà M, Gatto E, Dadda M, Bruzzone M, Dal Maschio M, Bisazza A. Exploring the Importance of Environmental Complexity for Newly Hatched Zebrafish. Animals (Basel) 2024; 14:1031. [PMID: 38612270 PMCID: PMC11011065 DOI: 10.3390/ani14071031] [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: 03/07/2024] [Revised: 03/25/2024] [Accepted: 03/26/2024] [Indexed: 04/14/2024] Open
Abstract
The effects of an early impoverished social or physical environment on vertebrate neural development and cognition has been known for decades. While existing studies have focused on the long-term effects, measuring adult cognitive phenotypes, studies on the effects of environmental complexity on the early stages of development are lacking. Zebrafish (Danio rerio) hatchlings are assumed to have minimal interaction with their environment and are routinely reared in small, bare containers. To investigate the effects of being raised under such conditions on development of behaviour and cognition, hatchlings housed for 10 days in either an enriched or a standard environment underwent two cognitive tasks. The results were mixed. Subjects of the two treatments did not differ in performance when required to discriminate two areas. Conversely, we found a significant effect in a number discrimination task, with subjects from impoverished condition performing significantly worse. In both experiments, larvae reared in impoverished environment showed a reduced locomotor activity. Given the effects that enrichment appears to exert on larvae, a third experiment explored whether hatchlings exhibit a spontaneous preference for more complex environments. When offered a choice between a bare setting and one with objects of different shapes and colors, larvae spent over 70% of time in the enriched sector. Deepening these effects of an early impoverished environment on cognitive development is crucial for the welfare of captive zebrafish populations and for enhancing the quality and reliability of studies on larval zebrafish.
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Affiliation(s)
- Maria Santacà
- Department of Behavioral and Cognitive Biology, University of Vienna, 1030 Vienna, Austria
- Department of General Psychology, University of Padova, 35131 Padova, Italy; (M.D.)
| | - Elia Gatto
- Department of Chemical, Pharmaceutical and Agricultural Science, University of Ferrara, 44121 Ferrara, Italy;
- Department of Life Science and Biotechnology, University of Ferrara, 44121 Ferrara, Italy
| | - Marco Dadda
- Department of General Psychology, University of Padova, 35131 Padova, Italy; (M.D.)
| | - Matteo Bruzzone
- Padua Neuroscience Center, University of Padova, 35131 Padova, Italy (M.D.M.)
- Department of Biomedical Sciences, University of Padova, 35131 Padova, Italy
| | - Marco Dal Maschio
- Padua Neuroscience Center, University of Padova, 35131 Padova, Italy (M.D.M.)
- Department of Biomedical Sciences, University of Padova, 35131 Padova, Italy
| | - Angelo Bisazza
- Department of General Psychology, University of Padova, 35131 Padova, Italy; (M.D.)
- Padua Neuroscience Center, University of Padova, 35131 Padova, Italy (M.D.M.)
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7
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Hofmann W, Kinder A, Pekár J. How learning influences non-symbolic numerical processing: effects of feedback in the dot comparison task. Front Psychol 2024; 14:1287429. [PMID: 38352965 PMCID: PMC10861774 DOI: 10.3389/fpsyg.2023.1287429] [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: 09/01/2023] [Accepted: 12/18/2023] [Indexed: 02/16/2024] Open
Abstract
It has long been debated how humans estimate the numerosity of sets of elements and what role continuous visual properties play in this process. The dot comparison task, in which the more numerous of two dot arrays must be selected, is a dominant method to investigate this phenomenon. It has been shown that the visual properties of the two dot patterns strongly influence the comparison. This influence can be systematically investigated by manipulating visual properties congruently and incongruently with numerosity. However, it remains unclear how learning and prior experience affect the influence of the visual properties. To address this question, we introduced feedback into the classical dot comparison task: during the learning phase, participants in the experimental group received feedback after each trial indicating whether their answer was correct whereas participants in the control group did not. After the learning phase, neither group received feedback. The convex hull of the dot patterns and the average dot diameter were manipulated congruently and incongruently with numerosity. Our results show that feedback had no effect on overall performance. However, when manipulated separately, dot diameter no longer affected performance in the experimental group after the learning phase, but it did in the control group. Moreover, this effect remained visible even when diameter and convex hull were manipulated simultaneously. This pattern of results is consistent with the notion of sensory integration which proposes that weights are assigned to different visual cues and that numerical judgments depend on an additive combination of these weights. We also found a correlation between performance on an arithmetic task and performance on trials in which dot size was manipulated incongruently with numerosity. However, there were no correlations between an inhibition task and performance in the dot comparison task. Taken together, the current results suggest that learning with feedback may affect some visual properties but not others. Future studies should further investigate a wider range of visual properties to examine which of them can be influenced by learning and under what conditions learning occurs.
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Affiliation(s)
- Wiebke Hofmann
- Institute of Psychology of Learning, Department of Education and Psychology, Free University of Berlin, Berlin, Germany
- Department of Psychiatry and Neurosciences, Charité – Universitätsmedizin Berlin, Corporate Member of Freie Universität Berlin and Humboldt Universität Zu Berlin, Charité Campus Mitte (CCM), Berlin, Germany
| | - Annette Kinder
- Institute of Psychology of Learning, Department of Education and Psychology, Free University of Berlin, Berlin, Germany
| | - Judit Pekár
- Institute of Psychology of Learning, Department of Education and Psychology, Free University of Berlin, Berlin, Germany
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8
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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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9
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Georges C, Cornu V, Schiltz C. The importance of spatial language for early numerical development in preschool: Going beyond verbal number skills. PLoS One 2023; 18:e0292291. [PMID: 37773948 PMCID: PMC10540965 DOI: 10.1371/journal.pone.0292291] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2023] [Accepted: 09/17/2023] [Indexed: 10/01/2023] Open
Abstract
Recent evidence suggests that spatial language in preschool positively affects the development of verbal number skills, as indexed by aggregated performances on counting and number naming tasks. We firstly aimed to specify whether spatial language (the knowledge of locative prepositions) significantly relates to both of these measures. In addition, we assessed whether the predictive value of spatial language extends beyond verbal number skills to numerical subdomains without explicit verbal component, such as number writing, symbolic magnitude classifications, ordinal judgments and numerosity comparisons. To determine the unique contributions of spatial language to these numerical skills, we controlled in our regression analyses for intrinsic and extrinsic spatial abilities, phonological awareness as well as age, socioeconomic status and home language. With respect to verbal number skills, it appeared that spatial language uniquely predicted forward and backward counting but not number naming, which was significantly affected only by phonological awareness. Regarding numerical tasks that do not contain explicit verbal components, spatial language did not relate to number writing or numerosity comparisons. Conversely, it explained unique variance in symbolic magnitude classifications and was the only predictor of ordinal judgments. These findings thus highlight the importance of spatial language for early numerical development beyond verbal number skills and suggest that the knowledge of spatial terms is especially relevant for processing cardinal and ordinal relations between symbolic numbers. Promoting spatial language in preschool might thus be an interesting avenue for fostering the acquisition of these symbolic numerical skills prior to formal schooling.
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Affiliation(s)
- Carrie Georges
- Department of Behavioural and Cognitive Sciences, Faculty of Humanities, Education and Social Sciences, University of Luxembourg, Esch-Belval, Luxembourg
| | - Véronique Cornu
- Centre pour le Développement des Apprentissages Grande-Duchesse Maria Teresa, Ministère de l’Éducation Nationale, de l’Enfance et de la Jeunesse, Strassen, Luxembourg
| | - Christine Schiltz
- Department of Behavioural and Cognitive Sciences, Faculty of Humanities, Education and Social Sciences, University of Luxembourg, Esch-Belval, Luxembourg
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10
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O’Shaughnessy DM, Cruz Cordero T, Mollica F, Boni I, Jara-Ettinger J, Gibson E, Piantadosi ST. Diverse mathematical knowledge among indigenous Amazonians. Proc Natl Acad Sci U S A 2023; 120:e2215999120. [PMID: 37603761 PMCID: PMC10469040 DOI: 10.1073/pnas.2215999120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2022] [Accepted: 05/12/2023] [Indexed: 08/23/2023] Open
Abstract
We investigate number and arithmetic learning among a Bolivian indigenous people, the Tsimane', for whom formal schooling is comparatively recent in history and variable in both extent and consistency. We first present a large-scale meta-analysis on child number development involving over 800 Tsimane' children. The results emphasize the impact of formal schooling: Children are only found to be full counters when they have attended school, suggesting the importance of cultural support for early mathematics. We then test especially remote Tsimane' communities and document the development of specialized arithmetical knowledge in the absence of direct formal education. Specifically, we describe individuals who succeed on arithmetic problems involving the number five-which has a distinct role in the local economy-even though they do not succeed on some lower numbers. Some of these participants can perform multiplication with fives at greater accuracy than addition by one. These results highlight the importance of cultural factors in early mathematics and suggest that psychological theories of number where quantities are derived from lower numbers via repeated addition (e.g., a successor function) are unlikely to explain the diversity of human mathematical ability.
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Affiliation(s)
| | | | - Francis Mollica
- School of Informatics, University of Edinburgh, EdinburghEH8 9AB, United Kingdom
| | - Isabelle Boni
- Department of Psychology, University of California, Berkeley, CA94720-1650
| | | | - Edward Gibson
- Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA02139-4307
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11
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Lepoittevin S, Keymolen G, Andres M, Visscher AD. Arabic digit processing in adults with mathematical learning disability. Q J Exp Psychol (Hove) 2023; 76:1913-1924. [PMID: 36113204 DOI: 10.1177/17470218221128498] [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: 07/20/2023]
Abstract
The processing of Arabic digits is a core difficulty of children suffering from mathematical learning disability (MLD). Dominant accounts assume a semantic impairment affecting either the magnitude representation per se or its access from numerical symbols. But recent data have raised the hypothesis that the impaired processing of Arabic digits may be explained by a selective deficit of digit visual recognition (i.e., recognising a symbol as one of the digits, no matter its identity or numerical meaning). This study aims at testing whether the difficulty to process Arabic digits remains prevalent in adults with MLD and whether it is effectively associated with a digit visual recognition deficit. To do so, we compared 19 adults with MLD to 19 matched controls in an Arabic digit comparison task that required to identify the largest of two digits, and in an Arabic digit lexical decision task that required to decide whether a visual stimulus is a digit or not. The results showed that MLD participants took more time than control participants to perform the comparison task. In contrast, their performance in the digit lexical decision task was within the range of the control participants. Overall, this finding indicates that adults with MLD continue to experience difficulties to process the magnitude of Arabic digits efficiently, and this cannot be explained by a visual recognition deficit for Arabic digits. We conclude that their difficulties are best explained by an impaired representation of number magnitude or by an impaired access to this representation.
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Affiliation(s)
- Samuel Lepoittevin
- Psychological Sciences Research Institute, Université catholique de Louvain, Louvain-la-Neuve, Belgium
- Institute of NeuroScience, Université catholique de Louvain, Louvain-la-Neuve, Belgium
| | - Gaétane Keymolen
- Psychological Sciences Research Institute, Université catholique de Louvain, Louvain-la-Neuve, Belgium
| | - Michael Andres
- Psychological Sciences Research Institute, Université catholique de Louvain, Louvain-la-Neuve, Belgium
- Institute of NeuroScience, Université catholique de Louvain, Louvain-la-Neuve, Belgium
| | - Alice De Visscher
- Research Center in the Psychology of Cognition, Language, and Emotion (PsyCLE), Aix-Marseille Université, Marseille, France
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12
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Ciccione L, Sablé-Meyer M, Boissin E, Josserand M, Potier-Watkins C, Caparos S, Dehaene S. Trend judgment as a perceptual building block of graphicacy and mathematics, across age, education, and culture. Sci Rep 2023; 13:10266. [PMID: 37355745 PMCID: PMC10290641 DOI: 10.1038/s41598-023-37172-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2023] [Accepted: 06/17/2023] [Indexed: 06/26/2023] Open
Abstract
Data plots are widely used in science, journalism and politics, since they efficiently allow to depict a large amount of information. Graphicacy, the ability to understand graphs, has thus become a fundamental cultural skill comparable to literacy or numeracy. Here, we introduce a measure of intuitive graphicacy that assesses the perceptual ability to detect a trend in noisy scatterplots ("does this graph go up or down?"). In 3943 educated participants, responses vary as a sigmoid function of the t-value that a statistician would compute to detect a significant trend. We find a minimum level of core intuitive graphicacy even in unschooled participants living in remote Namibian villages (N = 87) and 6-year-old 1st-graders who never read a graph (N = 27). The sigmoid slope that we propose as a proxy of intuitive graphicacy increases with education and tightly correlates with statistical and mathematical knowledge, showing that experience contributes to refining graphical intuitions. Our tool, publicly available online, allows to quickly evaluate and formally quantify a perceptual building block of graphicacy.
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Affiliation(s)
- Lorenzo Ciccione
- Cognitive Neuroimaging Unit, CEA, INSERM, NeuroSpin Center, Université Paris-Saclay, 91191, Gif-sur-Yvette, France.
- Collège de France, Université Paris Sciences Lettres (PSL), 75005, Paris, France.
| | - Mathias Sablé-Meyer
- Cognitive Neuroimaging Unit, CEA, INSERM, NeuroSpin Center, Université Paris-Saclay, 91191, Gif-sur-Yvette, France
- Collège de France, Université Paris Sciences Lettres (PSL), 75005, Paris, France
| | - Esther Boissin
- LaPsyDÉ, CNRS, Université Paris Cité, 75005, Paris, France
| | - Mathilde Josserand
- Laboratoire Dynamique Du Langage, UMR 5596, Université Lumière Lyon 2, 69363, Lyon, France
| | | | - Serge Caparos
- DysCo Lab, Department of Psychology, Université Paris 8, 93526, Saint-Denis, France
- Human Sciences Section, Institut Universitaire de France, 75005, Paris, France
| | - Stanislas Dehaene
- Cognitive Neuroimaging Unit, CEA, INSERM, NeuroSpin Center, Université Paris-Saclay, 91191, Gif-sur-Yvette, France
- Collège de France, Université Paris Sciences Lettres (PSL), 75005, Paris, France
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13
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Spelke ES. Précis of What Babies Know. Behav Brain Sci 2023; 47:e120. [PMID: 37248696 DOI: 10.1017/s0140525x23002443] [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: 05/31/2023]
Abstract
Where does human knowledge begin? Research on human infants, children, adults, and nonhuman animals, using diverse methods from the cognitive, brain, and computational sciences, provides evidence for six early emerging, domain-specific systems of core knowledge. These automatic, unconscious systems are situated between perceptual systems and systems of explicit concepts and beliefs. They emerge early in infancy, guide children's learning, and function throughout life.
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Affiliation(s)
- Elizabeth S Spelke
- Department of Psychology, Center for Brains, Minds, and Machines, Harvard University, Cambridge, MA, USA
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14
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Gennari G, Dehaene S, Valera C, Dehaene-Lambertz G. Spontaneous supra-modal encoding of number in the infant brain. Curr Biol 2023; 33:1906-1915.e6. [PMID: 37071994 DOI: 10.1016/j.cub.2023.03.062] [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: 10/17/2022] [Revised: 01/30/2023] [Accepted: 03/21/2023] [Indexed: 04/20/2023]
Abstract
The core knowledge hypothesis postulates that infants automatically analyze their environment along abstract dimensions, including numbers. According to this view, approximate numbers should be encoded quickly, pre-attentively, and in a supra-modal manner by the infant brain. Here, we directly tested this idea by submitting the neural responses of sleeping 3-month-old infants, measured with high-density electroencephalography (EEG), to decoders designed to disentangle numerical and non-numerical information. The results show the emergence, in approximately 400 ms, of a decodable number representation, independent of physical parameters, that separates auditory sequences of 4 vs. 12 tones and generalizes to visual arrays of 4 vs. 12 objects. Thus, the infant brain contains a number code that transcends sensory modality, sequential or simultaneous presentation, and arousal state.
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Affiliation(s)
- Giulia Gennari
- Cognitive Neuroimaging Unit U992, Institut National de la Santé et de la Recherche Médicale, Commissariat à l'Énergie Atomique et aux Énergies Alternatives, Direction de la Recherche Fondamentale/Institut Joliot, Centre National de la Recherche Scientifique ERL9003, NeuroSpin Center, Université Paris-Saclay, 91191 Gif-sur-Yvette, France; Neuroscience Institute, New York University Grossman School of Medicine, New York, NY 10016, USA.
| | - Stanislas Dehaene
- Cognitive Neuroimaging Unit U992, Institut National de la Santé et de la Recherche Médicale, Commissariat à l'Énergie Atomique et aux Énergies Alternatives, Direction de la Recherche Fondamentale/Institut Joliot, Centre National de la Recherche Scientifique ERL9003, NeuroSpin Center, Université Paris-Saclay, 91191 Gif-sur-Yvette, France; Collège de France, Université Paris Sciences Lettres (PSL), 75005 Paris, France
| | - Chanel Valera
- Cognitive Neuroimaging Unit U992, Institut National de la Santé et de la Recherche Médicale, Commissariat à l'Énergie Atomique et aux Énergies Alternatives, Direction de la Recherche Fondamentale/Institut Joliot, Centre National de la Recherche Scientifique ERL9003, NeuroSpin Center, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
| | - Ghislaine Dehaene-Lambertz
- Cognitive Neuroimaging Unit U992, Institut National de la Santé et de la Recherche Médicale, Commissariat à l'Énergie Atomique et aux Énergies Alternatives, Direction de la Recherche Fondamentale/Institut Joliot, Centre National de la Recherche Scientifique ERL9003, NeuroSpin Center, Université Paris-Saclay, 91191 Gif-sur-Yvette, France
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15
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Mou Y, Zhang B, Hyde DC. Directionality in the interrelations between approximate number, verbal number, and mathematics in preschool-aged children. Child Dev 2023; 94:e67-e84. [PMID: 36528845 DOI: 10.1111/cdev.13879] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
A fundamental question in numerical development concerns the directional relation between an early-emerging non-verbal approximate number system (ANS) and culturally acquired verbal number and mathematics knowledge. Using path models on longitudinal data collected in preschool children (Mage = 3.86 years; N = 216; 99 males; 80.8% White; 10.8% Multiracial, 3.8% Latino; 1.9% Black; collected 2013-2017) over 1 year, this study showed that earlier verbal number knowledge was associated with later ANS precision (average β = .32), even after controlling for baseline differences in numerical, general cognitive, and language abilities. In contrast, earlier ANS precision was not associated with later verbal number knowledge (β = -.07) or mathematics abilities (average β = .10). These results suggest that learning about verbal numbers is associated with a sharpening of pre-existing non-verbal numerical abilities.
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Affiliation(s)
- Yi Mou
- Department of Psychology, Sun Yat-sen University, Guangzhou, People's Republic of China
| | - Bo Zhang
- School of Labor and Employment Relations, University of Illinois Urbana-Champaign, Champaign, Illinois, USA.,Department of Psychology, University of Illinois at Urbana-Champaign, Champaign, Illinois, USA
| | - Daniel C Hyde
- Department of Psychology, University of Illinois at Urbana-Champaign, Champaign, Illinois, USA
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16
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Aulet LS, Lourenco SF. No intrinsic number bias: Evaluating the role of perceptual discriminability in magnitude categorization. Dev Sci 2023; 26:e13305. [PMID: 35851738 DOI: 10.1111/desc.13305] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2021] [Revised: 04/13/2022] [Accepted: 07/05/2022] [Indexed: 01/29/2023]
Abstract
Accumulating evidence suggests that there is a spontaneous preference for numerical, compared to non-numerical (e.g., cumulative surface area), information. However, given a paucity of research on the perception of non-numerical magnitudes, it is unclear whether this preference reflects a specific bias towards number, or a general bias towards the more perceptually discriminable dimension (i.e., number). Here, we found that when the number and area of visual dot displays were matched in mathematical ratio, number was more perceptually discriminable than area in both adults and children. Moreover, both adults and children preferentially categorized these ratio-matched stimuli based on number, consistent with previous work. However, when number and area were matched in perceptual discriminability, a different pattern of results emerged. In particular, children preferentially categorized stimuli based on area, suggesting that children's previously observed number bias may be due to a mismatch in the perceptual discriminability of number and area, not an intrinsic salience of number. Interestingly, adults continued to categorize the displays on the basis of number. Altogether, these findings suggest a dominant role for area during childhood, refuting the claim that number is inherently and uniquely salient. Yet they also reveal an increased salience of number that emerges over development. Potential explanations for this developmental shift are discussed. RESEARCH HIGHLIGHTS: Previous work found that children and adults spontaneously categorized dot array stimuli by number, over other magnitudes (e.g., area), suggesting number is uniquely salient. However, here we found that when number and area were matched by ratio, as in prior work, number was significantly more perceptually discriminable than area. When number and area were made equally discriminable ('perceptually-matched'), children, contra adults, spontaneously categorized stimuli by area over number (and other non-numerical magnitudes). These findings suggest that area may be uniquely salient early in childhood, with the previously-observed number bias not emerging until later in development.
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Affiliation(s)
- Lauren S Aulet
- Department of Psychology, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA
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17
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Nakai T, Girard C, Longo L, Chesnokova H, Prado J. Cortical representations of numbers and nonsymbolic quantities expand and segregate in children from 5 to 8 years of age. PLoS Biol 2023; 21:e3001935. [PMID: 36603025 PMCID: PMC9815645 DOI: 10.1371/journal.pbio.3001935] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2022] [Accepted: 11/30/2022] [Indexed: 01/06/2023] Open
Abstract
Number symbols, such as Arabic numerals, are cultural inventions that have transformed human mathematical skills. Although their acquisition is at the core of early elementary education in children, it remains unknown how the neural representations of numerals emerge during that period. It is also unclear whether these relate to an ontogenetically earlier sense of approximate quantity. Here, we used multivariate fMRI adaptation coupled with within- and between-format machine learning to probe the cortical representations of Arabic numerals and approximate nonsymbolic quantity in 89 children either at the beginning (age 5) or four years into formal education (age 8). Although the cortical representations of both numerals and nonsymbolic quantities expanded from age 5 to age 8, these representations also segregated with learning and development. Specifically, a format-independent neural representation of quantity was found in the right parietal cortex, but only for 5-year-olds. These results are consistent with the so-called symbolic estrangement hypothesis, which argues that the relation between symbolic and nonsymbolic quantity weakens with exposure to formal mathematics in children.
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Affiliation(s)
- Tomoya Nakai
- Lyon Neuroscience Research Center (CRNL), INSERM U1028—CNRS UMR5292, University of Lyon, Bron, France
- * E-mail: (TN); (JP)
| | - Cléa Girard
- Lyon Neuroscience Research Center (CRNL), INSERM U1028—CNRS UMR5292, University of Lyon, Bron, France
| | - Léa Longo
- Lyon Neuroscience Research Center (CRNL), INSERM U1028—CNRS UMR5292, University of Lyon, Bron, France
| | - Hanna Chesnokova
- Lyon Neuroscience Research Center (CRNL), INSERM U1028—CNRS UMR5292, University of Lyon, Bron, France
| | - Jérôme Prado
- Lyon Neuroscience Research Center (CRNL), INSERM U1028—CNRS UMR5292, University of Lyon, Bron, France
- * E-mail: (TN); (JP)
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18
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Anobile G, Bartoli M, Masi G, Tacchi A, Tinelli F. Math difficulties in attention deficit hyperactivity disorder do not originate from the visual number sense. Front Hum Neurosci 2022; 16:949391. [DOI: 10.3389/fnhum.2022.949391] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2022] [Accepted: 10/12/2022] [Indexed: 01/29/2023] Open
Abstract
There is ample evidence from literature and clinical practice indicating mathematical difficulties in individuals with ADHD, even when there is no concomitant diagnosis of developmental dyscalculia. What factors underlie these difficulties is still an open question. Research on dyscalculia and neurotypical development suggests visual perception of numerosity (the number sense) as a building block for math learning. Participants with lower numerosity estimation thresholds (higher precision) are often those with higher math capabilities. Strangely, the role of numerosity perception in math skills in ADHD has been neglected, leaving open the question whether math difficulties in ADHD also originate from a deficitary visual number sense. In the current study we psychophysically measured numerosity thresholds and accuracy in a sample of children/adolescents with ADHD, but not concomitant dyscalculia (N = 20, 8–16 years). Math abilities were also measured by tasks indexing different mathematical competences. Numerosity performance and math scores were then compared to those obtained from an age-matched control group (N = 20). Bayesian statistics indicated no difference between ADHD and controls on numerosity perception, despite many of the symbolic math tasks being impaired in participants with ADHD. Moreover, the math deficits showed by the group with ADHD remained substantial even when numerosity thresholds were statistically regressed out. Overall, these results indicate that math difficulties in ADHD are unlikely to originate from an impaired visual number sense.
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19
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Bachman HJ, Miller P, Elliott L, Duong S, Libertus M, Votruba-Drzal E. Associations among socioeconomic status and preschool-aged children's, number skills, and spatial skills: The role of executive function. J Exp Child Psychol 2022; 221:105453. [PMID: 35605526 DOI: 10.1016/j.jecp.2022.105453] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2021] [Revised: 02/24/2022] [Accepted: 04/17/2022] [Indexed: 01/29/2023]
Abstract
Extensive literature has documented socioeconomic status (SES) disparities in young children's standardized math achievement, which primarily reflect differences in basic number and arithmetic skills. In addition, growing evidence indicates that direct assessments of executive function (EF) both predict standardized math achievement and mediate SES differences in standardized math tests. However, early spatial skills and children's approximate number system (ANS) acuity, critical components of later math competence, have been largely absent in this past research. The current study examined SES associations with multiple direct assessments of early ANS, cardinality, and spatial skills, as well as standardized math achievement, in a socioeconomically diverse sample of 4-year-old children (N = 149). Structural equation modeling revealed SES effect sizes of .21 for geometric sensitivity skills, .23 for ANS acuity, .39 for cardinality skills, and .28 for standardized math achievement. Furthermore, relations between SES and children's spatial skills, ANS acuity, cardinality, and standardized math skills were mediated by a composite measure of children's EF skills. Implications of pervasive SES disparities across multiple domains of early math development, as well as the mitigating role of EF, are discussed.
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Affiliation(s)
- Heather J Bachman
- Department of Health and Human Development, University of Pittsburgh, Pittsburgh, PA 15260, USA; Learning Research and Development Center, University of Pittsburgh, Pittsburgh, PA 15260, USA.
| | - Portia Miller
- Learning Research and Development Center, University of Pittsburgh, Pittsburgh, PA 15260, USA
| | - Leanne Elliott
- Learning Research and Development Center, University of Pittsburgh, Pittsburgh, PA 15260, USA
| | - Shirley Duong
- Learning Research and Development Center, University of Pittsburgh, Pittsburgh, PA 15260, USA; Department of Psychology, University of Pittsburgh, Pittsburgh, PA 15260, USA
| | - Melissa Libertus
- Learning Research and Development Center, University of Pittsburgh, Pittsburgh, PA 15260, USA; Department of Psychology, University of Pittsburgh, Pittsburgh, PA 15260, USA
| | - Elizabeth Votruba-Drzal
- Learning Research and Development Center, University of Pittsburgh, Pittsburgh, PA 15260, USA; Department of Psychology, University of Pittsburgh, Pittsburgh, PA 15260, USA
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20
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Izard V, Pica P, Spelke ES. Visual foundations of Euclidean geometry. Cogn Psychol 2022; 136:101494. [PMID: 35751917 DOI: 10.1016/j.cogpsych.2022.101494] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2019] [Revised: 05/10/2022] [Accepted: 06/06/2022] [Indexed: 01/29/2023]
Abstract
Geometry defines entities that can be physically realized in space, and our knowledge of abstract geometry may therefore stem from our representations of the physical world. Here, we focus on Euclidean geometry, the geometry historically regarded as "natural". We examine whether humans possess representations describing visual forms in the same way as Euclidean geometry - i.e., in terms of their shape and size. One hundred and twelve participants from the U.S. (age 3-34 years), and 25 participants from the Amazon (age 5-67 years) were asked to locate geometric deviants in panels of 6 forms of variable orientation. Participants of all ages and from both cultures detected deviant forms defined in terms of shape or size, while only U.S. adults drew distinctions between mirror images (i.e. forms differing in "sense"). Moreover, irrelevant variations of sense did not disrupt the detection of a shape or size deviant, while irrelevant variations of shape or size did. At all ages and in both cultures, participants thus retained the same properties as Euclidean geometry in their analysis of visual forms, even in the absence of formal instruction in geometry. These findings show that representations of planar visual forms provide core intuitions on which humans' knowledge in Euclidean geometry could possibly be grounded.
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Affiliation(s)
- Véronique Izard
- Université Paris Cité, CNRS, Integrative Neuroscience and Cognition Center, F-75006 Paris, France
- Department of Psychology, Harvard University, 33 Kirkland St, Cambridge, MA 02138, USA.
| | - Pierre Pica
- Instituto do Cérebro, Universidade Federal do Rio grande do Norte, R. do Horto, Lagoa Nova, Natal, RN 59076-550, Brazil
- UMR 7023, Structures Formelles du Langage, Université Paris 8, 2 rue de la Liberté, 93200 Saint-Denis, France
| | - Elizabeth S Spelke
- Department of Psychology, Harvard University, 33 Kirkland St, Cambridge, MA 02138, USA; NSF-STC Center for Brains, Minds and Machines, 43 Vassar St, Cambridge, MA 02139, USA
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21
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Liang X, Yin Y, Kang J, Wang L. Can training in the approximate number system improve the informal mathematics ability of preschoolers? Acta Psychol (Amst) 2022; 228:103638. [PMID: 35690026 DOI: 10.1016/j.actpsy.2022.103638] [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: 04/21/2021] [Revised: 05/28/2022] [Accepted: 05/31/2022] [Indexed: 01/29/2023] Open
Abstract
Recent studies show that comparison or arithmetic training in the approximate number system (ANS) can improve the early mathematics ability of preschool children. However, no studies have compared the training effects of ANS comparison training with those of ANS arithmetic training on the early mathematics ability of preschool children. The current study pseudorandomly assigned 87 children aged 4-5 years to one of three training groups (the ANS comparison, ANS arithmetic, and control groups) for 4 weeks of training. The results showed that compared with the control group, the ANS comparison training and ANS arithmetic training equally improved the ANS acuity and informal mathematics ability of preschool children. In addition, the study found that there may be a bidirectional causal relationship between ANS and mathematics in preschoolers, but this relationship needs to be further investigated using longitudinal studies. Taken together, these findings emphasize the importance of ANS-based training in improving preschoolers' ANS acuity and informal mathematics ability before formal school enrollment.
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Affiliation(s)
- Xiao Liang
- School of Psychology, Northeast Normal University, No. 5268 Renmin Street, 130024 Changchun, China; Jilin Provincial Experimental Teaching Demonstration Center of Psychology, Northeast Normal University, Changchun, China.
| | - Yueyang Yin
- School of Education Science, Jiangsu Normal University, No.101 Shanghai road, tongshan new district, 221116 Xuzhou, China.
| | - Jingmei Kang
- School of Psychology, Northeast Normal University, No. 5268 Renmin Street, 130024 Changchun, China; Jilin Provincial Experimental Teaching Demonstration Center of Psychology, Northeast Normal University, Changchun, China.
| | - Lijuan Wang
- School of Psychology, Northeast Normal University, No. 5268 Renmin Street, 130024 Changchun, China; Jilin Provincial Experimental Teaching Demonstration Center of Psychology, Northeast Normal University, Changchun, China.
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22
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An undeniable interplay: Both numerosity and visual features affect estimation of non-symbolic stimuli. Cognition 2022; 222:104944. [DOI: 10.1016/j.cognition.2021.104944] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2019] [Revised: 09/02/2021] [Accepted: 10/19/2021] [Indexed: 01/29/2023]
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23
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Ciccione L, Sablé-Meyer M, Dehaene S. Analyzing the misperception of exponential growth in graphs. Cognition 2022; 225:105112. [PMID: 35366484 DOI: 10.1016/j.cognition.2022.105112] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2021] [Revised: 01/11/2022] [Accepted: 03/23/2022] [Indexed: 01/29/2023]
Abstract
Exponential growth is frequently underestimated, an error that can have a heavy social cost in the context of epidemics. To clarify its origins, we measured the human capacity (N = 521) to extrapolate linear and exponential trends in scatterplots. Four factors were manipulated: the function underlying the data (linear or exponential), the response modality (pointing or venturing a number), the scale on the y axis (linear or logarithmic), and the amount of noise in the data. While linear extrapolation was precise and largely unbiased, we observed a consistent underestimation of noisy exponential growth, present for both pointing and numerical responses. A biased ideal-observer model could explain these data as an occasional misperception of noisy exponential graphs as quadratic curves. Importantly, this underestimation bias was mitigated by participants' math knowledge, by using a logarithmic scale, and by presenting a noiseless exponential curve rather than a noisy data plot, thus suggesting concrete avenues for interventions.
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Affiliation(s)
- Lorenzo Ciccione
- Cognitive Neuroimaging Unit, CEA, INSERM, Université Paris-Saclay, NeuroSpin Center, 91191 Gif/Yvette, France; Collège de France, Université Paris Sciences Lettres (PSL), 11 Place Marcelin Berthelot, 75005 Paris, France.
| | - Mathias Sablé-Meyer
- Cognitive Neuroimaging Unit, CEA, INSERM, Université Paris-Saclay, NeuroSpin Center, 91191 Gif/Yvette, France; Collège de France, Université Paris Sciences Lettres (PSL), 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Stanislas Dehaene
- Cognitive Neuroimaging Unit, CEA, INSERM, Université Paris-Saclay, NeuroSpin Center, 91191 Gif/Yvette, France; Collège de France, Université Paris Sciences Lettres (PSL), 11 Place Marcelin Berthelot, 75005 Paris, France
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24
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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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25
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Hutchison JE, Ansari D, Zheng S, De Jesus S, Lyons IM. Extending ideas of numerical order beyond the count-list from kindergarten to first grade. Cognition 2022; 223:105019. [PMID: 35121431 DOI: 10.1016/j.cognition.2022.105019] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2021] [Revised: 12/22/2021] [Accepted: 01/06/2022] [Indexed: 01/29/2023]
Abstract
Ordinal processing plays a fundamental role in both the representation and manipulation of symbolic numbers. As such, it is important to understand how children come to develop a sense of ordinality in the first place. The current study examines the role of the count-list in the development of ordinal knowledge through the investigation of two research questions: (1) Do K-1 children struggle to extend the notion of numerical order beyond the count-list, and if so (2) does this extension develop incrementally or manifest as a qualitative re-organization of how children recognize the ordinality of numerical sequences. Overall, we observed that although young children reliably identified adjacent ordered sequences (i.e., those that match the count-list; '2-3-4') as being in the correct ascending order, they performed significantly below chance on non-adjacent ordered trials (i.e., those that do not match the count-list but are in the correct order; '2-4-6') from the beginning of kindergarten to the end of first grade. Further, both qualitative and quantitative analyses supported the conclusion that the ability to extend notions of ordinality beyond the count-list emerged as a conceptual shift in ordinal understanding rather than through incremental improvements. These findings are the first to suggest that the ability to extend notions of ordinality beyond the count-list to include non-adjacent numbers is non-trivial and reflects a significant developmental hurdle that most children must overcome in order to develop a mature sense of ordinality.
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Affiliation(s)
- Jane E Hutchison
- Georgetown University, Department of Psychology, United States of America
| | - Daniel Ansari
- University of Western Ontario, Department of Psychology and Brain & Mind Institute, Canada
| | - Samuel Zheng
- Toronto District School Board, Research and Development, Canada
| | | | - Ian M Lyons
- Georgetown University, Department of Psychology, United States of America.
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26
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Wilkey ED, Shanley L, Sabb F, Ansari D, Cohen JC, Men V, Heller NA, Clarke B. Sharpening, focusing, and developing: A study of change in nonsymbolic number comparison skills and math achievement in 1st grade. Dev Sci 2021; 25:e13194. [PMID: 34800342 DOI: 10.1111/desc.13194] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2020] [Revised: 10/06/2021] [Accepted: 11/08/2021] [Indexed: 01/29/2023]
Abstract
Children's ability to discriminate nonsymbolic number (e.g., the number of items in a set) is a commonly studied predictor of later math skills. Number discrimination improves throughout development, but what drives this improvement is unclear. Competing theories suggest that it may be due to a sharpening numerical representation or an improved ability to pay attention to number and filter out non-numerical information. We investigate this issue by studying change in children's performance (N = 65) on a nonsymbolic number comparison task, where children decide which of two dot arrays has more dots, from the middle to the end of 1st grade (mean age at time 1 = 6.85 years old). In this task, visual properties of the dot arrays such as surface area are either congruent (the more numerous array has more surface area) or incongruent. Children rely more on executive functions during incongruent trials, so improvements in each congruency condition provide information about the underlying cognitive mechanisms. We found that accuracy rates increased similarly for both conditions, indicating a sharpening sense of numerical magnitude, not simply improved attention to the numerical task dimension. Symbolic number skills predicted change in congruent trials, but executive function did not predict change in either condition. No factor predicted change in math achievement. Together, these findings suggest that nonsymbolic number processing undergoes development related to existing symbolic number skills, development that appears not to be driving math gains during this period. Children's ability to discriminate nonsymbolic number improves throughout development. Competing theories suggest improvement due to sharpening magnitude representations or changes in attention and inhibition. The current study investigates change in nonsymbolic number comparison performance during first grade and whether symbolic number skills, math skills, or executive function predict change. Children's performance increased across visual control conditions (i.e., congruent or incongruent with number) suggesting an overall sharpening of number processing. Symbolic number skills predicted change in nonsymbolic number comparison performance.
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Affiliation(s)
- Eric D Wilkey
- Brain & Mind Institute, Western University, London, Ontario, Canada
| | - Lina Shanley
- Center on Teaching and Learning, University of Oregon, Eugene, Oregon, USA
| | - Fred Sabb
- Center on Teaching and Learning, University of Oregon, Eugene, Oregon, USA
| | - Daniel Ansari
- Brain & Mind Institute, Western University, London, Ontario, Canada
| | - Jason C Cohen
- Center on Teaching and Learning, University of Oregon, Eugene, Oregon, USA
| | - Virany Men
- Center on Teaching and Learning, University of Oregon, Eugene, Oregon, USA
| | - Nicole A Heller
- Center on Teaching and Learning, University of Oregon, Eugene, Oregon, USA
| | - Ben Clarke
- Center on Teaching and Learning, University of Oregon, Eugene, Oregon, USA
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27
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Messina A, Potrich D, Schiona I, Sovrano VA, Vallortigara G. The Sense of Number in Fish, with Particular Reference to Its Neurobiological Bases. Animals (Basel) 2021; 11:ani11113072. [PMID: 34827804 PMCID: PMC8614421 DOI: 10.3390/ani11113072] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2021] [Revised: 10/13/2021] [Accepted: 10/22/2021] [Indexed: 01/29/2023] Open
Abstract
Simple Summary The ability to deal with quantity, both discrete (numerosities) and continuous (spatial or temporal extent) developed from an evolutionarily conserved system for approximating numerical magnitude. Non-symbolic number cognition based on an approximate sense of magnitude has been documented in a variety of vertebrate species, including fish. Fish, in particular zebrafish, are widely used as models for the investigation of the genetics and molecular mechanisms of behavior, and thus may be instrumental to development of a neurobiology of number cognition. We review here the behavioural studies that have permitted to identify numerical abilities in fish, and the current status of the research related to the neurobiological bases of these abilities with special reference to zebrafish. Combining behavioural tasks with molecular genetics, molecular biology and confocal microscopy, a role of the retina and optic tectum in the encoding of continuous magnitude in larval zebrafish has been reported, while the thalamus and the dorso-central subdivision of pallium in the encoding of discrete magnitude (number) has been documented in adult zebrafish. Research in fish, in particular zebrafish, may reveal instrumental for identifying and characterizing the molecular signature of neurons involved in quantity discrimination processes of all vertebrates, including humans. Abstract It is widely acknowledged that vertebrates can discriminate non-symbolic numerosity using an evolutionarily conserved system dubbed Approximate Number System (ANS). Two main approaches have been used to assess behaviourally numerosity in fish: spontaneous choice tests and operant training procedures. In the first, animals spontaneously choose between sets of biologically-relevant stimuli (e.g., conspecifics, food) differing in quantities (smaller or larger). In the second, animals are trained to associate a numerosity with a reward. Although the ability of fish to discriminate numerosity has been widely documented with these methods, the molecular bases of quantities estimation and ANS are largely unknown. Recently, we combined behavioral tasks with molecular biology assays (e.g c-fos and egr1 and other early genes expression) showing that the thalamus and the caudal region of dorso-central part of the telencephalon seem to be activated upon change in numerousness in visual stimuli. In contrast, the retina and the optic tectum mainly responded to changes in continuous magnitude such as stimulus size. We here provide a review and synthesis of these findings.
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Affiliation(s)
- Andrea Messina
- Centre for Mind/Brain Sciences, University of Trento, 38068 Rovereto, Italy; (D.P.); (I.S.); (V.A.S.)
- Correspondence: (A.M.); (G.V.)
| | - Davide Potrich
- Centre for Mind/Brain Sciences, University of Trento, 38068 Rovereto, Italy; (D.P.); (I.S.); (V.A.S.)
| | - Ilaria Schiona
- Centre for Mind/Brain Sciences, University of Trento, 38068 Rovereto, Italy; (D.P.); (I.S.); (V.A.S.)
| | - Valeria Anna Sovrano
- Centre for Mind/Brain Sciences, University of Trento, 38068 Rovereto, Italy; (D.P.); (I.S.); (V.A.S.)
- Department of Psychology and Cognitive Science, University of Trento, 38068 Rovereto, Italy
| | - Giorgio Vallortigara
- Centre for Mind/Brain Sciences, University of Trento, 38068 Rovereto, Italy; (D.P.); (I.S.); (V.A.S.)
- Correspondence: (A.M.); (G.V.)
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Wang L, Liang X, Yin Y, Kang J. Bidirectional Mapping Between the Symbolic Number System and the Approximate Number System. Exp Psychol 2021; 68:243-263. [DOI: 10.1027/1618-3169/a000533] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Abstract. Previous studies have discussed the symmetry of bidirectional mapping between approximate number system (ANS) and symbolic number system (SNS). However, these studies neglected the essential significance of bidirectional mapping in the development of numerical cognition. That is, with age, the connection strength between the ANS and SNS in ANS-SNS mapping could be higher than that in SNS-ANS mapping. Therefore, this study attempted to explore the symmetry of bidirectional mapping by examining whether the connection between the ANS and SNS is the same. Using two types of dot array materials (extensive and intensive) and sequence priming paradigms, this study found a stable negative priming effect in the ANS-SNS priming task, but no priming effect in the SNS-ANS priming task. In addition, although sensory cues (extensive and intensive) could affect performance in the ANS-SNS mapping task, these cues did not affect performance in the ANS-SNS priming task. In general, this study provides valuable insight into the symmetry of bidirectional mapping.
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Affiliation(s)
- Lijuan Wang
- School of Psychology, Northeast Normal University, Changchun, Jilin, PR China
| | - Xiao Liang
- School of Psychology, Northeast Normal University, Changchun, Jilin, PR China
| | - Yueyang Yin
- School of Psychology, Northeast Normal University, Changchun, Jilin, PR China
| | - Jingmei Kang
- School of Psychology, Northeast Normal University, Changchun, Jilin, PR China
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Number is not just an illusion: Discrete numerosity is encoded independently from perceived size. Psychon Bull Rev 2021; 29:123-133. [PMID: 34379268 PMCID: PMC8356546 DOI: 10.3758/s13423-021-01979-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 06/26/2021] [Indexed: 01/29/2023]
Abstract
While seminal theories suggest that nonsymbolic visual numerosity is mainly extracted from segmented items, more recent views advocate that numerosity cannot be processed independently of nonnumeric continuous features confounded with the numerical set (i.e., such as the density, the convex hull, etc.). To disentangle these accounts, here we employed two different visual illusions presented in isolation or in a merged condition (e.g., combining the effects of the two illusions). In particular, in a number comparison task, we concurrently manipulated both the perceived object segmentation by connecting items with Kanizsa-like illusory lines, and the perceived convex-hull/density of the set by embedding the stimuli in a Ponzo illusion context, keeping constant other low-level features. In Experiment 1, the two illusions were manipulated in a compatible direction (i.e., both triggering numerical underestimation), whereas in Experiment 2 they were manipulated in an incompatible direction (i.e., with the Ponzo illusion triggering numerical overestimation and the Kanizsa illusion numerical underestimation). Results from psychometric functions showed that, in the merged condition, the biases of each illusion summated (i.e., largest underestimation as compared with the conditions in which illusions were presented in isolation) in Experiment 1, while they averaged and competed against each other in Experiment 2. These findings suggest that discrete nonsymbolic numerosity can be extracted independently from continuous magnitudes. They also point to the need of more comprehensive theoretical views accounting for the operations by which both discrete elements and continuous variables are computed and integrated by the visual system.
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30
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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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31
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Saga M, Rkhaila A, Ounine K, Oubaha D. Developmental dyscalculia: the progress of cognitive modeling in the field of numerical cognition deficits for children. APPLIED NEUROPSYCHOLOGY-CHILD 2021; 11:904-914. [PMID: 34320331 DOI: 10.1080/21622965.2021.1955679] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
The study of dyscalculia requires an analysis of the current developed hypotheses which describe the cognitive mechanisms involved in this neurodevelopmental disorder. The objective of our review is to determine any progress in modeling developmental dyscalculia. The first hypothesis suggests that dyscalculia is the consequence of a specific deficit level number on the precise number system and the approximate system. Then, the second hypothesis states that developmental dyscalculia is linked to a failure to process non-symbolic representations of numbers. On the other hand, the third suggests that dyscalculia is caused by a lack of access to numerical quantities from symbols. However, the last hypothesis asserts that developmental dyscalculia is linked to general deficits. All these hypotheses are compatible with recent neuroimaging results and raise new horizons for experimentation, which will allow the development of precise diagnostic tools and the improvement of intervention strategies and the remediation of developmental dyscalculia.
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Affiliation(s)
- Mouhatti Saga
- Faculty of Sciences, Ibn Tofail University, Kenitra, Morocco
| | - Amine Rkhaila
- Faculty of Sciences, Ibn Tofail University, Kenitra, Morocco
| | - Khadija Ounine
- Faculty of Sciences, Ibn Tofail University, Kenitra, Morocco
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32
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Castaldi E, Arrighi R, Cicchini GM, Andolfi A, Maduli G, Burr DC, Anobile G. Perception of geometric sequences and numerosity both predict formal geometric competence in primary school children. Sci Rep 2021; 11:14243. [PMID: 34244592 PMCID: PMC8271001 DOI: 10.1038/s41598-021-93710-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2021] [Accepted: 06/21/2021] [Indexed: 01/29/2023] Open
Abstract
While most animals have a sense of number, only humans have developed symbolic systems to describe and organize mathematical knowledge. Some studies suggest that human arithmetical knowledge may be rooted in an ancient mechanism dedicated to perceiving numerosity, but it is not known if formal geometry also relies on basic, non-symbolic mechanisms. Here we show that primary-school children who spontaneously detect and predict geometrical sequences (non-symbolic geometry) perform better in school-based geometry tests indexing formal geometric knowledge. Interestingly, numerosity discrimination thresholds also predicted and explained a specific portion of variance of formal geometrical scores. The relation between these two non-symbolic systems and formal geometry was not explained by age or verbal reasoning skills. Overall, the results are in line with the hypothesis that some human-specific, symbolic systems are rooted in non-symbolic mechanisms.
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Affiliation(s)
- Elisa Castaldi
- Department of Translational Research and New Technologies in Medicine and Surgery, University of Pisa, 56126, Pisa, Italy.,Department of Neuroscience, Psychology, Pharmacology, and Child Health, University of Florence, 50139, Florence, Italy
| | - Roberto Arrighi
- Department of Neuroscience, Psychology, Pharmacology, and Child Health, University of Florence, 50139, Florence, Italy.
| | | | - Arianna Andolfi
- Department of Neuroscience, Psychology, Pharmacology, and Child Health, University of Florence, 50139, Florence, Italy
| | - Giuseppe Maduli
- Department of Neuroscience, Psychology, Pharmacology, and Child Health, University of Florence, 50139, Florence, Italy
| | - David C Burr
- Department of Neuroscience, Psychology, Pharmacology, and Child Health, University of Florence, 50139, Florence, Italy.,CNR Neuroscience Institute, 56100, Pisa, Italy
| | - Giovanni Anobile
- Department of Neuroscience, Psychology, Pharmacology, and Child Health, University of Florence, 50139, Florence, Italy
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Kanjlia S, Feigenson L, Bedny M. Neural basis of approximate number in congenital blindness. Cortex 2021; 142:342-356. [PMID: 34352637 DOI: 10.1016/j.cortex.2021.06.004] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2020] [Revised: 01/06/2021] [Accepted: 06/01/2021] [Indexed: 01/29/2023]
Abstract
Although humans are unique among animals in their ability to manipulate symbolic numbers, we share with other species an approximate number sense that allows us to estimate and compare the number of objects or events in a set, such as the number of apples in a tree. Our ability to discriminate the numerosity of two sets decreases as the ratio between them becomes smaller (e.g., 8 vs 16 items is harder to discriminate than 8 vs 32 items). The intraparietal sulcus (IPS) plays a key role in this numerical approximation. Neuronal populations within the IPS code for numerosity, with stimuli of different numerosities eliciting discriminable spatial patterns of activity. The developmental origins of these IPS number representations are not known. Here, we tested the hypothesis that representations of number in the IPS require visual experience with object sets, by working with individuals blind from birth. While undergoing fMRI, congenitally blind (n = 17) and blindfolded sighted (n = 25) participants judged which of two sequences of beeps was more numerous. In both sighted and blind individuals, patterns of activity in the IPS discriminated among different numerosities (4, 8, 16 vs 32), with better discrimination in the IPS of the blind group. In both groups, decoding performance decreased as the ratio between numerosities decreased (e.g., 8 vs 16 was less discriminable than 8 vs 32). These findings suggest that number representations in the IPS either have innate precursors, or that auditory or tactile experience with sets is sufficient for typical development.
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Affiliation(s)
- Shipra Kanjlia
- Department of Psychology, Carnegie Mellon University, USA; Department of Psychological and Brain Sciences, Johns Hopkins University, USA.
| | - Lisa Feigenson
- Department of Psychological and Brain Sciences, Johns Hopkins University, USA
| | - Marina Bedny
- Department of Psychological and Brain Sciences, Johns Hopkins University, USA
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34
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Malykh S, Kuzmina Y, Tikhomirova T. Developmental Changes in ANS Precision Across Grades 1-9: Different Patterns of Accuracy and Reaction Time. Front Psychol 2021; 12:589305. [PMID: 33841232 PMCID: PMC8024480 DOI: 10.3389/fpsyg.2021.589305] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2020] [Accepted: 03/03/2021] [Indexed: 01/29/2023] Open
Abstract
The main aim of this study was to analyze the patterns of changes in Approximate Number Sense (ANS) precision from grade 1 (mean age: 7.84 years) to grade 9 (mean age: 15.82 years) in a sample of Russian schoolchildren. To fulfill this aim, the data from a longitudinal study of two cohorts of children were used. The first cohort was assessed at grades 1-5 (elementary school education plus the first year of secondary education), and the second cohort was assessed at grades 5-9 (secondary school education). ANS precision was assessed by accuracy and reaction time (RT) in a non-symbolic comparison test ("blue-yellow dots" test). The patterns of change were estimated via mixed-effect growth models. The results revealed that in the first cohort, the average accuracy increased from grade 1 to grade 5 following a non-linear pattern and that the rate of growth slowed after grade 3 (7-9 years old). The non-linear pattern of changes in the second cohort indicated that accuracy started to increase from grade 7 to grade 9 (13-15 years old), while there were no changes from grade 5 to grade 7. However, the RT in the non-symbolic comparison test decreased evenly from grade 1 to grade 7 (7-13 years old), and the rate of processing non-symbolic information tended to stabilize from grade 7 to grade 9. Moreover, the changes in the rate of processing non-symbolic information were not explained by the changes in general processing speed. The results also demonstrated that accuracy and RT were positively correlated across all grades. These results indicate that accuracy and the rate of non-symbolic processing reflect two different processes, namely, the maturation and development of a non-symbolic representation system.
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Affiliation(s)
- Sergey Malykh
- Department of Psychology, Lomonosov Moscow State University, Moscow, Russia.,Psychological Institute of Russian Academy of Education, Moscow, Russia
| | - Yulia Kuzmina
- Psychological Institute of Russian Academy of Education, Moscow, Russia
| | - Tatiana Tikhomirova
- Department of Psychology, Lomonosov Moscow State University, Moscow, Russia.,Psychological Institute of Russian Academy of Education, Moscow, Russia
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35
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Attentional bias induced by stimulus control (ABC) impairs measures of the approximate number system. Atten Percept Psychophys 2021; 83:1684-1698. [PMID: 33462769 PMCID: PMC8084806 DOI: 10.3758/s13414-020-02229-2] [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] [Accepted: 12/02/2020] [Indexed: 01/29/2023]
Abstract
Pervasive congruency effects characterize approximate number discrimination tasks. Performance is better on congruent (the more numerous stimulus consists of objects of larger size that occupy a larger area) than on incongruent (where the opposite holds) items. The congruency effects typically occur when controlling for nonnumeric variables such as cumulative area. Furthermore, only performance on incongruent stimuli seems to predict math abilities. Here, we present evidence for an attentional-bias induced by stimulus control (ABC) where preattentive features such as item size reflexively influence decisions, which can explain these congruency effects. In three experiments, we tested predictions derived from the ABC. In Experiment 1, as predicted, we found that manipulation of size introduced congruency effects and eliminated the correlation with math ability for congruent items. However, performance on incongruent items and neutral, nonmanipulated items were still predictive of math ability. A negative correlation between performance on congruent and incongruent items even indicated that they measure different underlying constructs. Experiment 2 demonstrated, in line with the ABC account, that increasing presentation time reduced congruency effects. By directly measuring overt attention using eye-tracking, Experiment 3 revealed that people direct their first gaze toward the array with items of larger individual size, biasing them towards these arrays. The ABC explains why the relation between performance on approximate number discrimination tasks and math achievement has been fragile and suggests that stimulus control manipulations have contaminated the results. We discuss the importance of using stimuli that are representative of the environment.
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36
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Decarli G, Paris E, Tencati C, Nardelli C, Vescovi M, Surian L, Piazza M. Impaired large numerosity estimation and intact subitizing in developmental dyscalculia. PLoS One 2020; 15:e0244578. [PMID: 33382740 PMCID: PMC7774972 DOI: 10.1371/journal.pone.0244578] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2020] [Accepted: 12/13/2020] [Indexed: 01/29/2023] Open
Abstract
It is believed that the approximate estimation of large sets and the exact quantification of small sets (subitizing) are supported by two different systems, the Approximate Number System (ANS) and Object Tracking System (OTS), respectively. It is a current matter of debate whether they are both impaired in developmental dyscalculia (DD), a specific learning disability in symbolic number processing and calculation. Here we tackled this question by asking 32 DD children and 32 controls to perform a series of tasks on visually presented sets, including exact enumeration of small sets as well as comparison of large, uncountable sets. In children with DD, we found poor sensitivity in processing large numerosities, but we failed to find impairments in the exact enumeration of sets within the subitizing range. We also observed deficits in visual short-term memory skills in children with dyscalculia that, however, did not account for their low ANS acuity. Taken together, these results point to a dissociation between quantification skills in dyscalculia, they highlight a link between DD and low ANS acuity and provide support for the notion that DD is a multifaceted disability that covers multiple cognitive skills.
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Affiliation(s)
- Gisella Decarli
- Department of Psychology and Cognitive Science, University of Trento, Rovereto, Italy
- Department of General Psychology, University of Padova, Padova, Italy
| | - Emanuela Paris
- Servizio di Logopedia, Azienda Pubblica di Servizi alla Persona “Beato de Tschiderer”, Trento, Italy
| | - Chiara Tencati
- Servizio di Logopedia, Azienda Pubblica di Servizi alla Persona “Beato de Tschiderer”, Trento, Italy
| | - Chiara Nardelli
- Department of Psychology and Cognitive Science, University of Trento, Rovereto, Italy
| | - Massimo Vescovi
- Center for Mind/Brain Sciences—CIMeC, University of Trento, Rovereto, Italy
| | - Luca Surian
- Department of Psychology and Cognitive Science, University of Trento, Rovereto, Italy
| | - Manuela Piazza
- Center for Mind/Brain Sciences—CIMeC, University of Trento, Rovereto, Italy
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37
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Lê MLT, Noël MP. Transparent number-naming system gives only limited advantage for preschooler's numerical development: Comparisons of Vietnamese and French-speaking children. PLoS One 2020; 15:e0243472. [PMID: 33284824 PMCID: PMC7721146 DOI: 10.1371/journal.pone.0243472] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2020] [Accepted: 11/21/2020] [Indexed: 01/29/2023] Open
Abstract
Several cross-sectional studies have suggested that the transparency of the number-naming system of East Asian languages (Chinese, Japanese) facilitates children's numerical development. The Vietnamese number-naming system also makes the base-10 system very explicit (eleven is "mười một," literally "ten-one," and thirty is "ba mươi," literally "three-ten"). In contrast, Western languages (English, French) include teen words (eleven to sixteen) and ten words (twenty to ninety) that make their counting systems less transparent. The main question addressed in this paper is: To what extent does a language's number-naming system impact preschoolers' numerical development? Our study participants comprised 104 Vietnamese and 104 French-speaking Belgian children between 3½ and 5½ years of age, as well as their parents. We tested the children on eight numerical tasks (counting, advanced counting, enumeration, Give-N, number-word comparison, collection comparison, addition, and approximate addition) and some general cognitive abilities (IQ and phonological loop by letter span). The parents completed a questionnaire on the frequency with which they stimulated their child's numeracy and literacy at home. The results indicated that Vietnamese children outperformed Belgian children only in counting. However, neither group differed in other symbolic or non-symbolic abilities, although Vietnamese parents tended to stimulate their child at home slightly more than Belgian parents. We concluded that the Vietnamese number-naming system's transparency led to faster acquisition of basic counting for preschoolers but did not support other more advanced numerical skills or non-symbolic numerical abilities. In addition, we extended the evidence that both transparent number-naming system and home numeracy influence young children's counting development.
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Affiliation(s)
- Mai-Liên T. Lê
- Psychological Sciences Research Institute, Université Catholique de Louvain, Louvain-la-Neuve, Belgium
- Faculty of Psychology, University of Social Sciences and Humanities, National University of Vietnam in Ho Chi Minh City, Ho Chi Minh City, Vietnam
| | - Marie-Pascale Noël
- Psychological Sciences Research Institute, Université Catholique de Louvain, Louvain-la-Neuve, Belgium
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The contribution of attentional processes to calculation skills in second and third grade in a typically developing sample. EUROPEAN JOURNAL OF PSYCHOLOGY OF EDUCATION 2020. [DOI: 10.1007/s10212-020-00515-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
AbstractAttention is an important, multifaceted cognitive domain that includes many key cognitive processes involved in learning. This study aimed to identify the predictive links between different components of attentional skills and core calculation skills development, using two standardized measures assessing calculation (AC-MT 6–11) and attention skills (CAS) in a sample of 143 typically developing children of age range from 7.6 years to 9.4 years. The results showed that in 2nd grade, selective visuo-spatial attention emerged as an important predictor in the written calculation task, while the ability to inhibit distracting information seemed to better predict accuracy in oral calculation. In 3rd grade, visuo-spatial components of attention emerged as no longer predictive, whereas planning and active visuo-spatial attention abilities emerged as predictive of accuracy in the oral calculation task. These results confirm previous findings about the contribution that attentional skills may have in calculation skills development, supporting evidence for progressive automation attentional components over time.
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Ciccione L, Dehaene S. Grouping Mechanisms in Numerosity Perception. Open Mind (Camb) 2020; 4:102-118. [PMID: 34485793 PMCID: PMC8412191 DOI: 10.1162/opmi_a_00037] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/29/2020] [Accepted: 08/25/2020] [Indexed: 01/29/2023] Open
Abstract
Enumeration of a dot array is faster and easier if the items form recognizable subgroups. This phenomenon, which has been termed "groupitizing," appears in children after one year of formal education and correlates with arithmetic abilities. We formulated and tested the hypothesis that groupitizing reflects an ability to sidestep counting by using arithmetic shortcuts, for instance, using the grouping structure to add or multiply rather than just count. Three groups of students with different levels of familiarity with mathematics were asked to name the numerosity of sets of 1-15 dots in various arrangements, for instance, 9 represented as a single group of 9 items, three distinct groups of 2, 3, and 4 items (affording addition 2 + 3 + 4), or three identical groups of 3 items (affording multiplication 3 × 3). Grouping systematically improved enumeration performance, regardless of whether the items were grouped spatially or by color alone, but only when an array was divided into subgroups with the same number of items. Response times and error patterns supported the hypothesis of a multiplication process. Our results demonstrate that even a simple enumeration task involves mental arithmetic.
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Affiliation(s)
- Lorenzo Ciccione
- Cognitive Neuroimaging Unit, CEA DSV/I2BM, INSERM, Université Paris Sud, Université Paris-Saclay, NeuroSpin Center, Gif-sur-Yvette, France
- Collège de France, Paris, France
- PSL University, Paris, France
| | - Stanislas Dehaene
- Cognitive Neuroimaging Unit, CEA DSV/I2BM, INSERM, Université Paris Sud, Université Paris-Saclay, NeuroSpin Center, Gif-sur-Yvette, France
- Collège de France, Paris, France
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40
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Wang JJ, Feigenson L. Dynamic changes in numerical acuity in 4-month-old infants. INFANCY 2020; 26:47-62. [PMID: 33111486 DOI: 10.1111/infa.12373] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2020] [Revised: 09/22/2020] [Accepted: 09/29/2020] [Indexed: 01/29/2023]
Abstract
Preverbal infants represent the approximate numerosity of visual and auditory arrays: By 6 months old, they reliably discriminate eight dots or tones from 16 (a 1:2 ratio), but not eight from 12 (a 2:3 ratio). The precision of this approximate number sense improves gradually over childhood and into adulthood. However, less is known about numerical abilities in younger infants, and in particular, whether there is developmental change in the number sense in the first half year of life. Here, in four experiments, we measured numerical precision in 4-month-old infants (N = 128) using a visual habituation task comparable to that in studies of older infants. We found that 4-month-olds exhibited poorer numerical discrimination than the 6-month-olds tested in previous studies, dishabituating to a 1:4 change in numerical ratio, but not a 1:3 change. Like older infants, 4-month-olds' numerical precision improved when they were provided with redundant visual and auditory input; when both visual and auditory information were present, 4-month-olds discriminated a 1:3 but not a 1:2 ratio. These results suggest that Approximate Number System precision develops in early infancy and may be sensitive to intersensory redundancy as early as four months of age.
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Affiliation(s)
- Jinjing Jenny Wang
- Department of Psychological and Brain Sciences, Johns Hopkins University, Baltimore, MD, USA.,Department of Psychology, Rutgers University, New Brunswick, NJ, USA
| | - Lisa Feigenson
- Department of Psychological and Brain Sciences, Johns Hopkins University, Baltimore, MD, USA
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Libertus ME, Odic D, Feigenson L, Halberda J. Effects of Visual Training of Approximate Number Sense on Auditory Number Sense and School Math Ability. Front Psychol 2020; 11:2085. [PMID: 32973627 PMCID: PMC7481447 DOI: 10.3389/fpsyg.2020.02085] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2019] [Accepted: 07/28/2020] [Indexed: 01/29/2023] Open
Abstract
Research with children and adults suggests that people's math performance is predicted by individual differences in an evolutionarily ancient ability to estimate and compare numerical quantities without counting (the approximate number system or ANS). However, previous work has almost exclusively used visual stimuli to measure ANS precision, leaving open the possibility that the observed link might be driven by aspects of visuospatial competence, rather than the amodal ANS. We addressed this possibility in an ANS training study. Sixty-eight 6-year-old children participated in a 5-week study that either trained their visual ANS ability or their phonological awareness (an active control group). Immediately before and after training, we assessed children's visual and auditory ANS precision, as well as their symbolic math ability and phonological awareness. We found that, prior to training, children's precision in a visual ANS task related to their math performance - replicating recent studies. Importantly, precision in an auditory ANS task also related to math performance. Furthermore, we found that children who completed visual ANS training showed greater improvements in auditory ANS precision than children who completed phonological awareness training. Finally, children in the ANS training group showed significant improvements in math ability but not phonological awareness. These results suggest that the link between ANS precision and school math ability goes beyond visuospatial abilities and that the modality-independent ANS is causally linked to math ability in early childhood.
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Affiliation(s)
- Melissa E Libertus
- Department of Psychology and Learning Research and Development Center, University of Pittsburgh, Pittsburgh, PA, United States.,Department of Psychological and Brain Sciences, Johns Hopkins University, Baltimore, MD, United States
| | - Darko Odic
- Department of Psychological and Brain Sciences, Johns Hopkins University, Baltimore, MD, United States.,Department of Psychology, The University of British Columbia, Vancouver, BC, Canada
| | - Lisa Feigenson
- Department of Psychological and Brain Sciences, Johns Hopkins University, Baltimore, MD, United States
| | - Justin Halberda
- Department of Psychological and Brain Sciences, Johns Hopkins University, Baltimore, MD, United States
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42
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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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43
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Gomez A, Huron C. Subitizing and counting impairments in children with developmental coordination disorder. RESEARCH IN DEVELOPMENTAL DISABILITIES 2020; 104:103717. [PMID: 32585441 DOI: 10.1016/j.ridd.2020.103717] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2020] [Revised: 06/03/2020] [Accepted: 06/10/2020] [Indexed: 06/11/2023]
Abstract
Developmental coordination disorder (DCD) interferes with academic achievement and daily life, and is associated with persistent academic difficulties, in particular within mathematical learning. In the present study, we aimed to study numerical cognition using an approach that taps very basic numerical processes such as subitizing and counting abilities in DCD. We used a counting task and a subitizing task in forty 7-10 years-old children with or without DCD. In both tasks, children were presented with arrays of one to eight dots and asked to name aloud the number of dots as accurately and quickly as possible. In the subitizing task, dots were presented during 250 ms whereas in the counting task they stayed on the screen until the participants gave a verbal response. The results showed that children with DCD were less accurate and slower in the two enumeration tasks (with and without a time limit), providing evidence that DCD impairs both counting and subitizing. These impairments might have a deleterious impact on the ability to improve the acuity of the Approximate Number System through counting, and thus could play a role in the underachievement of children with DCD in mathematics.
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Affiliation(s)
- Alice Gomez
- Institute of Cognitive Science Marc Jeannerod, CNRS, UMR 5229, Bron, France; Université Claude Bernard Lyon 1, Inspé, France; INSERM, U992, Cognitive Neuroimaging Unit, CEA/SAC/DSV/DRM/NeuroSpin, Bat 145, Point Courrier 156, F-91191 Gif/Yvette, France; CEA, DSV/I2BM, NeuroSpin Center, Bât 145, Point Courrier 156, F-91191 Gif/Yvette, France; Univ Paris-Sud, Cognitive Neuroimaging Unit, Bât 300, 91405 Orsay Cedex, France; INSERM U1284, France.
| | - Caroline Huron
- INSERM, U992, Cognitive Neuroimaging Unit, CEA/SAC/DSV/DRM/NeuroSpin, Bat 145, Point Courrier 156, F-91191 Gif/Yvette, France; CEA, DSV/I2BM, NeuroSpin Center, Bât 145, Point Courrier 156, F-91191 Gif/Yvette, France; Univ Paris-Sud, Cognitive Neuroimaging Unit, Bât 300, 91405 Orsay Cedex, France; Center for Research and Interdisciplinarity (CRI), France; Université de Paris, France; INSERM U1284, France
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44
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Wang JJ, Halberda J, Feigenson L. Emergence of the Link Between the Approximate Number System and Symbolic Math Ability. Child Dev 2020; 92:e186-e200. [PMID: 32816346 DOI: 10.1111/cdev.13454] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Experimentally manipulating Approximate Number System (ANS) precision has been found to influence children's subsequent symbolic math performance. Here in three experiments (N = 160; 81 girls; 3-5 year old) we replicated this effect and examined its duration and developmental trajectory. We found that modulation of 5-year-olds' ANS precision continued to affect their symbolic math performance after a 30-min delay. Furthermore, our cross-sectional investigation revealed that children 4.5 years and older experienced a significant transfer effect of ANS manipulation on math performance, whereas younger children showed no such transfer, despite experiencing significant changes in ANS precision. These findings support the existence of a causal link between nonverbal numerical approximation and symbolic math performance that first emerges during the preschool years.
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45
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Castaldi E, Turi M, Gassama S, Piazza M, Eger E. Excessive visual crowding effects in developmental dyscalculia. J Vis 2020; 20:7. [PMID: 32756882 PMCID: PMC7438630 DOI: 10.1167/jov.20.8.7] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2020] [Accepted: 06/12/2020] [Indexed: 01/29/2023] Open
Abstract
Visual crowding refers to the inability to identify objects when surrounded by other similar items. Crowding-like mechanisms are thought to play a key role in numerical perception by determining the sensory mechanisms through which ensembles are perceived. Enhanced visual crowding might hence prevent the normal development of a system involved in segregating and perceiving discrete numbers of items and ultimately the acquisition of more abstract numerical skills. Here, we investigated whether excessive crowding occurs in developmental dyscalculia (DD), a neurodevelopmental disorder characterized by difficulty in learning the most basic numerical and arithmetical concepts, and whether it is found independently of associated major reading and attentional difficulties. We measured spatial crowding in two groups of adult individuals with DD and control subjects. In separate experiments, participants were asked to discriminate the orientation of a Gabor patch either in isolation or under spatial crowding. Orientation discrimination thresholds were comparable across groups when stimuli were shown in isolation, yet they were much higher for the DD group with respect to the control group when the target was crowded by closely neighbouring flanking gratings. The difficulty in discriminating orientation (as reflected by the combination of accuracy and reaction times) in the DD compared to the control group persisted over several larger target flanker distances. Finally, we found that the degree of such spatial crowding correlated with impairments in mathematical abilities even when controlling for visual attention and reading skills. These results suggest that excessive crowding effects might be a characteristic of DD, independent of other associated neurodevelopmental disorders.
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Affiliation(s)
- Elisa Castaldi
- Department of Translational Research and New Technologies in Medicine and Surgery, University of Pisa, Pisa, Italy
- Department of Neuroscience, Psychology, Pharmacology and Child Health, University of Florence, Florence, Italy
- Cognitive Neuroimaging Unit, NeuroSpin Center, CEA DRF/JOLIOT, INSERM, Université Paris-Saclay, Gif-sur-Yvette, Paris, France
| | - Marco Turi
- Fondazione Stella Maris Mediterraneo, Potenza, Italy
| | - Sahawanatou Gassama
- Paris Santé Réussite, Centre de diagnostic des troubles des apprentissages, Paris, France
| | - Manuela Piazza
- Center for Mind/Brain Sciences, University of Trento, Italy
| | - Evelyn Eger
- Cognitive Neuroimaging Unit, NeuroSpin Center, CEA DRF/JOLIOT, INSERM, Université Paris-Saclay, Gif-sur-Yvette, Paris, France
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46
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Haman M, Lipowska K. Moving attention along the mental number line in preschool age: Study of the operational momentum in 3- to 5-year-old children's non-symbolic arithmetic. Dev Sci 2020; 24:e13007. [PMID: 32567767 DOI: 10.1111/desc.13007] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2018] [Revised: 05/03/2020] [Accepted: 06/02/2020] [Indexed: 01/29/2023]
Abstract
People tend to underestimate subtraction and overestimate addition outcomes and to associate subtraction with the left side and addition with the right side. These two phenomena are collectively labeled 'operational momentum' (OM) and thought to have their origins in the same mechanism of 'moving attention along the mental number line'. OM in arithmetic has never been tested in children at the preschool age, which is critical for numerical development. In this study, 3-5 years old were tested with non-symbolic addition and subtraction tasks. Their level of understanding of counting principles (CP) was assessed using the give-a-number task. When the second operand's cardinality was 5 or 6 (Experiment 1), the child's reaction time was shorter in addition/subtraction tasks after cuing attention appropriately to the right/left. Adding/subtracting one element (Experiment 2) revealed a more complex developmental pattern. Before acquiring CP, the children showed generalized overestimation bias. Underestimation in addition and overestimation in subtraction emerged only after mastering CP. No clear spatial-directional OM pattern was found, however, the response time to rightward/leftward cues in addition/subtraction again depended on stage of mastering CP. Although the results support the hypothesis about engagement of spatial attention in early numerical processing, they point to at least partial independence of the spatial-directional and magnitude OM. This undermines the canonical version of the number line-based hypothesis. Mapping numerical magnitudes to space may be a complex process that undergoes reorganization during the period of acquisition of symbolic representations of numbers. Some hypotheses concerning the role of spatial-numerical associations in numerical development are proposed.
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Affiliation(s)
- Maciej Haman
- Faculty of Psychology, University of Warsaw, Warszawa, Poland
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47
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Tomlinson RC, DeWind NK, Brannon EM. Number sense biases children's area judgments. Cognition 2020; 204:104352. [PMID: 32629292 DOI: 10.1016/j.cognition.2020.104352] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2019] [Revised: 03/25/2020] [Accepted: 06/02/2020] [Indexed: 01/29/2023]
Abstract
Humans are thought to use the approximate number system (ANS) to make quick approximations based on quantity even before learning to count. However, there has long been controversy regarding the salience of number versus other stimulus dimensions throughout development, including a recent proposal that number sense is derived from a sense of general magnitude. Here, we used a regression approach to disentangle numerical acuity from sensitivity to total surface area in both 5-year-old children and adults. We found that both children and adults displayed higher acuity when making numerosity judgments than total surface area judgments. Adults were largely able to ignore irrelevant stimulus features when making numerosity or total area judgments. Children were more biased by numerosity when making total area judgments than by total area when making numerosity judgments. These results provide evidence that number is more salient than total surface area even before the start of formal education and are inconsistent with the Sense of Magnitude proposal.
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Affiliation(s)
- Rachel C Tomlinson
- Department of Psychology, University of Michigan, East Hall, 530 Church Street, Ann Arbor, MI 48109, United States of America.
| | - Nicholas K DeWind
- Department of Psychology, University of Pennsylvania, 3720 Walnut St, Philadelphia, PA 19104, United States of America
| | - Elizabeth M Brannon
- Department of Psychology, University of Pennsylvania, 3720 Walnut St, Philadelphia, PA 19104, United States of America
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48
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Maldonado Moscoso PA, Anobile G, Primi C, Arrighi R. Math Anxiety Mediates the Link Between Number Sense and Math Achievements in High Math Anxiety Young Adults. Front Psychol 2020; 11:1095. [PMID: 32528392 PMCID: PMC7264265 DOI: 10.3389/fpsyg.2020.01095] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2019] [Accepted: 04/29/2020] [Indexed: 01/29/2023] Open
Abstract
In the past few years, many studies have suggested that subjects with high sensory precision in the processing of non-symbolic numerical quantities (approximate number system; ANS) also have higher math abilities. At the same time, there has been interest in another non-cognitive factor affecting mathematical learning: mathematical anxiety (MA). MA is defined as a debilitating emotional reaction to mathematics that interferes with the manipulation of numbers and the solving of mathematical problems. Few studies have been dedicated to uncovering the interplay between ANS and MA and those have provided conflicting evidence. Here we measured ANS precision (numerosity discrimination thresholds) in a cohort of university students with either a high (>75th percentile; n = 49) or low (<25th percentile; n = 39) score on the Abbreviate Math Anxiety Scale (AMAS). We also assessed math proficiency using a standardized test (MPP: Mathematics Prerequisites for Psychometrics), visuo-spatial attention capacity by means of a Multiple Objects Tracking task (MOT) and sensory precision for non-numerical quantities (disk size). Our results confirmed previous studies showing that math abilities and ANS precision correlate in subjects with high math anxiety. Neither precision in size-discrimination nor visuo-spatial attentional capacity were found to correlate with math capacities. Interestingly, within the group with high MA, our data also revealed a relationship between ANS precision and MA, with MA playing a key role in mediating the correlation between ANS and math achievement. Taken together, our results suggest an interplay between extreme levels of MA and the sensory precision in the processing of non-symbolic numerosity.
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Affiliation(s)
| | - Giovanni Anobile
- Department of Neuroscience, Psychology, Pharmacology and Child Health, University of Florence, Florence, Italy
| | - Caterina Primi
- 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
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49
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Rubinsten O, Korem N, Levin N, Furman T. Frequency-based Dissociation of Symbolic and Nonsymbolic Numerical Processing during Numerical Comparison. J Cogn Neurosci 2020; 32:762-782. [DOI: 10.1162/jocn_a_01550] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Abstract
Recent evidence suggests that during numerical calculation, symbolic and nonsymbolic processing are functionally distinct operations. Nevertheless, both roughly recruit the same brain areas (spatially overlapping networks in the parietal cortex) and happen at the same time (roughly 250 msec poststimulus onset). We tested the hypothesis that symbolic and nonsymbolic processing are segregated by means of functionally relevant networks in different frequency ranges: high gamma (above 50 Hz) for symbolic processing and lower beta (12–17 Hz) for nonsymbolic processing. EEG signals were quantified as participants compared either symbolic numbers or nonsymbolic quantities. Larger EEG gamma-band power was observed for more difficult symbolic comparisons (ratio of 0.8 between the two numbers) than for easier comparisons (ratio of 0.2) over frontocentral regions. Similarly, beta-band power was larger for more difficult nonsymbolic comparisons than for easier ones over parietal areas. These results confirm the existence of a functional dissociation in EEG oscillatory dynamics during numerical processing that is compatible with the notion of distinct linguistic processing of symbolic numbers and approximation of nonsymbolic numerical information.
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50
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Symbolic fractions elicit an analog magnitude representation in school-age children. J Exp Child Psychol 2020; 195:104844. [PMID: 32244000 DOI: 10.1016/j.jecp.2020.104844] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2019] [Revised: 02/28/2020] [Accepted: 03/04/2020] [Indexed: 01/29/2023]
Abstract
A fundamental question about fractions is whether they are grounded in an abstract nonsymbolic magnitude code similar to that postulated for whole numbers. Mounting evidence suggests that symbolic fractions could be grounded in mechanisms for perceiving nonsymbolic ratio magnitudes. However, systematic examination of such mechanisms in children has been lacking. We asked second- and fifth-grade children (prior to and after formal instructions with fractions, respectively) to compare pairs of symbolic fractions, nonsymbolic ratios, and mixed symbolic-nonsymbolic pairs. This paradigm allowed us to test three key questions: (a) whether children show an analog magnitude code for rational numbers, (b) whether that code is compatible with mental representations of symbolic fractions, and (c) how formal education with fractions affects the symbolic-nonsymbolic relation. We examined distance effects as a marker of analog ratio magnitude processing and notation effects as a marker of converting across numerical codes. Second and fifth graders' reaction times and error rates showed classic distance and notation effects. Nonsymbolic ratios were processed most efficiently, with mixed and symbolic notations being relatively slower. Children with more formal instruction in symbolic fractions had a significant advantage in comparing symbolic fractions but had a smaller advantage for nonsymbolic ratio stimuli. Supplemental analyses showed that second graders relied on numerator distance more than holistic distance and that fifth graders relied on holistic fraction magnitude distance more than numerator distance. These results suggest that children have a nonsymbolic ratio magnitude code and that symbolic fractions can be translated into that magnitude code.
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