1
|
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.
Collapse
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
| |
Collapse
|
2
|
Get in touch with numbers - an approximate number comparison task in the haptic modality. Atten Percept Psychophys 2022; 84:943-959. [PMID: 35064556 PMCID: PMC9001573 DOI: 10.3758/s13414-021-02427-6] [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: 12/08/2021] [Indexed: 11/12/2022]
Abstract
The Approximate Number System (ANS) is conceptualized as an innate cognitive system that allows humans to perceive numbers of objects or events (>4) in a fuzzy, imprecise manner. The representation of numbers is assumed to be abstract and not bound to a particular sense. In the present study, we test the assumption of a shared cross-sensory system. We investigated approximate number processing in the haptic modality and compared performance to that of the visual modality. We used a dot comparison task (DCT), in which participants compare two dot arrays and decide which one contains more dots. In the haptic DCT, 67 participants had to compare two simultaneously presented dot arrays with the palms of their hands; in the visual DCT, participants inspected and compared dot arrays on a screen. Tested ratios ranged from 2.0 (larger/smaller number) to 1.1. As expected, in both the haptic and the visual DCT responses similarly depended on the ratio of the numbers of dots in the two arrays. However, on an individual level, we found evidence against medium or stronger positive correlations between “ANS acuity” in the visual and haptic DCTs. A regression model furthermore revealed that besides number, spacing-related features of dot patterns (e.g., the pattern’s convex hull) contribute to the percept of numerosity in both modalities. Our results contradict the strong theory of the ANS solely processing number and being independent of a modality. According to our regression and response prediction model, our results rather point towards a modality-specific integration of number and number-related features.
Collapse
|
3
|
Response bias in numerosity perception at early judgments and systematic underestimation. Atten Percept Psychophys 2021; 84:188-204. [PMID: 34518971 DOI: 10.3758/s13414-021-02365-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 07/26/2021] [Indexed: 01/29/2023]
Abstract
Mental number representation relies on mapping numerosity based on nonsymbolic stimuli to symbolic magnitudes. It is known that mental number representation builds on a logarithmic scale, and thus numerosity decisions result in underestimation. In the current study, we investigated the temporal dynamics of numerosity perception in four experiments by employing the response-deadline SAT procedure. We presented random number of dots and required participants to make a numerosity judgment by comparing the perceived number of dots to 50. Using temporal dynamics in numerosity perception allowed us to observe a response bias at early decisions and a systematic underestimation at late decisions. In all three experiments, providing feedback diminished the magnitude of underestimation, whereas in Experiment 3 the absence of feedback resulted in greater underestimation errors. These results were in accordance with the findings that suggested feedback is necessary for the calibration of the mental number representation.
Collapse
|
4
|
Georges C, Guillaume M, Schiltz C. A robust electrophysiological marker of spontaneous numerical discrimination. Sci Rep 2020; 10:18376. [PMID: 33110202 PMCID: PMC7591903 DOI: 10.1038/s41598-020-75307-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2020] [Accepted: 10/12/2020] [Indexed: 01/29/2023] Open
Abstract
Humans have a Number Sense that enables them to represent and manipulate numerical quantities. Behavioral data suggest that the acuity of numerical discrimination is predictively associated with math ability-especially in children-but some authors argued that its assessment is problematic. In the present study, we used frequency-tagged electroencephalography to objectively measure spontaneous numerical discrimination during passive viewing of dot or picture arrays in healthy adults. During 1-min sequences, we introduced periodic numerosity changes and we progressively increased the magnitude of such changes every ten seconds. We found significant brain synchronization to the periodic numerosity changes from the 1.2 ratio over medial occipital regions, and amplitude strength increased with the numerical ratio. Brain responses were reliable across both stimulus formats. Interestingly, electrophysiological responses also mirrored performances on a number comparison task and seemed to be linked to math fluency. In sum, we present a neural marker of numerical acuity that is passively evaluated in short sequences, independent of stimulus format and that reflects behavioural performances on explicit number comparison tasks.
Collapse
Affiliation(s)
- Carrie Georges
- Department of Behavioural and Cognitive Sciences (DBCS), Faculty of Humanities, Education and Social Sciences (FHSE), Institute of Cognitive Science and Assessment (COSA), University of Luxembourg, Campus Belval, Maison des Sciences Humaines, Porte des Sciences 11, 4366, Esch-sur-Alzette, Luxembourg.
| | - Mathieu Guillaume
- Center for Research in Cognitive Neuroscience (CRCN), Université Libre de Bruxelles, Avenue Franklin Roosevelt 50 (CP 191), 1050, Brussels, Belgium
| | - Christine Schiltz
- Department of Behavioural and Cognitive Sciences (DBCS), Faculty of Humanities, Education and Social Sciences (FHSE), Institute of Cognitive Science and Assessment (COSA), University of Luxembourg, Campus Belval, Maison des Sciences Humaines, Porte des Sciences 11, 4366, Esch-sur-Alzette, Luxembourg
| |
Collapse
|
5
|
Simplicio H, Gasteiger H, Dorneles BV, Grimes KR, Haase VG, Ruiz C, Liedtke FV, Moeller K. Cognitive Research and Mathematics Education-How Can Basic Research Reach the Classroom? Front Psychol 2020; 11:773. [PMID: 32390919 PMCID: PMC7191005 DOI: 10.3389/fpsyg.2020.00773] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2019] [Accepted: 03/30/2020] [Indexed: 01/05/2023] Open
Affiliation(s)
- Henrique Simplicio
- Developmental Neuropsychology Laboratory, Biological Sciences Institute, Neurosciences Department, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil
| | - Hedwig Gasteiger
- Mathematics Education, School for Mathematics and Computer Science, Institute of Mathematics, Osnabrück University, Osnabrueck, Germany
| | - Beatriz Vargas Dorneles
- Post-Graduate Program of Education, School of Education, Universidade Federal Do Rio Grande Do Sul, Porto Alegre, Brazil
| | - Ka Rene Grimes
- Department of Special Education, The University of Texas at Austin, Austin, TX, United States
| | - Vitor Geraldi Haase
- Department of Psychology, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil
| | - Carola Ruiz
- Neurocognition Department, Universidad Católica del Uruguay, Montevideo, Uruguay
| | - Francéia Veiga Liedtke
- Post-Graduate Program of Psychology, Psychology Institute, Universidade Federal Do Rio Grande Do Sul, Porto Alegre, Brazil
| | - Korbinian Moeller
- Centre for Mathematical Cognition, Loughborough University, Loughborough, United Kingdom.,Leibniz-Institut für Wissensmedien, Tübingen, Germany.,Department of Psychology, University of Tübingen, Tübingen, Germany.,LEAD Graduate School & Research Network, University of Tübingen, Tübingen, Germany
| |
Collapse
|
6
|
Testolin A, Zou WY, McClelland JL. Numerosity discrimination in deep neural networks: Initial competence, developmental refinement and experience statistics. Dev Sci 2020; 23:e12940. [PMID: 31977137 DOI: 10.1111/desc.12940] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2019] [Revised: 12/17/2019] [Accepted: 01/16/2020] [Indexed: 01/29/2023]
Abstract
Both humans and non-human animals exhibit sensitivity to the approximate number of items in a visual array, as indexed by their performance in numerosity discrimination tasks, and even neonates can detect changes in numerosity. These findings are often interpreted as evidence for an innate 'number sense'. However, recent simulation work has challenged this view by showing that human-like sensitivity to numerosity can emerge in deep neural networks that build an internal model of the sensory data. This emergentist perspective posits a central role for experience in shaping our number sense and might explain why numerical acuity progressively increases over the course of development. Here we substantiate this hypothesis by introducing a progressive unsupervised deep learning algorithm, which allows us to model the development of numerical acuity through experience. We also investigate how the statistical distribution of numerical and non-numerical features in natural environments affects the emergence of numerosity representations in the computational model. Our simulations show that deep networks can exhibit numerosity sensitivity prior to any training, as well as a progressive developmental refinement that is modulated by the statistical structure of the learning environment. To validate our simulations, we offer a refinement to the quantitative characterization of the developmental patterns observed in human children. Overall, our findings suggest that it may not be necessary to assume that animals are endowed with a dedicated system for processing numerosity, since domain-general learning mechanisms can capture key characteristics others have attributed to an evolutionarily specialized number system.
Collapse
Affiliation(s)
- Alberto Testolin
- Department of General Psychology, University of Padova, Padova, Italy.,Department of Information Engineering, University of Padova, Padova, Italy
| | - Will Y Zou
- Department of Electrical Engineering, Stanford University, Stanford, CA, USA
| | | |
Collapse
|