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Kuhl U, Friederici AD, Skeide MA, Friederici AD, Emmrich F, Brauer J, Wilcke A, Neef N, Boltze J, Skeide M, Kirsten H, Schaadt G, Müller B, Kraft I, Czepezauer I, Dörr L. Early cortical surface plasticity relates to basic mathematical learning. Neuroimage 2020; 204:116235. [DOI: 10.1016/j.neuroimage.2019.116235] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2019] [Revised: 09/09/2019] [Accepted: 09/27/2019] [Indexed: 01/20/2023] Open
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de Hevia MD, Addabbo M, Nava E, Croci E, Girelli L, Macchi Cassia V. Infants’ detection of increasing numerical order comes before detection of decreasing number. Cognition 2017; 158:177-188. [DOI: 10.1016/j.cognition.2016.10.022] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2016] [Revised: 10/27/2016] [Accepted: 10/29/2016] [Indexed: 01/29/2023]
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How approximate and exact number skills are related to each other across development: A review☆. DEVELOPMENTAL REVIEW 2016. [DOI: 10.1016/j.dr.2014.11.001] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
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Pinhas M, Donohue SE, Woldorff MG, Brannon EM. Electrophysiological evidence for the involvement of the approximate number system in preschoolers' processing of spoken number words. J Cogn Neurosci 2014; 26:1891-904. [PMID: 24702455 DOI: 10.1162/jocn_a_00631] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Little is known about the neural underpinnings of number word comprehension in young children. Here we investigated the neural processing of these words during the crucial developmental window in which children learn their meanings and asked whether such processing relies on the Approximate Number System. ERPs were recorded as 3- to 5-year-old children heard the words one, two, three, or six while looking at pictures of 1, 2, 3, or 6 objects. The auditory number word was incongruent with the number of visual objects on half the trials and congruent on the other half. Children's number word comprehension predicted their ERP incongruency effects. Specifically, children with the least number word knowledge did not show any ERP incongruency effects, whereas those with intermediate and high number word knowledge showed an enhanced, negative polarity incongruency response (N(inc)) over centroparietal sites from 200 to 500 msec after the number word onset. This negativity was followed by an enhanced, positive polarity incongruency effect (P(inc)) that emerged bilaterally over parietal sites at about 700 msec. Moreover, children with the most number word knowledge showed ratio dependence in the P(inc) (larger for greater compared with smaller numerical mismatches), a hallmark of the Approximate Number System. Importantly, a similar modulation of the P(inc) from 700 to 800 msec was found in children with intermediate number word knowledge. These results provide the first neural correlates of spoken number word comprehension in preschoolers and are consistent with the view that children map number words onto approximate number representations before they fully master the verbal count list.
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Mussolin C, Nys J, Content A, Leybaert J. Symbolic number abilities predict later approximate number system acuity in preschool children. PLoS One 2014; 9:e91839. [PMID: 24637785 PMCID: PMC3956743 DOI: 10.1371/journal.pone.0091839] [Citation(s) in RCA: 60] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2013] [Accepted: 02/15/2014] [Indexed: 01/29/2023] Open
Abstract
An ongoing debate in research on numerical cognition concerns the extent to which the approximate number system and symbolic number knowledge influence each other during development. The current study aims at establishing the direction of the developmental association between these two kinds of abilities at an early age. Fifty-seven children of 3-4 years performed two assessments at 7 months interval. In each assessment, children's precision in discriminating numerosities as well as their capacity to manipulate number words and Arabic digits was measured. By comparing relationships between pairs of measures across the two time points, we were able to assess the predictive direction of the link. Our data indicate that both cardinality proficiency and symbolic number knowledge predict later accuracy in numerosity comparison whereas the reverse links are not significant. The present findings are the first to provide longitudinal evidence that the early acquisition of symbolic numbers is an important precursor in the developmental refinement of the approximate number representation system.
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Affiliation(s)
- Christophe Mussolin
- Center for Research in Cognition and Neurosciences, Laboratory Cognition Language Development, Université Libre de Bruxelles, Brussels, Belgium
- * E-mail:
| | - Julie Nys
- Center for Research in Cognition and Neurosciences, Laboratory Cognition Language Development, Université Libre de Bruxelles, Brussels, Belgium
| | - Alain Content
- Center for Research in Cognition and Neurosciences, Laboratory Cognition Language Development, Université Libre de Bruxelles, Brussels, Belgium
| | - Jacqueline Leybaert
- Center for Research in Cognition and Neurosciences, Laboratory Cognition Language Development, Université Libre de Bruxelles, Brussels, Belgium
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Aagten-Murphy D, Iversen J, Williams C, Meck W. Novel Inversions in Auditory Sequences Provide Evidence for Spontaneous Subtraction of Time and Number. TIMING & TIME PERCEPTION 2014. [DOI: 10.1163/22134468-00002028] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Animals, including fish, birds, rodents, non-human primates, and pre-verbal infants are able to discriminate the duration and number of events without the use of language. In this paper, we present the results of six experiments exploring the capability of adult rats to count 2–6 sequentially presented white-noise stimuli. The investigation focuses on the animal’s ability to exhibit spontaneous subtraction following the presentation of novel stimulus inversions in the auditory signals being counted. Results suggest that a subtraction operation between two opposite sensory representations may be a general processing strategy used for the comparison of stimulus magnitudes. These findings are discussed within the context of a mode-control model of timing and counting that relies on an analog temporal-integration process for the addition and subtraction of sequential events.
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Affiliation(s)
- David Aagten-Murphy
- Department of Psychology, Ludwig-Maximilians-Universität München, Münich, Germany
| | - John R. Iversen
- Swartz Center for Computational Neuroscience and Institute for Neural Computation, University of California, San Diego, La Jolla, CA, USA
| | | | - Warren H. Meck
- Department of Psychology and Neuroscience, Duke University, Durham, NC, USA
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Relationships between approximate number system acuity and early symbolic number abilities. Trends Neurosci Educ 2012. [DOI: 10.1016/j.tine.2012.09.003] [Citation(s) in RCA: 48] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Wagner JB, Johnson SC. An association between understanding cardinality and analog magnitude representations in preschoolers. Cognition 2011; 119:10-22. [PMID: 21288508 DOI: 10.1016/j.cognition.2010.11.014] [Citation(s) in RCA: 66] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2009] [Revised: 10/13/2010] [Accepted: 11/24/2010] [Indexed: 10/18/2022]
Abstract
The preschool years are a time of great advances in children's numerical thinking, most notably as they master verbal counting. The present research assessed the relation between analog magnitude representations and cardinal number knowledge in preschool-aged children to ask two questions: (1) Is there a relationship between acuity in the analog magnitude system and cardinality proficiency? (2) Can evidence of the analog magnitude system be found within mappings of number words children have not successfully mastered? To address the first question, Study 1 asked three- to five-year-old children to discriminate side-by-side dot arrays with varying differences in numerical ratio, as well as to complete an assessment of cardinality. Consistent with the analog magnitude system, children became less accurate at discriminating dot arrays as the ratio between the two numbers approached one. Further, contrary to prior work with preschoolers, a significant correlation was found between cardinal number knowledge and non-symbolic numerical discrimination. Study 2 aimed to look for evidence of the analog magnitude system in mappings to the words in preschoolers' verbal counting list. Based on a modified give-a-number task (Wynn, 1990, 1992), three- to five-year-old children were asked to give quantities between 1 and 10 as many times as possible in order to assess analog magnitude variability within their developing cardinality understanding. In this task, even children who have not yet induced the cardinality principle showed signs of analog representations in their understanding of the verbal count list. Implications for the contribution of analog magnitude representations towards mastery of the verbal count list are discussed in light of the present work.
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Affiliation(s)
- Jennifer B Wagner
- Division of Developmental Medicine, Children's Hospital Boston, Harvard Medical School, Boston, MA 02215, USA.
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Shinskey JL, Chan CHM, Coleman R, Moxom L, Yamamoto E. Preschoolers’ nonsymbolic arithmetic with large sets: Is addition more accurate than subtraction? J Exp Child Psychol 2009; 103:409-20. [PMID: 19285685 DOI: 10.1016/j.jecp.2009.01.012] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2008] [Revised: 12/03/2008] [Accepted: 01/27/2009] [Indexed: 01/29/2023]
Affiliation(s)
- Jeanne L Shinskey
- Department of Psychology, Royal Holloway, University of London, Surrey, UK.
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Barth H, Baron A, Spelke E, Carey S. Children's multiplicative transformations of discrete and continuous quantities. J Exp Child Psychol 2009; 103:441-54. [PMID: 19289237 DOI: 10.1016/j.jecp.2009.01.014] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2008] [Revised: 12/02/2008] [Accepted: 01/28/2009] [Indexed: 11/17/2022]
Abstract
Recent studies have documented an evolutionarily primitive, early emerging cognitive system for the mental representation of numerical quantity (the analog magnitude system). Studies with nonhuman primates, human infants, and preschoolers have shown this system to support computations of numerical ordering, addition, and subtraction involving whole number concepts prior to arithmetic training. Here we report evidence that this system supports children's predictions about the outcomes of halving and perhaps also doubling transformations. A total of 138 kindergartners and first graders were asked to reason about the quantity resulting from the doubling or halving of an initial numerosity (of a set of dots) or an initial length (of a bar). Controls for dot size, total dot area, and dot density ensured that children were responding to the number of dots in the arrays. Prior to formal instruction in symbolic multiplication, division, or rational number, halving (and perhaps doubling) computations appear to be deployed over discrete and possibly continuous quantities. The ability to apply simple multiplicative transformations to analog magnitude representations of quantity may form a part of the toolkit that children use to construct later concepts of rational number.
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Affiliation(s)
- Hilary Barth
- Department of Psychology, Wesleyan University, Middletown, CT 06459, USA.
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Barth H, Beckmann L, Spelke ES. Nonsymbolic, approximate arithmetic in children: abstract addition prior to instruction. Dev Psychol 2008; 44:1466-77. [PMID: 18793077 PMCID: PMC3489021 DOI: 10.1037/a0013046] [Citation(s) in RCA: 67] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Do children draw upon abstract representations of number when they perform approximate arithmetic operations? In this study, kindergarten children viewed animations suggesting addition of a sequence of sounds to an array of dots, and they compared the sum to a second dot array that differed from the sum by 1 of 3 ratios. Children performed this task successfully with all the signatures of adults' nonsymbolic number representations: accuracy modulated by the ratio of the sum and the comparison quantity, equal performance for within- and cross-modality tasks and for addition and comparison tasks, and performance superior to that of a matched subtraction task. The findings provide clear evidence for nonsymbolic numerical operations on abstract numerical quantities in children who have not yet been taught formal arithmetic.
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Affiliation(s)
- Hilary Barth
- Department of Psychology, Wesleyan University, Middletown, CT 06459, USA.
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