101
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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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102
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Almaatouq A, Rahimian MA, Burton JW, Alhajri A. The distribution of initial estimates moderates the effect of social influence on the wisdom of the crowd. Sci Rep 2022; 12:16546. [PMID: 36192623 PMCID: PMC9530231 DOI: 10.1038/s41598-022-20551-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2022] [Accepted: 09/14/2022] [Indexed: 01/29/2023] Open
Abstract
Whether, and under what conditions, groups exhibit “crowd wisdom” has been a major focus of research across the social and computational sciences. Much of this work has focused on the role of social influence in promoting the wisdom of the crowd versus leading the crowd astray and has resulted in conflicting conclusions about how social network structure determines the impact of social influence. Here, we demonstrate that it is not enough to consider the network structure in isolation. Using theoretical analysis, numerical simulation, and reanalysis of four experimental datasets (totaling 2885 human subjects), we find that the wisdom of crowds critically depends on the interaction between (i) the centralization of the social influence network and (ii) the distribution of the initial individual estimates. By adopting a framework that integrates both the structure of the social influence and the distribution of the initial estimates, we bring previously conflicting results under one theoretical framework and clarify the effects of social influence on the wisdom of crowds.
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Affiliation(s)
- Abdullah Almaatouq
- Sloan School of Management, Massachusetts Institute of Technology, Cambridge, USA.
| | - M Amin Rahimian
- Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, USA
| | - Jason W Burton
- Department of Digitalization, Copenhagen Business School, Copenhagen, Denmark
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103
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Alonso-Díaz S, Penagos-Londoño GI. Reduced choice-confidence in negative numerals. PLoS One 2022; 17:e0272796. [PMID: 36190954 PMCID: PMC9529092 DOI: 10.1371/journal.pone.0272796] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2021] [Accepted: 07/26/2022] [Indexed: 11/07/2022] Open
Abstract
Negative numbers are central in math. However, they are abstract, hard to learn, and manipulated slower than positive numbers regardless of math ability. It suggests that confidence, namely the post-decision estimate of being correct, should be lower than positives. We asked participants to pick the larger single-digit numeral in a pair and collected their implicit confidence with button pressure (button pressure was validated with three empirical signatures of confidence). We also modeled their choices with a drift-diffusion decision model to compute the post-decision estimate of being correct. We found that participants had relatively low confidence with negative numerals. Given that participants compared with high accuracy the basic base-10 symbols (0–9), reduced confidence may be a general feature of manipulating abstract negative numerals as they produce more uncertainty than positive numerals per unit of time.
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Affiliation(s)
- Santiago Alonso-Díaz
- Department of Economics, Pontificia Universidad Javeriana, Bogotá, Colombia
- * E-mail:
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104
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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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105
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Stengård E, Juslin P, Hahn U, van den Berg R. On the generality and cognitive basis of base-rate neglect. Cognition 2022; 226:105160. [DOI: 10.1016/j.cognition.2022.105160] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2021] [Revised: 04/27/2022] [Accepted: 05/04/2022] [Indexed: 01/29/2023]
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106
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EmBody/EmFace as a new open tool to assess emotion recognition from body and face expressions. Sci Rep 2022; 12:14165. [PMID: 35986068 PMCID: PMC9391359 DOI: 10.1038/s41598-022-17866-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2022] [Accepted: 08/02/2022] [Indexed: 01/29/2023] Open
Abstract
Nonverbal expressions contribute substantially to social interaction by providing information on another person’s intentions and feelings. While emotion recognition from dynamic facial expressions has been widely studied, dynamic body expressions and the interplay of emotion recognition from facial and body expressions have attracted less attention, as suitable diagnostic tools are scarce. Here, we provide validation data on a new open source paradigm enabling the assessment of emotion recognition from both 3D-animated emotional body expressions (Task 1: EmBody) and emotionally corresponding dynamic faces (Task 2: EmFace). Both tasks use visually standardized items depicting three emotional states (angry, happy, neutral), and can be used alone or together. We here demonstrate successful psychometric matching of the EmBody/EmFace items in a sample of 217 healthy subjects with excellent retest reliability and validity (correlations with the Reading-the-Mind-in-the-Eyes-Test and Autism-Spectrum Quotient, no correlations with intelligence, and given factorial validity). Taken together, the EmBody/EmFace is a novel, effective (< 5 min per task), highly standardized and reliably precise tool to sensitively assess and compare emotion recognition from body and face stimuli. The EmBody/EmFace has a wide range of potential applications in affective, cognitive and social neuroscience, and in clinical research studying face- and body-specific emotion recognition in patient populations suffering from social interaction deficits such as autism, schizophrenia, or social anxiety.
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107
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Dehaene S, Al Roumi F, Lakretz Y, Planton S, Sablé-Meyer M. Symbols and mental programs: a hypothesis about human singularity. Trends Cogn Sci 2022; 26:751-766. [PMID: 35933289 DOI: 10.1016/j.tics.2022.06.010] [Citation(s) in RCA: 28] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2022] [Revised: 06/22/2022] [Accepted: 06/22/2022] [Indexed: 01/29/2023]
Abstract
Natural language is often seen as the single factor that explains the cognitive singularity of the human species. Instead, we propose that humans possess multiple internal languages of thought, akin to computer languages, which encode and compress structures in various domains (mathematics, music, shape…). These languages rely on cortical circuits distinct from classical language areas. Each is characterized by: (i) the discretization of a domain using a small set of symbols, and (ii) their recursive composition into mental programs that encode nested repetitions with variations. In various tasks of elementary shape or sequence perception, minimum description length in the proposed languages captures human behavior and brain activity, whereas non-human primate data are captured by simpler nonsymbolic models. Our research argues in favor of discrete symbolic models of human thought.
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Affiliation(s)
- 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.
| | - Fosca Al Roumi
- Cognitive Neuroimaging Unit, CEA, INSERM, Université Paris-Saclay, NeuroSpin Center, 91191 Gif/Yvette, France
| | - Yair Lakretz
- Cognitive Neuroimaging Unit, CEA, INSERM, Université Paris-Saclay, NeuroSpin Center, 91191 Gif/Yvette, France
| | - Samuel Planton
- Cognitive Neuroimaging Unit, CEA, INSERM, Université Paris-Saclay, NeuroSpin Center, 91191 Gif/Yvette, France
| | - Mathias Sablé-Meyer
- Cognitive Neuroimaging Unit, CEA, INSERM, Université Paris-Saclay, NeuroSpin Center, 91191 Gif/Yvette, France
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108
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Zhang Y, An N, Chen J, Zhou X, Cui Z. Numerosity sense correlates with fluent mathematical abilities. Acta Psychol (Amst) 2022; 228:103655. [DOI: 10.1016/j.actpsy.2022.103655] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2021] [Revised: 05/11/2022] [Accepted: 06/20/2022] [Indexed: 01/29/2023] Open
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109
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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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110
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Boni I, Jara-Ettinger J, Sackstein S, Piantadosi ST. Verbal counting and the timing of number acquisition in an indigenous Amazonian group. PLoS One 2022; 17:e0270739. [PMID: 35913931 PMCID: PMC9342773 DOI: 10.1371/journal.pone.0270739] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Accepted: 06/16/2022] [Indexed: 01/29/2023] Open
Abstract
Children in industrialized cultures typically succeed on Give-N, a test of counting ability, by age 4. On the other hand, counting appears to be learned much later in the Tsimane’, an indigenous group in the Bolivian Amazon. This study tests three hypotheses for what may cause this difference in timing: (a) Tsimane’ children may be shy in providing behavioral responses to number tasks, (b) Tsimane’ children may not memorize the verbal list of number words early in acquisition, and/or (c) home environments may not support mathematical learning in the same way as in US samples, leading Tsimane’ children to primarily acquire mathematics through formalized schooling. Our results suggest that most of our subjects are not inhibited by shyness in responding to experimental tasks. We also find that Tsimane’ children (N = 100, ages 4-11) learn the verbal list later than US children, but even upon acquiring this list, still take time to pass Give-N tasks. We find that performance in counting varies across tasks and is related to formal schooling. These results highlight the importance of formal education, including instruction in the count list, in learning the meanings of the number words.
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Affiliation(s)
- Isabelle Boni
- Department of Psychology, University of California Berkeley, Berkeley, CA, United States of America
- * E-mail:
| | - Julian Jara-Ettinger
- Department of Psychology, Yale University, New Haven, CT, United States of America
| | - Sophie Sackstein
- Department of Brain and Cognitive Sciences, University of Rochester, Rochester, NY, United States of America
| | - Steven T. Piantadosi
- Department of Psychology, University of California Berkeley, Berkeley, CA, United States of America
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111
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Karin O, Alon U. The dopamine circuit as a reward-taxis navigation system. PLoS Comput Biol 2022; 18:e1010340. [PMID: 35877694 PMCID: PMC9352198 DOI: 10.1371/journal.pcbi.1010340] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2022] [Revised: 08/04/2022] [Accepted: 06/29/2022] [Indexed: 01/29/2023] Open
Abstract
Studying the brain circuits that control behavior is challenging, since in addition to their structural complexity there are continuous feedback interactions between actions and sensed inputs from the environment. It is therefore important to identify mathematical principles that can be used to develop testable hypotheses. In this study, we use ideas and concepts from systems biology to study the dopamine system, which controls learning, motivation, and movement. Using data from neuronal recordings in behavioral experiments, we developed a mathematical model for dopamine responses and the effect of dopamine on movement. We show that the dopamine system shares core functional analogies with bacterial chemotaxis. Just as chemotaxis robustly climbs chemical attractant gradients, the dopamine circuit performs ‘reward-taxis’ where the attractant is the expected value of reward. The reward-taxis mechanism provides a simple explanation for scale-invariant dopaminergic responses and for matching in free operant settings, and makes testable quantitative predictions. We propose that reward-taxis is a simple and robust navigation strategy that complements other, more goal-directed navigation mechanisms.
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Affiliation(s)
- Omer Karin
- Dept. of Molecular Cell Biology, Weizmann Institute of Science, Rehovot Israel
- Dept. of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge, United Kingdom
- Wellcome Trust/Cancer Research UK Gurdon Institute, University of Cambridge, Cambridge, United Kingdom
- * E-mail: (OK); (UA)
| | - Uri Alon
- Dept. of Molecular Cell Biology, Weizmann Institute of Science, Rehovot Israel
- * E-mail: (OK); (UA)
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112
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Abstract
Four studies demonstrate that the public's understanding of government budgetary expenditures is hampered by difficulty in representing large numerical magnitudes. Despite orders of magnitude difference between millions and billions, study participants struggle with the budgetary magnitudes of government programs. When numerical values are rescaled as smaller magnitudes (in the thousands or lower), lay understanding improves, as indicated by greater sensitivity to numerical ratios and more accurate rank ordering of expenses. A robust benefit of numerical rescaling is demonstrated across a variety of experimental designs, including policy relevant choices and incentive-compatible accuracy measures. This improved sensitivity ultimately impacts funding choices and public perception of respective budgets, indicating the importance of numerical cognition for good citizenship.
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113
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Silver AM, Libertus ME. Environmental influences on mathematics performance in early childhood. NATURE REVIEWS PSYCHOLOGY 2022; 1:407-418. [PMID: 36330081 PMCID: PMC9624502 DOI: 10.1038/s44159-022-00061-z] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/15/2022] [Indexed: 06/16/2023]
Abstract
Math skills relate to lifelong career, health, and financial outcomes. Individuals' own cognitive abilities predict math performance and there is growing recognition that environmental influences including differences in culture and variability in math engagement also impact math skills. In this Review, we summarize evidence indicating that differences between languages, exposure to math-focused language, socioeconomic status, attitudes and beliefs about math, and engagement with math activities influence young children's math performance. These influences play out at the community and individual level. However, research on the role of these environmental influences for foundational number skills, including understanding of number words, is limited. Future research is needed to understand individual differences in the development of early emerging math skills such as number word skills, examining to what extent different types of environmental input are necessary and how children's cognitive abilities shape the impact of environmental input.
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Affiliation(s)
- Alex M. Silver
- Department of Psychology, University of Pittsburgh, Pittsburgh, PA, USA
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114
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Dotan D, Dehaene S. Tracking priors and their replacement: Mental dynamics of decision making in the number-line task. Cognition 2022; 224:105069. [DOI: 10.1016/j.cognition.2022.105069] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2021] [Revised: 01/02/2022] [Accepted: 02/16/2022] [Indexed: 01/29/2023]
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115
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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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116
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Lee SH, Kim D, Opfer JE, Pitt MA, Myung JI. A number-line task with a Bayesian active learning algorithm provides insights into the development of non-symbolic number estimation. Psychon Bull Rev 2022; 29:971-984. [PMID: 34918270 DOI: 10.3758/s13423-021-02041-5] [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] [Accepted: 11/11/2021] [Indexed: 01/29/2023]
Abstract
To characterize numerical representations, the number-line task asks participants to estimate the location of a given number on a line flanked with zero and an upper-bound number. An open question is whether estimates for symbolic numbers (e.g., Arabic numerals) and non-symbolic numbers (e.g., number of dots) rely on common processes with a common developmental pathway. To address this question, we explored whether well-established findings in symbolic number-line estimation generalize to non-symbolic number-line estimation. For exhaustive investigations without sacrificing data quality, we applied a novel Bayesian active learning algorithm, dubbed Gaussian process active learning (GPAL), that adaptively optimizes experimental designs. The results showed that the non-symbolic number estimation in participants of diverse ages (5-73 years old, n = 238) exhibited three characteristic features of symbolic number estimation.
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Affiliation(s)
- Sang Ho Lee
- Department of Psychology, The Ohio State University, 212 Psychology Building, 1835 Neil Avenue, Columbus, OH, 43210, USA.
| | - Dan Kim
- Department of Psychology, The Ohio State University, 212 Psychology Building, 1835 Neil Avenue, Columbus, OH, 43210, USA
| | - John E Opfer
- Department of Psychology, The Ohio State University, 212 Psychology Building, 1835 Neil Avenue, Columbus, OH, 43210, USA
| | - Mark A Pitt
- Department of Psychology, The Ohio State University, 212 Psychology Building, 1835 Neil Avenue, Columbus, OH, 43210, USA
| | - Jay I Myung
- Department of Psychology, The Ohio State University, 212 Psychology Building, 1835 Neil Avenue, Columbus, OH, 43210, USA
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117
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Efficient coding of numbers explains decision bias and noise. Nat Hum Behav 2022; 6:1142-1152. [DOI: 10.1038/s41562-022-01352-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2020] [Accepted: 04/12/2022] [Indexed: 01/29/2023]
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118
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Rational arbitration between statistics and rules in human sequence processing. Nat Hum Behav 2022; 6:1087-1103. [PMID: 35501360 DOI: 10.1038/s41562-021-01259-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2020] [Accepted: 11/17/2021] [Indexed: 01/29/2023]
Abstract
Detecting and learning temporal regularities is essential to accurately predict the future. A long-standing debate in cognitive science concerns the existence in humans of a dissociation between two systems, one for handling statistical regularities governing the probabilities of individual items and their transitions, and another for handling deterministic rules. Here, to address this issue, we used finger tracking to continuously monitor the online build-up of evidence, confidence, false alarms and changes-of-mind during sequence processing. All these aspects of behaviour conformed tightly to a hierarchical Bayesian inference model with distinct hypothesis spaces for statistics and rules, yet linked by a single probabilistic currency. Alternative models based either on a single statistical mechanism or on two non-commensurable systems were rejected. Our results indicate that a hierarchical Bayesian inference mechanism, capable of operating over distinct hypothesis spaces for statistics and rules, underlies the human capability for sequence processing.
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119
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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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120
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Girelli L. What does gender has to do with math? Complex questions require complex answers. J Neurosci Res 2022; 101:679-688. [PMID: 35443070 DOI: 10.1002/jnr.25056] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2021] [Revised: 03/31/2022] [Accepted: 04/03/2022] [Indexed: 01/29/2023]
Abstract
Whether mathematics is a gendered domain or not is a long-lasting issue bringing along major social and educational implications. The females' underrepresentation in science, technology, engineering, and mathematics (STEM) has been considered one of the key signs of the math gender gap, although the current view largely attributes the origin of this phenomenon to sociocultural factors. Indeed, recent approaches to math gender differences reached the universal conclusion that nature and nurture exert reciprocal effects on each other, establishing the need for approaching the study of the math gender issue only once its intrinsic complexity has been accepted. Building upon a flourishing literature, this review provides an updated synthesis of the evidence for math gender equality at the start, and for math gender inequality on the go, challenging the role of biological factors. In particular, by combining recent findings from different research areas, the paper discusses the persistence of the "math male myth" and the associated "female are not good at math myth," drawing attention to the complex interplay of social and cultural forces that support such stereotypes. The suggestion is made that longevity of these myths results from the additive effects of two independent cognitive biases associated with gender stereotypes and with math stereotypes, respectively. Scholars' responsibility in amplifying these myths by pursuing some catching lines of research is also discussed.
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Affiliation(s)
- Luisa Girelli
- Department of Psychology, University of Milano-Bicocca, Milano, Italy.,NeuroMI, Milan Center for Neuroscience, Milano, Italy
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121
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Numerosity perception is tuned to salient environmental features. iScience 2022; 25:104104. [PMID: 35402866 PMCID: PMC8983381 DOI: 10.1016/j.isci.2022.104104] [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: 12/06/2021] [Revised: 02/03/2022] [Accepted: 03/15/2022] [Indexed: 01/29/2023] Open
Abstract
Numerosity perception is a key ability to guide behavior. However, current models propose that number units encode an abstract representation of numerosity regardless of the non-numerical attributes of the stimuli, suggesting rather coarse environmental tuning. Here we investigated whether numerosity systems spontaneously adapt to all visible items, or to subsets segregated by salient attributes such as color or pitch. We measured perceived numerosity after participants adapted to highly numerous stimuli with color either matched to or different from the test. Matched colors caused a 25% underestimation of numerosity, while different colors had virtually no effect. This was true both for physically different colors, and for the same colors perceived as different, via a color-assimilation illusion. A similar result occurred in the acoustic domain, where adaptation magnitude was halved when the adaptor and test differed in pitch. Taken together, our results support the idea that numerosity perception is selectively tuned to salient environmental attributes.
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Lazzaro G, Fucà E, Caciolo C, Battisti A, Costanzo F, Varuzza C, Vicari S, Menghini D. Understanding the Effects of Transcranial Electrical Stimulation in Numerical Cognition: A Systematic Review for Clinical Translation. J Clin Med 2022; 11:jcm11082082. [PMID: 35456176 PMCID: PMC9032363 DOI: 10.3390/jcm11082082] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2022] [Revised: 03/31/2022] [Accepted: 04/02/2022] [Indexed: 02/04/2023] Open
Abstract
Atypical development of numerical cognition (dyscalculia) may increase the onset of neuropsychiatric symptoms, especially when untreated, and it may have long-term detrimental social consequences. However, evidence-based treatments are still lacking. Despite plenty of studies investigating the effects of transcranial electrical stimulation (tES) on numerical cognition, a systematized synthesis of results is still lacking. In the present systematic review (PROSPERO ID: CRD42021271139), we found that the majority of reports (20 out of 26) showed the effectiveness of tES in improving both number (80%) and arithmetic (76%) processing. In particular, anodal tDCS (regardless of lateralization) over parietal regions, bilateral tDCS (regardless of polarity/lateralization) over frontal regions, and tRNS (regardless of brain regions) strongly enhance number processing. While bilateral tDCS and tRNS over parietal and frontal regions and left anodal tDCS over frontal regions consistently improve arithmetic skills. In addition, tACS seems to be more effective than tDCS at ameliorating arithmetic learning. Despite the variability of methods and paucity of clinical studies, tES seems to be a promising brain-based treatment to enhance numerical cognition. Recommendations for clinical translation, future directions, and limitations are outlined.
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Affiliation(s)
- Giulia Lazzaro
- Child and Adolescent Neuropsychiatry Unit, Department of Neuroscience, Bambino Gesù Children’s Hospital, IRCCS, 00146 Rome, Italy; (G.L.); (E.F.); (C.C.); (A.B.); (F.C.); (C.V.); (S.V.)
| | - Elisa Fucà
- Child and Adolescent Neuropsychiatry Unit, Department of Neuroscience, Bambino Gesù Children’s Hospital, IRCCS, 00146 Rome, Italy; (G.L.); (E.F.); (C.C.); (A.B.); (F.C.); (C.V.); (S.V.)
| | - Cristina Caciolo
- Child and Adolescent Neuropsychiatry Unit, Department of Neuroscience, Bambino Gesù Children’s Hospital, IRCCS, 00146 Rome, Italy; (G.L.); (E.F.); (C.C.); (A.B.); (F.C.); (C.V.); (S.V.)
| | - Andrea Battisti
- Child and Adolescent Neuropsychiatry Unit, Department of Neuroscience, Bambino Gesù Children’s Hospital, IRCCS, 00146 Rome, Italy; (G.L.); (E.F.); (C.C.); (A.B.); (F.C.); (C.V.); (S.V.)
- Department of Human Science, LUMSA University, 00193 Rome, Italy
| | - Floriana Costanzo
- Child and Adolescent Neuropsychiatry Unit, Department of Neuroscience, Bambino Gesù Children’s Hospital, IRCCS, 00146 Rome, Italy; (G.L.); (E.F.); (C.C.); (A.B.); (F.C.); (C.V.); (S.V.)
| | - Cristiana Varuzza
- Child and Adolescent Neuropsychiatry Unit, Department of Neuroscience, Bambino Gesù Children’s Hospital, IRCCS, 00146 Rome, Italy; (G.L.); (E.F.); (C.C.); (A.B.); (F.C.); (C.V.); (S.V.)
| | - Stefano Vicari
- Child and Adolescent Neuropsychiatry Unit, Department of Neuroscience, Bambino Gesù Children’s Hospital, IRCCS, 00146 Rome, Italy; (G.L.); (E.F.); (C.C.); (A.B.); (F.C.); (C.V.); (S.V.)
- Department of Life Science and Public Health, Università Cattolica del Sacro Cuore, 00168 Rome, Italy
- Centro di Riabilitazione Casa San Giuseppe, Opera Don Guanella, 00165 Rome, Italy
| | - Deny Menghini
- Child and Adolescent Neuropsychiatry Unit, Department of Neuroscience, Bambino Gesù Children’s Hospital, IRCCS, 00146 Rome, Italy; (G.L.); (E.F.); (C.C.); (A.B.); (F.C.); (C.V.); (S.V.)
- Correspondence: ; Tel.: +39-066-859-7091
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123
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Cui J, Xiao R, Ma M, Yuan L, Cohen Kodash R, Zhou X. Children skilled in mental abacus show enhanced non-symbolic number sense. CURRENT PSYCHOLOGY 2022. [DOI: 10.1007/s12144-020-00717-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
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124
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Ching BHH, Kong KHC. Understanding additive composition is important for symbolic numerical magnitude processing. COGNITIVE DEVELOPMENT 2022. [DOI: 10.1016/j.cogdev.2022.101170] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
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125
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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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126
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Pop CM, Wilson L, Browne CL. Evaluating landscape knowledge and lithic resource selection at the French Middle Paleolithic site of the Bau de l'Aubesier. J Hum Evol 2022; 166:103152. [PMID: 35338861 DOI: 10.1016/j.jhevol.2022.103152] [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: 02/16/2021] [Revised: 01/05/2022] [Accepted: 01/09/2022] [Indexed: 01/29/2023]
Abstract
We report on the application of a novel approach to exploring the degree of landscape knowledge, wayfinding abilities, and the nature of decision-making processes reflected in the utilization of stone resources in the French Middle Paleolithic. Specifically, we use data from the site of the Bau de l'Aubesier to explore the reasons why a majority of the 350 raw material sources cataloged in the surrounding region appear not to have been utilized, including several located near the site and yielding high-quality lithic materials. To this end, we focus on the spatial relationships between sources as an explanatory variable, operationalized in terms of minimum travel times. Using geographic information system software and a generalized linear model of resource selection derived from the Bau assemblages, we compute source utilization probabilities from the perspective of hominins located off-site. We do so under three optimization scenarios, factoring in the intrinsic characteristics (e.g., quality) and time required to reach each source on the way to the Bau. More generally, we find that in slightly more than 50% of cases, seemingly viable sources may have been ignored simply because the minimum cost path leading back to the Bau passes through or requires only minimal deviations to reach, higher quality options. More generally, we found that throughout the entire region, a cost/benefit analysis of competing sources favors those from source areas known to have been utilized. Virtually all the available information on lithic procurement at the Bau is consistent with a model of landscape utilization premised on detailed knowledge of a very large area, an ability to accurately estimate travel times between locations, and a pragmatic strategy of stone resource exploitation based on minimizing costs (travel and search times) and maximizing utility.
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Affiliation(s)
- Cornel Marian Pop
- Department of Human Evolution, Max Planck Institute for Evolutionary Anthropology, Deutscher Platz 6, Leipzig, 04103, Germany; Department of Anthropology and Sociology, Columbia College, 438 Terminal Avenue, Vancouver, B.C., V6A 0C1, Canada.
| | - Lucy Wilson
- Department of Biological Sciences, University of New Brunswick, 100 Tucker Park Road, Saint John, N.B., E2L 4L5, Canada
| | - Constance L Browne
- Department of Biological Sciences, University of New Brunswick, 100 Tucker Park Road, Saint John, N.B., E2L 4L5, Canada
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127
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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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128
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Arzy S, Kaplan R. Transforming Social Perspectives with Cognitive Maps. Soc Cogn Affect Neurosci 2022; 17:939-955. [PMID: 35257155 PMCID: PMC9527473 DOI: 10.1093/scan/nsac017] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2021] [Revised: 12/17/2021] [Accepted: 03/07/2022] [Indexed: 01/29/2023] Open
Abstract
Growing evidence suggests that cognitive maps represent relations between social knowledge similar to how spatial locations are represented in an environment. Notably, the extant human medial temporal lobe literature assumes associations between social stimuli follow a linear associative mapping from an egocentric viewpoint to a cognitive map. Yet, this form of associative social memory doesn't account for a core phenomenon of social interactions in which social knowledge learned via comparisons to the self, other individuals, or social networks are assimilated within a single frame of reference. We argue that hippocampal-entorhinal coordinate transformations, known to integrate egocentric and allocentric spatial cues, inform social perspective switching between the self and others. We present evidence that the hippocampal formation helps inform social interactions by relating self versus other social attribute comparisons to society in general, which can afford rapid and flexible assimilation of knowledge about the relationship between the self and social networks of varying proximities. We conclude by discussing the ramifications of cognitive maps in aiding this social perspective transformation process in states of health and disease.
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Affiliation(s)
- Shahar Arzy
- Faculty of Medicine and the Department of Cognitive Sciences, Hebrew University of Jerusalem, Jerusalem 91120, Israel
- Department of Neurology, Hadassah Hebrew University Medical School, Jerusalem 91120, Israel
| | - Raphael Kaplan
- Correspondence should be addressed to Raphael Kaplan, Department of Basic Psychology, Clinical Psychology, and Psychobiology, Universitat Jaume I, Avinguda de Vicent Sos Baynat, Castelló de la Plana, Spain. E-mail:
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129
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Pitt B, Gibson E, Piantadosi ST. Exact Number Concepts Are Limited to the Verbal Count Range. Psychol Sci 2022; 33:371-381. [PMID: 35132893 PMCID: PMC9096449 DOI: 10.1177/09567976211034502] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2021] [Accepted: 06/25/2021] [Indexed: 01/29/2023] Open
Abstract
Previous findings suggest that mentally representing exact numbers larger than four depends on a verbal count routine (e.g., "one, two, three . . ."). However, these findings are controversial because they rely on comparisons across radically different languages and cultures. We tested the role of language in number concepts within a single population-the Tsimane' of Bolivia-in which knowledge of number words varies across individual adults. We used a novel data-analysis model to quantify the point at which participants (N = 30) switched from exact to approximate number representations during a simple numerical matching task. The results show that these behavioral switch points were bounded by participants' verbal count ranges; their representations of exact cardinalities were limited to the number words they knew. Beyond that range, they resorted to numerical approximation. These results resolve competing accounts of previous findings and provide unambiguous evidence that large exact number concepts are enabled by language.
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Affiliation(s)
- Benjamin Pitt
- Department of Psychology, University of
California, Berkeley
| | - Edward Gibson
- Department of Brain and Cognitive
Sciences, Massachusetts Institute of Technology
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130
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131
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Szkudlarek E, Zhang H, DeWind NK, Brannon EM. Young Children Intuitively Divide Before They Recognize the Division Symbol. Front Hum Neurosci 2022; 16:752190. [PMID: 35280204 PMCID: PMC8913505 DOI: 10.3389/fnhum.2022.752190] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Accepted: 01/24/2022] [Indexed: 01/29/2023] Open
Abstract
Children bring intuitive arithmetic knowledge to the classroom before formal instruction in mathematics begins. For example, children can use their number sense to add, subtract, compare ratios, and even perform scaling operations that increase or decrease a set of dots by a factor of 2 or 4. However, it is currently unknown whether children can engage in a true division operation before formal mathematical instruction. Here we examined the ability of 6- to 9-year-old children and college students to perform symbolic and non-symbolic approximate division. Subjects were presented with non-symbolic (dot array) or symbolic (Arabic numeral) dividends ranging from 32 to 185, and non-symbolic divisors ranging from 2 to 8. Subjects compared their imagined quotient to a visible target quantity. Both children (Experiment 1 N = 89, Experiment 2 N = 42) and adults (Experiment 3 N = 87) were successful at the approximate division tasks in both dots and numeral formats. This was true even among the subset of children that could not recognize the division symbol or solve simple division equations, suggesting intuitive division ability precedes formal division instruction. For both children and adults, the ability to divide non-symbolically mediated the relation between Approximate Number System (ANS) acuity and symbolic math performance, suggesting that the ability to calculate non-symbolically may be a mechanism of the relation between ANS acuity and symbolic math. Our findings highlight the intuitive arithmetic abilities children possess before formal math instruction.
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132
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Bryer MAH, Koopman SE, Cantlon JF, Piantadosi ST, MacLean EL, Baker JM, Beran MJ, Jones SM, Jordan KE, Mahamane S, Nieder A, Perdue BM, Range F, Stevens JR, Tomonaga M, Ujfalussy DJ, Vonk J. The evolution of quantitative sensitivity. Philos Trans R Soc Lond B Biol Sci 2022; 377:20200529. [PMID: 34957840 PMCID: PMC8710878 DOI: 10.1098/rstb.2020.0529] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Abstract
The ability to represent approximate quantities appears to be phylogenetically widespread, but the selective pressures and proximate mechanisms favouring this ability remain unknown. We analysed quantity discrimination data from 672 subjects across 33 bird and mammal species, using a novel Bayesian model that combined phylogenetic regression with a model of number psychophysics and random effect components. This allowed us to combine data from 49 studies and calculate the Weber fraction (a measure of quantity representation precision) for each species. We then examined which cognitive, socioecological and biological factors were related to variance in Weber fraction. We found contributions of phylogeny to quantity discrimination performance across taxa. Of the neural, socioecological and general cognitive factors we tested, cortical neuron density and domain-general cognition were the strongest predictors of Weber fraction, controlling for phylogeny. Our study is a new demonstration of evolutionary constraints on cognition, as well as of a relation between species-specific neuron density and a particular cognitive ability. This article is part of the theme issue ‘Systems neuroscience through the lens of evolutionary theory’.
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Affiliation(s)
- Margaret A H Bryer
- Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213, USA.,Department of Psychology, University of California-Berkeley, Berkeley, CA 94720, USA
| | - Sarah E Koopman
- School of Psychology and Neuroscience, University of St. Andrews, St Andrews KY16 9AJ, UK
| | - Jessica F Cantlon
- Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213, USA
| | - Steven T Piantadosi
- Department of Psychology, University of California-Berkeley, Berkeley, CA 94720, USA
| | - Evan L MacLean
- School of Anthropology, University of Arizona, Tucson, AZ 85719, USA.,College of Veterinary Medicine, University of Arizona, Tucson, AZ 85719, USA
| | - Joseph M Baker
- Center for Interdisciplinary Brain Sciences Research, Division of Brain Sciences, Department of Psychiatry and Behavioral Sciences, School of Medicine, Stanford University, Stanford, CA 94305, USA
| | - Michael J Beran
- Department of Psychology and Language Research Center, Georgia State University, Atlanta, GA 30302, USA
| | - Sarah M Jones
- Psychology Program, Berea College, Berea, KY 40403, USA
| | - Kerry E Jordan
- Department of Psychology, Utah State University, Logan, UT 84322, USA
| | - Salif Mahamane
- Behavioral and Social Sciences Department, Western Colorado University, Gunnison, CO 81231, USA
| | - Andreas Nieder
- Animal Physiology Unit, Institute of Neurobiology, University of Tübingen, Tübingen 72076, Germany
| | - Bonnie M Perdue
- Department of Psychology, Agnes Scott College, Decatur, GA 30030, USA
| | - Friederike Range
- Domestication Lab, Konrad Lorenz Institute of Ethology, Department of Interdisciplinary Life Sciences, University of Veterinary Medicine Vienna, Savoyenstrasse 1a, Vienna 1160, Austria
| | - Jeffrey R Stevens
- Department of Psychology and Center for Brain, Biology and Behavior, University of Nebraska-Lincoln, Lincoln, NE 68588, USA
| | | | - Dorottya J Ujfalussy
- MTA-ELTE Comparative Ethology Research Group, Eötvös Loránd University of Sciences (ELTE), Budapest 1117, Hungary.,Department of Ethology, Eötvös Loránd University of Sciences (ELTE), Budapest 1117, Hungary
| | - Jennifer Vonk
- Department of Psychology, Oakland University, Rochester, MI 48309, USA
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133
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Zhang H, Zhen Y, Yu S, Long T, Zhang B, Jiang X, Li J, Fang W, Sigman M, Dehaene S, Wang L. Working Memory for Spatial Sequences: Developmental and Evolutionary Factors in Encoding Ordinal and Relational Structures. J Neurosci 2022; 42:850-864. [PMID: 34862186 PMCID: PMC8808738 DOI: 10.1523/jneurosci.0603-21.2021] [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: 03/22/2021] [Revised: 11/08/2021] [Accepted: 11/19/2021] [Indexed: 11/21/2022] Open
Abstract
Sequence learning is a ubiquitous facet of human and animal cognition. Here, using a common sequence reproduction task, we investigated whether and how the ordinal and relational structures linking consecutive elements are acquired by human adults, children, and macaque monkeys. While children and monkeys exhibited significantly lower precision than adults for spatial location and temporal order information, only monkeys appeared to exceedingly focus on the first item. Most importantly, only humans, regardless of age, spontaneously extracted the spatial relations between consecutive items and used a chunking strategy to compress sequences in working memory. Monkeys did not detect such relational structures, even after extensive training. Monkey behavior was captured by a conjunctive coding model, whereas a chunk-based conjunctive model explained more variance in humans. These age- and species-related differences are indicative of developmental and evolutionary mechanisms of sequence encoding and may provide novel insights into the uniquely human cognitive capacities.SIGNIFICANCE STATEMENT Sequence learning, the ability to encode the order of discrete elements and their relationships presented within a sequence, is a ubiquitous facet of cognition among humans and animals. By exploring sequence-processing abilities at different human developmental stages and in nonhuman primates, we found that only humans, regardless of age, spontaneously extracted the spatial relations between consecutive items and used an internal language to compress sequences in working memory. The findings provided insights into understanding the origins of sequence capabilities in humans and how they evolve through development to identify the unique aspects of human cognitive capacity, which includes the comprehension, learning, and production of sequences, and perhaps, above all, language processing.
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Affiliation(s)
- He Zhang
- Institute of Neuroscience, Key Laboratory of Primate Neurobiology, CAS Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences, Shanghai 200031, People's Republic of China
- University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Yanfen Zhen
- Institute of Neuroscience, Key Laboratory of Primate Neurobiology, CAS Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences, Shanghai 200031, People's Republic of China
| | - Shijing Yu
- Institute of Neuroscience, Key Laboratory of Primate Neurobiology, CAS Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences, Shanghai 200031, People's Republic of China
| | - Tenghai Long
- Institute of Neuroscience, Key Laboratory of Primate Neurobiology, CAS Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences, Shanghai 200031, People's Republic of China
- University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Bingqian Zhang
- Institute of Neuroscience, Key Laboratory of Primate Neurobiology, CAS Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences, Shanghai 200031, People's Republic of China
- University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
- School of Life Science and Technology, ShanghaiTech University, Shanghai 200031, People's Republic of China
| | - Xinjian Jiang
- Institute of Neuroscience, Key Laboratory of Primate Neurobiology, CAS Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences, Shanghai 200031, People's Republic of China
| | - Junru Li
- Institute of Neuroscience, Key Laboratory of Primate Neurobiology, CAS Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences, Shanghai 200031, People's Republic of China
| | - Wen Fang
- Institute of Neuroscience, Key Laboratory of Primate Neurobiology, CAS Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences, Shanghai 200031, People's Republic of China
| | - Mariano Sigman
- Laboratory Neuroscience, Universidad Torcuato di Tella, C1428 Buenos Aires, Argentina
- School of Language and Education, Universidad Nebrija, 28015 Madrid, Spain
| | - Stanislas Dehaene
- Collège de France, 75231 Paris Cedex 05, France
- Cognitive Neuroimaging Unit, CEA DSV/I2BM, INSERM, NeuroSpin Center, Université Paris Sud/Université Paris-Saclay, 91191 Gif-sur-Yvette, France
| | - Liping Wang
- Institute of Neuroscience, Key Laboratory of Primate Neurobiology, CAS Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences, Shanghai 200031, People's Republic of China
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134
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Abstract
A major goal of linguistics and cognitive science is to understand what class of learning systems can acquire natural language. Until recently, the computational requirements of language have been used to argue that learning is impossible without a highly constrained hypothesis space. Here, we describe a learning system that is maximally unconstrained, operating over the space of all computations, and is able to acquire many of the key structures present in natural language from positive evidence alone. We demonstrate this by providing the same learning model with data from 74 distinct formal languages which have been argued to capture key features of language, have been studied in experimental work, or come from an interesting complexity class. The model is able to successfully induce the latent system generating the observed strings from small amounts of evidence in almost all cases, including for regular (e.g., an , [Formula: see text], and [Formula: see text]), context-free (e.g., [Formula: see text], and [Formula: see text]), and context-sensitive (e.g., [Formula: see text], and xx) languages, as well as for many languages studied in learning experiments. These results show that relatively small amounts of positive evidence can support learning of rich classes of generative computations over structures. The model provides an idealized learning setup upon which additional cognitive constraints and biases can be formalized.
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135
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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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136
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Hart Y, Mahadevan L, Dillon MR. Euclid's Random Walk: Developmental Changes in the Use of Simulation for Geometric Reasoning. Cogn Sci 2022; 46:e13070. [PMID: 35085405 DOI: 10.1111/cogs.13070] [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: 11/20/2020] [Revised: 09/04/2021] [Accepted: 11/10/2021] [Indexed: 01/29/2023]
Abstract
Euclidean geometry has formed the foundation of architecture, science, and technology for millennia, yet the development of human's intuitive reasoning about Euclidean geometry is not well understood. The present study explores the cognitive processes and representations that support the development of humans' intuitive reasoning about Euclidean geometry. One-hundred-twenty-five 7- to 12-year-old children and 30 adults completed a localization task in which they visually extrapolated missing parts of fragmented planar triangles and a reasoning task in which they answered verbal questions about the general properties of planar triangles. While basic Euclidean principles guided even young children's visual extrapolations, only older children and adults reasoned about triangles in ways that were consistent with Euclidean geometry. Moreover, a relation beteen visual extrapolation and reasoning appeared only in older children and adults. Reasoning consistent with Euclidean geometry may thus emerge when children abandon incorrect, axiomatic-based reasoning strategies and come to reason using mental simulations of visual extrapolations.
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Affiliation(s)
- Yuval Hart
- Department of Psychology, The Hebrew University of Jerusalem.,Paulson School of Engineering and Applied Sciences, Harvard University
| | - L Mahadevan
- Paulson School of Engineering and Applied Sciences, Harvard University.,Department of Physics, Harvard University.,Center for Brain Science, Harvard University.,Department of Organismic and Evolutionary Biology, Harvard University
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137
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Fargier-Bochaton O, Wang X, Dipasquale G, Laouiti M, Kountouri M, Gorobets O, Nguyen NP, Miralbell R, Vinh-Hung V. Prone versus supine free-breathing for right-sided whole breast radiotherapy. Sci Rep 2022; 12:525. [PMID: 35017568 PMCID: PMC8752750 DOI: 10.1038/s41598-021-04385-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 11/24/2021] [Indexed: 01/29/2023] Open
Abstract
Prone setup has been advocated to improve organ sparing in whole breast radiotherapy without impairing breast coverage. We evaluate the dosimetric advantage of prone setup for the right breast and look for predictors of the gain. Right breast cancer patients treated in 2010-2013 who had a dual supine and prone planning were retrospectively identified. A penalty score was computed from the mean absolute dose deviation to heart, lungs, breasts, and tumor bed for each patient's supine and prone plan. Dosimetric advantage of prone was assessed by the reduction of penalty score from supine to prone. The effect of patients' characteristics on the reduction of penalty was analyzed using robust linear regression. A total of 146 patients with right breast dual plans were identified. Prone compared to supine reduced the penalty score in 119 patients (81.5%). Lung doses were reduced by 70.8%, from 4.8 Gy supine to 1.4 Gy prone. Among patient's characteristics, the only significant predictors were the breast volumes, but no cutoff could identify when prone would be less advantageous than supine. Prone was associated with a dosimetric advantage in most patients. It sets a benchmark of achievable lung dose reduction.Trial registration: ClinicalTrials.gov NCT02237469, HUGProne, September 11, 2014, retrospectively registered.
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Affiliation(s)
| | - Xinzhuo Wang
- Radiation Oncology Department, Geneva University Hospitals, Geneva, Switzerland
- Radiation Oncology, Tianjin Union Medical Center, Tianjin, 300121, China
| | - Giovanna Dipasquale
- Radiation Oncology Department, Geneva University Hospitals, Geneva, Switzerland
| | - Mohamed Laouiti
- Radiation Oncology Department, Geneva University Hospitals, Geneva, Switzerland
- Service de Radio-Oncologie, Hôpital Riviera-Chablais, Rennaz, Switzerland
| | - Melpomeni Kountouri
- Radiation Oncology Department, Geneva University Hospitals, Geneva, Switzerland
| | | | - Nam P Nguyen
- Radiation Oncology, Howard University, Washington, DC, USA
| | - Raymond Miralbell
- Radiation Oncology Department, Geneva University Hospitals, Geneva, Switzerland.
- Université de Genève, Geneva, Switzerland.
- Centro de Protonterapia Quirónsalud, Pozuelo de Alarcón, 28223, Madrid, Spain.
- Servei de Radiooncologia, Institut Oncològic Teknon, Quironsalud, Vilana 12, 08022, Barcelona, Spain.
| | - Vincent Vinh-Hung
- Radiation Oncology Department, Geneva University Hospitals, Geneva, Switzerland
- CHU de Martinique, Fort-de-France, Martinique, France
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138
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Abstract
A robust left digit effect arises in number line estimation such that adults' estimates for numerals with different hundreds place digits but nearly identical magnitudes are systematically different from one another (e.g., 299 is placed too far to the left of 302). In two experiments, we investigate whether brief feedback interventions designed to increase task effort can reduce or eliminate the left digit effect in a self-paced 0-1,000 number line estimation task. Participants were assigned to complete three blocks of 120 trials each where the middle block contained feedback or no feedback. Feedback was in the form of summary accuracy scores (Experiment 1; N = 153) or competitive (summary) accuracy scores (Experiment 2; N = 145). In both experiments, planned analyses revealed large left digit effects in all blocks regardless of feedback condition. Feedback did not lead to a reduction in the left digit effect in either experiment, but improvements in overall accuracy were observed. We conclude that there are no changes in the left digit effect resulting from either summary accuracy feedback or competitive accuracy feedback. Also reported are exploratory analyses of trial characteristics (e.g., whether 299 is presented before or after 302) and the left digit effect.
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139
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OUP accepted manuscript. Cereb Cortex 2022; 32:4733-4745. [DOI: 10.1093/cercor/bhab513] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2021] [Revised: 12/15/2021] [Accepted: 12/16/2021] [Indexed: 01/29/2023] Open
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140
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Cicchini GM, Anobile G, Chelli E, Arrighi R, Burr DC. Uncertainty and Prior Assumptions, Rather Than Innate Logarithmic Encoding, Explain Nonlinear Number-to-Space Mapping. Psychol Sci 2021; 33:121-134. [PMID: 34936846 DOI: 10.1177/09567976211034501] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Abstract
Mapping number to space is natural and spontaneous but often nonveridical, showing a clear compressive nonlinearity that is thought to reflect intrinsic logarithmic encoding of numerical values. We asked 78 adult participants to map dot arrays onto a number line across nine trials. Combining participant data, we confirmed that on the first trial, mapping was heavily compressed along the number line, but it became more linear across trials. Responses were well described by logarithmic compression but also by a parameter-free Bayesian model of central tendency, which quantitatively predicted the relationship between nonlinearity and number acuity. To experimentally test the Bayesian hypothesis, we asked 90 new participants to complete a color-line task in which they mapped noise-perturbed color patches to a "color line." When there was more noise at the high end of the color line, the mapping was logarithmic, but it became exponential with noise at the low end. We conclude that the nonlinearity of both number and color mapping reflects contextual Bayesian inference processes rather than intrinsic logarithmic encoding.
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Affiliation(s)
| | - Giovanni Anobile
- Department of Neuroscience, Psychology, Pharmacology, and Child Health, University of Florence
| | - Eleonora Chelli
- Department of Neuroscience, Psychology, Pharmacology, and Child Health, University of Florence
| | - Roberto Arrighi
- Department of Neuroscience, Psychology, Pharmacology, and Child Health, University of Florence
| | - David C Burr
- Institute of Neuroscience, National Research Council, Pisa, Italy.,Department of Neuroscience, Psychology, Pharmacology, and Child Health, University of Florence
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141
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Lopiccolo D, Chang CB. Cultural factors weaken but do not reverse left-to-right spatial biases in numerosity processing: Data from Arabic and English monoliterates and Arabic-English biliterates. PLoS One 2021; 16:e0261146. [PMID: 34914756 PMCID: PMC8675726 DOI: 10.1371/journal.pone.0261146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2020] [Accepted: 11/24/2021] [Indexed: 01/29/2023] Open
Abstract
Directional response biases due to a conceptual link between space and number, such as a left-to-right hand bias for increasing numerical magnitude, are known as the SNARC (Spatial-Numerical Association of Response Codes) effect. We investigated how the SNARC effect for numerosities would be influenced by reading-writing direction, task instructions, and ambient visual environment in four literate populations exemplifying opposite reading-writing cultures-namely, Arabic (right-to-left script) and English (left-to-right script). Monoliterates and biliterates in Jordan and the U.S. completed a speeded numerosity comparison task to assess the directionality and magnitude of a SNARC effect in their numerosity processing. Monoliterates' results replicated previously documented effects of reading-writing direction and task instructions: the SNARC effect found in left-to-right readers was weakened in right-to-left readers, and the left-to-right group exhibited a task-dependency effect (SNARC effect in the smaller condition, reverse SNARC effect in the larger condition). Biliterates' results did not show a clear effect of environment; instead, both biliterate groups resembled English monoliterates in showing a left-to-right, task-dependent SNARC effect, albeit weaker than English monoliterates'. The absence of significant biases in all Arabic-reading groups (biliterates and Arabic monoliterates) points to a potential conflict between distinct spatial-numerical mapping codes. This view is explained in terms of the proposed Multiple Competing Codes Theory (MCCT), which posits three distinct spatial-numerical mapping codes (innate, cardinal, ordinal) during numerical processing-each involved at varying levels depending on individual and task factors.
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Affiliation(s)
- Dominique Lopiccolo
- Department of Linguistics, Boston University, Boston, Massachusetts, United States of America
| | - Charles B. Chang
- Department of Linguistics, Boston University, Boston, Massachusetts, United States of America
- * E-mail:
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142
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Constructing rationals through conjoint measurement of numerator and denominator as approximate integer magnitudes in tradeoff relations. Behav Brain Sci 2021; 44:e204. [PMID: 34907890 DOI: 10.1017/s0140525x21001497] [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
To investigate mechanisms of rational representation, I consider (1) construction of an ordered continuum of psychophysical scale of magnitude of sensation; (2) counting mechanism leading to an approximate numerosity scale for integers; and (3) conjoint measurement structure pitting the denominator against the numerator in tradeoff positions. Number sense of resulting rationals is neither intuitive nor expedient in their manipulation.
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143
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Real models: The limits of behavioural evidence for understanding the ANS. Behav Brain Sci 2021; 44:e186. [PMID: 34907874 DOI: 10.1017/s0140525x21001151] [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
Clarke and Beck use behavioural evidence to argue that (1) approximate ratio computations are sufficient for claiming that the approximate number system (ANS) represents the rationals, and (2) the ANS does not represent the reals. We argue that pure behaviour is a poor litmus test for this problem, and that we should trust the psychophysical models that place ANS representations within the reals.
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144
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Sokolowski HM, Merkley R, Kingissepp SSB, Vaikuntharajan P, Ansari D. Children's attention to numerical quantities relates to verbal number knowledge: An introduction to the Build-A-Train task. Dev Sci 2021; 25:e13211. [PMID: 34889002 DOI: 10.1111/desc.13211] [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: 05/13/2021] [Revised: 10/24/2021] [Accepted: 12/02/2021] [Indexed: 01/29/2023]
Abstract
Which dimension of a set of objects is more salient to young children: number or size? The 'Build-A-Train' task was developed and used to examine whether children spontaneously use a number or physical size approach on an un-cued matching task. In the Build-A-Train task, an experimenter assembles a train using one to five blocks of a particular length and asks the child to build the same train. The child's blocks differ in length from the experimenter's blocks, causing the child to build a train that matches based on either the number of blocks or length of the train, as it is not possible to match on both. One hundred and nineteen children between 2 years 2 months and 6 years 0 months of age (M = 4.05, SD = 0.84) completed the Build-A-Train task, and the Give-a-Number task, a classic task used to assess children's conceptual knowledge of verbal number words. Across train lengths and verbal number knowledge levels, children used a number approach more than a size approach on the Build-A-Train task. However, children were especially likely to use a number approach over a size approach when they knew the verbal number word that corresponded to the quantity of blocks in the train, particularly for quantities smaller than four. Therefore, children's attention to number relates to their knowledge of verbal number words. The Build-A-Train task and findings from the current study set a foundation for future longitudinal research to investigate the causal relationship between children's acquisition of symbolic mathematical concepts and attention to number.
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Affiliation(s)
- H Moriah Sokolowski
- Rotman Research Institute, Baycrest Hospital, Toronto, Ontario, Canada.,Department of Psychology, Faculty of Education, Brain and Mind Institute, University of Western Ontario, London, Ontario, Canada
| | - Rebecca Merkley
- Department of Cognitive Science, Carleton University, Ottawa, Ontario, Canada
| | - Sarah Samantha Bray Kingissepp
- Department of Psychology, Faculty of Education, Brain and Mind Institute, University of Western Ontario, London, Ontario, Canada
| | - Praja Vaikuntharajan
- Department of Psychology, Faculty of Education, Brain and Mind Institute, University of Western Ontario, London, Ontario, Canada
| | - Daniel Ansari
- Department of Psychology, Faculty of Education, Brain and Mind Institute, University of Western Ontario, London, Ontario, Canada
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145
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Pantsar M. On the development of geometric cognition: Beyond nature vs. nurture. PHILOSOPHICAL PSYCHOLOGY 2021. [DOI: 10.1080/09515089.2021.2014441] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Affiliation(s)
- Markus Pantsar
- Department of Philosophy, History and Art Studies, University of Helsinki, Helsinki, Finland
- KHK Kolleg Cultures of Research, RWTH University, Aachen, Germany
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146
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Lõoke M, Marinelli L, Agrillo C, Guérineau C, Mongillo P. Dogs (canis familiaris) underestimate the quantity of connected items: first demonstration of susceptibility to the connectedness illusion in non-human animals. Sci Rep 2021; 11:23291. [PMID: 34857858 PMCID: PMC8639746 DOI: 10.1038/s41598-021-02791-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2021] [Accepted: 11/22/2021] [Indexed: 02/05/2023] Open
Abstract
In humans, numerical estimation is affected by perceptual biases, such as those originating from the spatial arrangement of elements. Different animal species can also make relative quantity judgements. This includes dogs, who have been proposed as a good model for comparative neuroscience. However, dogs do not show the same perceptual biases observed in humans. Thus, the exact perceptual/cognitive mechanisms underlying quantity estimations in dogs and their degree of similarity with humans are still a matter of debate. Here we explored whether dogs are susceptible to the connectedness illusion, an illusion based on the tendency to underestimate the quantity of interconnected items. Dogs were first trained to choose the larger of two food arrays. Then, they were presented with two arrays containing the same quantity of food, of which one had items interconnected by lines. Dogs significantly selected the array with unconnected items, suggesting that, like in humans, connectedness determines underestimation biases, possibly disrupting the perceptual system's ability to segment the display into discrete objects. The similarity in dogs' and humans' susceptibility to the connectedness, but not to other numerical illusions, suggests that different mechanisms are involved in the estimation of quantity of stimuli with different characteristics.
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Affiliation(s)
- Miina Lõoke
- Laboratory of Applied Ethology, Department of Comparative Biomedicine and Food Science, University of Padua, Padua, Italy
| | - Lieta Marinelli
- Laboratory of Applied Ethology, Department of Comparative Biomedicine and Food Science, University of Padua, Padua, Italy.
| | - Christian Agrillo
- Department of General Psychology, University of Padua, Padua, Italy
- Padua Neuroscience Centre, University of Padua, Padua, Italy
| | - Cécile Guérineau
- Laboratory of Applied Ethology, Department of Comparative Biomedicine and Food Science, University of Padua, Padua, Italy
| | - Paolo Mongillo
- Laboratory of Applied Ethology, Department of Comparative Biomedicine and Food Science, University of Padua, Padua, Italy
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147
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Nordt M, Gomez J, Natu VS, Rezai AA, Finzi D, Kular H, Grill-Spector K. Cortical recycling in high-level visual cortex during childhood development. Nat Hum Behav 2021; 5:1686-1697. [PMID: 34140657 PMCID: PMC8678383 DOI: 10.1038/s41562-021-01141-5] [Citation(s) in RCA: 31] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2020] [Accepted: 05/17/2021] [Indexed: 02/05/2023]
Abstract
Human ventral temporal cortex contains category-selective regions that respond preferentially to ecologically relevant categories such as faces, bodies, places and words and that are causally involved in the perception of these categories. How do these regions develop during childhood? We used functional magnetic resonance imaging to measure longitudinal development of category selectivity in school-age children over 1 to 5 years. We discovered that, from young childhood to the teens, face- and word-selective regions in ventral temporal cortex expand and become more category selective, but limb-selective regions shrink and lose their preference for limbs. Critically, as a child develops, increases in face and word selectivity are directly linked to decreases in limb selectivity, revealing that during childhood, limb selectivity in ventral temporal cortex is repurposed into word and face selectivity. These data provide evidence for cortical recycling during childhood development. This has important implications for understanding typical as well as atypical brain development and necessitates a rethinking of how cortical function develops during childhood.
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Affiliation(s)
- Marisa Nordt
- Department of Psychology, Stanford University, Stanford, CA, USA
| | - Jesse Gomez
- Princeton Neuroscience Institute, Princeton University, Princeton, NJ, USA
| | - Vaidehi S Natu
- Department of Psychology, Stanford University, Stanford, CA, USA
| | - Alex A Rezai
- Department of Psychology, Stanford University, Stanford, CA, USA
| | - Dawn Finzi
- Department of Psychology, Stanford University, Stanford, CA, USA
| | - Holly Kular
- Department of Psychology, Stanford University, Stanford, CA, USA
| | - Kalanit Grill-Spector
- Department of Psychology, Stanford University, Stanford, CA, USA.
- Neurosciences Program, Stanford University, Stanford, CA, USA.
- Wu Tsai Neurosciences Institute, Stanford University, Stanford, CA, USA.
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148
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Schneider RM, Brockbank E, Feiman R, Barner D. Counting and the ontogenetic origins of exact equality. Cognition 2021; 218:104952. [PMID: 34801862 DOI: 10.1016/j.cognition.2021.104952] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2021] [Revised: 10/28/2021] [Accepted: 11/03/2021] [Indexed: 01/29/2023]
Abstract
Humans are unique in their capacity to both represent number exactly and to express these representations symbolically. This correlation has prompted debate regarding whether symbolic number systems are necessary to represent large exact number. Previous work addressing this question in innumerate adults and semi-numerate children has been limited by conflicting results and differing methodologies, and has not yielded a clear answer. We address this debate by adapting methods used with innumerate populations (a "set-matching" task) for 3- to 5-year-old US children at varying stages of symbolic number acquisition. In five studies we find that children's ability to match sets exactly is related not simply to knowing the meanings of a few number words, but also to understanding how counting is used to generate sets (i.e., the cardinal principle). However, while children were more likely to match sets after acquiring the cardinal principle, they nevertheless demonstrated failures, compatible with the hypothesis that the ability to reason about exact equality emerges sometime later. These findings provide important data on the origin of exact number concepts, and point to knowledge of a counting system, rather than number language in general, as a key ingredient in the ability to reason about large exact number.
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Affiliation(s)
- Rose M Schneider
- Department of Psychology, University of California, San Diego, CA, United States of America; Department of Cognitive, Linguistic, and Psychological Sciences, Brown University, Providence, RI, United States of America.
| | - Erik Brockbank
- Department of Psychology, University of California, San Diego, CA, United States of America; Department of Cognitive, Linguistic, and Psychological Sciences, Brown University, Providence, RI, United States of America
| | - Roman Feiman
- Department of Psychology, University of California, San Diego, CA, United States of America; Department of Cognitive, Linguistic, and Psychological Sciences, Brown University, Providence, RI, United States of America
| | - David Barner
- Department of Psychology, University of California, San Diego, CA, United States of America; Department of Cognitive, Linguistic, and Psychological Sciences, Brown University, Providence, RI, United States of America
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149
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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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150
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Hyde DC, Mou Y, Berteletti I, Spelke ES, Dehaene S, Piazza M. Testing the role of symbols in preschool numeracy: An experimental computer-based intervention study. PLoS One 2021; 16:e0259775. [PMID: 34780526 PMCID: PMC8592431 DOI: 10.1371/journal.pone.0259775] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2021] [Accepted: 10/27/2021] [Indexed: 01/29/2023] Open
Abstract
Numeracy is of critical importance for scholastic success and modern-day living, but the precise mechanisms that drive its development are poorly understood. Here we used novel experimental training methods to begin to investigate the role of symbols in the development of numeracy in preschool-aged children. We assigned pre-school children in the U.S. and Italy (N = 215; Mean age = 49.15 months) to play one of five versions of a computer-based numerical comparison game for two weeks. The different versions of the game were equated on basic features of gameplay and demands but systematically varied in numerical content. Critically, some versions included non-symbolic numerical comparisons only, while others combined non-symbolic numerical comparison with symbolic aids of various types. Before and after training we assessed four components of early numeracy: counting proficiency, non-symbolic numerical comparison, one-to-one correspondence, and arithmetic set transformation. We found that overall children showed improvement in most of these components after completing these short trainings. However, children trained on numerical comparisons with symbolic aids made larger gains on assessments of one-to-one correspondence and arithmetic transformation compared to children whose training involved non-symbolic numerical comparison only. Further exploratory analyses suggested that, although there were no major differences between children trained with verbal symbols (e.g., verbal counting) and non-verbal visuo-spatial symbols (i.e., abacus counting), the gains in one-to-one correspondence may have been driven by abacus training, while the gains in non-verbal arithmetic transformations may have been driven by verbal training. These results provide initial evidence that the introduction of symbols may contribute to the emergence of numeracy by enhancing the capacity for thinking about exact equality and the numerical effects of set transformations. More broadly, this study provides an empirical basis to motivate further focused study of the processes by which children’s mastery of symbols influences children’s developing mastery of numeracy.
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Affiliation(s)
- Daniel C. Hyde
- Department of Psychology, University of Illinois at Urbana-Champaign, Champaign, IL, United States of America
- Neuroscience Program, University of Illinois at Urbana-Champaign, Champaign, IL, United States of America
- * E-mail:
| | - Yi Mou
- Department of Psychology, Guangdong Provincial Key Laboratory of Social Cognitive Neuroscience and Mental Health, Sun Yat-sen University, Guangzhou, China
| | - Ilaria Berteletti
- Educational Neuroscience Program, Gallaudet University, Washington, D.C, United States of America
| | - Elizabeth S. Spelke
- Department of Psychology, Harvard University, Cambridge, MA, United States of America
| | - Stanislas Dehaene
- Cognitive Neuroimaging Unit, CEA DRF/I2BM, INSERM, NeuroSpin Center, Université Paris-Sud, Université Paris-Saclay, Gif/Yvette, France
- Collège de France, Paris, France
| | - Manuela Piazza
- Center for Mind/Brain Sciences, University of Trento, Rovereto, Italy
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