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Ma M, Likhanov M, Zhou X. Number sense-arithmetic link in Grade 1 and Grade 2: A case of fluency. BRITISH JOURNAL OF EDUCATIONAL PSYCHOLOGY 2024; 94:897-918. [PMID: 38802998 DOI: 10.1111/bjep.12693] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Revised: 05/10/2024] [Accepted: 05/13/2024] [Indexed: 05/29/2024]
Abstract
BACKGROUND Recent research suggested fluent processing as an explanation on why number sense contributes to simple arithmetic tasks-'Fluency hypothesis'. AIMS The current study investigates whether number sense contributes to such arithmetic tasks when other cognitive factors are controlled for (including those that mediate the link); and whether this contribution varies as a function of participants' individual maths fluency levels. SAMPLE Four hundred and thirty-seven Chinese schoolchildren (186 females; Mage = 83.49 months) completed a range of cognitive measures in Grade 1 (no previous classroom training) and in Grade 2 (a year later). METHODS Number sense, arithmetic (addition and subtraction), spatial ability, visuo-spatial working memory, perception, reaction time, character reading and general intelligence were measured. RESULTS Our data showed that the link between number sense and arithmetic was weaker in Grade 1 (Beta = .15 for addition and .06 (ns) for subtraction) compared to Grade 2 (.23-.28), but still persisted in children with no previous maths training. Further, math's performance in Grade 1 did not affect the link between number sense and maths performance in Grade 2. CONCLUSION Our data extended previous findings by showing that number sense is linked with simple maths task performance even after controlling for multiple cognitive factors. Our results brought some evidence that number sense-arithmetic link is somewhat sensitive to previous formal maths education. Further research is needed, as the differences in effects between grades were quite small, and arithmetic in Grade 1 did not moderate the link at question in Grade 2.
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Affiliation(s)
- Mei Ma
- State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China
| | - Maxim Likhanov
- State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China
| | - Xinlin Zhou
- State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China
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2
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Ribner A, Silver AM, Elliott L, Libertus ME. Exploring effects of an early math intervention: The importance of parent-child interaction. Child Dev 2023; 94:395-410. [PMID: 36321367 PMCID: PMC9991950 DOI: 10.1111/cdev.13867] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
We explore whether training parents' math skills or playing number games improves children's mathematical skills. Participants were 162 parent-child dyads; 88.3% were white and children (79 female) were 4 years (M = 46.88 months). Dyads were assigned to a number game, shape game, parent-only approximate number system training, parent-only general trivia, or a no-training control condition and asked to play twice weekly for 8 weeks. Children in the number game condition gained over 15% SD on an assessment of mathematical skill than did those in the no-training control. After 8 additional weeks without training, effects diminished; however, children of parents in the ANS condition underperformed those in the no-treatment control, which was partially explained by changes in the home numeracy environment.
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Affiliation(s)
- Andrew Ribner
- University of Pittsburgh, Pittsburgh, Pennsylvania, USA
| | - Alex M Silver
- University of Pittsburgh, Pittsburgh, Pennsylvania, USA
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3
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Mou Y, Zhang B, Hyde DC. Directionality in the interrelations between approximate number, verbal number, and mathematics in preschool-aged children. Child Dev 2023; 94:e67-e84. [PMID: 36528845 DOI: 10.1111/cdev.13879] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
A fundamental question in numerical development concerns the directional relation between an early-emerging non-verbal approximate number system (ANS) and culturally acquired verbal number and mathematics knowledge. Using path models on longitudinal data collected in preschool children (Mage = 3.86 years; N = 216; 99 males; 80.8% White; 10.8% Multiracial, 3.8% Latino; 1.9% Black; collected 2013-2017) over 1 year, this study showed that earlier verbal number knowledge was associated with later ANS precision (average β = .32), even after controlling for baseline differences in numerical, general cognitive, and language abilities. In contrast, earlier ANS precision was not associated with later verbal number knowledge (β = -.07) or mathematics abilities (average β = .10). These results suggest that learning about verbal numbers is associated with a sharpening of pre-existing non-verbal numerical abilities.
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Affiliation(s)
- Yi Mou
- Department of Psychology, Sun Yat-sen University, Guangzhou, People's Republic of China
| | - Bo Zhang
- School of Labor and Employment Relations, University of Illinois Urbana-Champaign, Champaign, Illinois, USA.,Department of Psychology, University of Illinois at Urbana-Champaign, Champaign, Illinois, USA
| | - Daniel C Hyde
- Department of Psychology, University of Illinois at Urbana-Champaign, Champaign, Illinois, USA
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4
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Zaleznik E, Comeau O, Park J. EXPRESS: Arithmetic operations without symbols are unimpaired in adults with math anxiety. Q J Exp Psychol (Hove) 2022; 76:1264-1274. [PMID: 35775834 DOI: 10.1177/17470218221113555] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
This study characterizes a previously unstudied facet of a major causal model of math anxiety. The model posits that impaired "basic number abilities" can lead to math anxiety, but what constitutes a basic number ability remains underdefined. Previous work has raised the idea that our perceptual ability to represent quantities approximately without using symbols constitutes one of the basic number abilities. Indeed, several recent studies tested how participants with math anxiety estimate and compare non-symbolic quantities. However, little is known about how participants with math anxiety perform arithmetic operations (addition and subtraction) on non-symbolic quantities. This is an important question because poor arithmetic performance on symbolic numbers is one of the primary signatures of high math anxiety. To test the question, we recruited 92 participants and asked them to complete a math anxiety survey, two measures of working memory, a timed symbolic arithmetic test, and a non-symbolic "approximate arithmetic" task. We hypothesized that if impaired ability to perform operations was a potential causal factor to math anxiety, we should see relationships between math anxiety and both symbolic and approximate arithmetic. However, if math anxiety relates to precise or symbolic representation, only a relationship between math anxiety and symbolic arithmetic should appear. Our results show no relationship between math anxiety and the ability to perform operations with approximate quantities, suggesting that difficulties performing perceptually based arithmetic operations does not constitute a basic number ability linked to math anxiety.
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Affiliation(s)
- Eli Zaleznik
- Department of Psychological and Brain Sciences 14707
| | - Olivia Comeau
- Department of Psychological and Brain Sciences 14707.,Commonwealth Honors College University of Massachusetts Amherst, U.S.A
| | - Joonkoo Park
- Department of Psychological and Brain Sciences 14707.,Commonwealth Honors College University of Massachusetts Amherst, U.S.A
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5
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Coolen IEJI, Riggs KJ, Bugler M, Castronovo J. The approximate number system and mathematics achievement: it's complicated. A thorough investigation of different ANS measures and executive functions in mathematics achievement in children. JOURNAL OF COGNITIVE PSYCHOLOGY 2022. [DOI: 10.1080/20445911.2022.2044338] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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6
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Silver AM, Elliott L, Reynvoet B, Sasanguie D, Libertus ME. Teasing apart the unique contributions of cognitive and affective predictors of math performance. Ann N Y Acad Sci 2022; 1511:173-190. [PMID: 35092064 PMCID: PMC9117397 DOI: 10.1111/nyas.14747] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Math permeates everyday life, and math skills are linked to general educational attainment, income, career choice, likelihood of full-time employment, and health and financial decision making. Thus, researchers have attempted to understand factors predicting math performance in order to identify ways of supporting math development. Work examining individual differences in math performance typically focuses on either cognitive predictors, including inhibitory control and the approximate number system (ANS; a nonsymbolic numerical comparison system), or affective predictors, like math anxiety. Studies with children suggest that these factors are interrelated, warranting examination of whether and how each uniquely and independently contributes to math performance in adulthood. Here, we examined how inhibitory control, the ANS, and math anxiety predicted college students' math performance (n = 122, mean age = 19.70 years). Using structural equation modeling, we find that although inhibitory control and the ANS were closely related to each other, they did not predict math performance above and beyond the effects of the other while also controlling for math anxiety. Instead, math anxiety was the only unique predictor of math performance. These findings contradict previous results in children and reinforce the need to consider affective factors in our discussions and interventions for supporting math performance in college students.
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Affiliation(s)
- Alex M. Silver
- Department of Psychology, Learning Research and Development Center University of Pittsburgh Pittsburgh Pennsylvania
| | - Leanne Elliott
- Department of Psychology, Learning Research and Development Center University of Pittsburgh Pittsburgh Pennsylvania
| | - Bert Reynvoet
- Faculty of Psychology and Educational Sciences KU Leuven @Kulak Leuven Belgium
| | - Delphine Sasanguie
- Research Centre for Learning in Diversity University College Ghent (HOGENT) Ghent Belgium
| | - Melissa E. Libertus
- Department of Psychology, Learning Research and Development Center University of Pittsburgh Pittsburgh Pennsylvania
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7
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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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8
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Suárez-Pellicioni M, Demir-Lira ÖE, Booth JR. Neurocognitive mechanisms explaining the role of math attitudes in predicting children's improvement in multiplication skill. COGNITIVE, AFFECTIVE & BEHAVIORAL NEUROSCIENCE 2021; 21:917-935. [PMID: 33954927 PMCID: PMC8455431 DOI: 10.3758/s13415-021-00906-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/19/2021] [Indexed: 11/08/2022]
Abstract
Enhancing student's math achievement is a significant educational challenge. Numerous studies have shown that math attitudes can predict improvement in math performance, but no study has yet revealed the underlying neurocognitive mechanisms explaining this effect. To answer this question, 50 children underwent functional magnetic resonance imaging (fMRI) when they were 11 (time 1; T1) and 13 (time 2; T2) years old. Children solved a rhyming judgment and a single-digit multiplication task inside the scanner at T1. The rhyming task was used to independently define a verbal region of interest in the left inferior frontal gyrus (IFG). We focused on this region because of previous evidence showing math attitudes-related effects in the left IFG for children with low math skill (Demir-Lira et al., 2019). Children completed standardized testing of math attitudes at T1 and of multiplication skill both at T1 and T2. We performed a cluster-wise regression analysis to investigate the interaction between math attitudes and improvement in multiplication skill over time while controlling for the main effects of these variables, intelligence, and accuracy on the task. This analysis revealed a significant interaction in the left IFG, which was due to improvers with positive math attitudes showing enhanced activation. Our result suggests that IFG activation, possibly reflecting effort invested in retrieving multiplication facts, is one of the possible neurocognitive mechanism by which children with positive math attitudes improve in multiplication skill. Our finding suggests that teachers and parents can help children do better in math by promoting positive math attitudes.
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Affiliation(s)
- Macarena Suárez-Pellicioni
- Department of Educational Studies in Psychology, Research Methodology, and Counseling, University of Alabama, 270 Kilgore Ln, Tuscaloosa, AL, USA.
| | - Ö Ece Demir-Lira
- Department of Psychological and Brain Sciences, DeLTA Center, Iowa Neuroscience Institute, The University of Iowa, Iowa City, IA, USA
| | - James R Booth
- Department of Psychology and Human Development, Vanderbilt University, Nashville, TN, USA
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9
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Vogel SE, De Smedt B. Developmental brain dynamics of numerical and arithmetic abilities. NPJ SCIENCE OF LEARNING 2021; 6:22. [PMID: 34301948 PMCID: PMC8302738 DOI: 10.1038/s41539-021-00099-3] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2020] [Accepted: 06/24/2021] [Indexed: 05/07/2023]
Abstract
The development of numerical and arithmetic abilities constitutes a crucial cornerstone in our modern and educated societies. Difficulties to acquire these central skills can lead to severe consequences for an individual's well-being and nation's economy. In the present review, we describe our current broad understanding of the functional and structural brain organization that supports the development of numbers and arithmetic. The existing evidence points towards a complex interaction among multiple domain-specific (e.g., representation of quantities and number symbols) and domain-general (e.g., working memory, visual-spatial abilities) cognitive processes, as well as a dynamic integration of several brain regions into functional networks that support these processes. These networks are mainly, but not exclusively, located in regions of the frontal and parietal cortex, and the functional and structural dynamics of these networks differ as a function of age and performance level. Distinctive brain activation patterns have also been shown for children with dyscalculia, a specific learning disability in the domain of mathematics. Although our knowledge about the developmental brain dynamics of number and arithmetic has greatly improved over the past years, many questions about the interaction and the causal involvement of the abovementioned functional brain networks remain. This review provides a broad and critical overview of the known developmental processes and what is yet to be discovered.
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Affiliation(s)
- Stephan E Vogel
- Educational Neuroscience, Institute of Psychology, University of Graz, Graz, Austria.
| | - Bert De Smedt
- Faculty of Psychology and Educational Sciences, KU Leuven, University of Leuven, Leuven, Belgium
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10
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Libertus ME, Odic D, Feigenson L, Halberda J. Effects of Visual Training of Approximate Number Sense on Auditory Number Sense and School Math Ability. Front Psychol 2020; 11:2085. [PMID: 32973627 PMCID: PMC7481447 DOI: 10.3389/fpsyg.2020.02085] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2019] [Accepted: 07/28/2020] [Indexed: 01/29/2023] Open
Abstract
Research with children and adults suggests that people's math performance is predicted by individual differences in an evolutionarily ancient ability to estimate and compare numerical quantities without counting (the approximate number system or ANS). However, previous work has almost exclusively used visual stimuli to measure ANS precision, leaving open the possibility that the observed link might be driven by aspects of visuospatial competence, rather than the amodal ANS. We addressed this possibility in an ANS training study. Sixty-eight 6-year-old children participated in a 5-week study that either trained their visual ANS ability or their phonological awareness (an active control group). Immediately before and after training, we assessed children's visual and auditory ANS precision, as well as their symbolic math ability and phonological awareness. We found that, prior to training, children's precision in a visual ANS task related to their math performance - replicating recent studies. Importantly, precision in an auditory ANS task also related to math performance. Furthermore, we found that children who completed visual ANS training showed greater improvements in auditory ANS precision than children who completed phonological awareness training. Finally, children in the ANS training group showed significant improvements in math ability but not phonological awareness. These results suggest that the link between ANS precision and school math ability goes beyond visuospatial abilities and that the modality-independent ANS is causally linked to math ability in early childhood.
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Affiliation(s)
- Melissa E Libertus
- Department of Psychology and Learning Research and Development Center, University of Pittsburgh, Pittsburgh, PA, United States.,Department of Psychological and Brain Sciences, Johns Hopkins University, Baltimore, MD, United States
| | - Darko Odic
- Department of Psychological and Brain Sciences, Johns Hopkins University, Baltimore, MD, United States.,Department of Psychology, The University of British Columbia, Vancouver, BC, Canada
| | - Lisa Feigenson
- Department of Psychological and Brain Sciences, Johns Hopkins University, Baltimore, MD, United States
| | - Justin Halberda
- Department of Psychological and Brain Sciences, Johns Hopkins University, Baltimore, MD, United States
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11
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Wang JJ, Halberda J, Feigenson L. Emergence of the Link Between the Approximate Number System and Symbolic Math Ability. Child Dev 2020; 92:e186-e200. [PMID: 32816346 DOI: 10.1111/cdev.13454] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Experimentally manipulating Approximate Number System (ANS) precision has been found to influence children's subsequent symbolic math performance. Here in three experiments (N = 160; 81 girls; 3-5 year old) we replicated this effect and examined its duration and developmental trajectory. We found that modulation of 5-year-olds' ANS precision continued to affect their symbolic math performance after a 30-min delay. Furthermore, our cross-sectional investigation revealed that children 4.5 years and older experienced a significant transfer effect of ANS manipulation on math performance, whereas younger children showed no such transfer, despite experiencing significant changes in ANS precision. These findings support the existence of a causal link between nonverbal numerical approximation and symbolic math performance that first emerges during the preschool years.
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12
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Wilkey ED, Ansari D. Challenging the neurobiological link between number sense and symbolic numerical abilities. Ann N Y Acad Sci 2019; 1464:76-98. [PMID: 31549430 DOI: 10.1111/nyas.14225] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2019] [Revised: 07/25/2019] [Accepted: 08/06/2019] [Indexed: 01/29/2023]
Abstract
A significant body of research links individual differences in symbolic numerical abilities, such as arithmetic, to number sense, the neurobiological system used to approximate and manipulate quantities without language or symbols. However, recent findings from cognitive neuroscience challenge this influential theory. Our current review presents an overview of evidence for the number sense account of symbolic numerical abilities and then reviews recent studies that challenge this account, organized around the following four assertions. (1) There is no number sense as traditionally conceived. (2) Neural substrates of number sense are more widely distributed than common consensus asserts, complicating the neurobiological evidence linking number sense to numerical abilities. (3) The most common measures of number sense are confounded by other cognitive demands, which drive key correlations. (4) Number sense and symbolic number systems (Arabic digits, number words, and so on) rely on distinct neural mechanisms and follow independent developmental trajectories. The review follows each assertion with comments on future directions that may bring resolution to these issues.
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Affiliation(s)
- Eric D Wilkey
- Brain and Mind Institute, Western University, London, Ontario, Canada
| | - Daniel Ansari
- Brain and Mind Institute, Western University, London, Ontario, Canada
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13
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Gimbert F, Gentaz É, Mazens K. Approximate number system training with vision or touch in children. ANNEE PSYCHOLOGIQUE 2019. [DOI: 10.3917/anpsy1.191.0003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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14
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Abstract
Recent research suggests that humans perceive quantity using a non-symbolic "number sense." This sense is then thought to provide a foundation for understanding symbolic numbers in formal education. Given this link, there has been interest in the extent to which the approximate number system (ANS) can be improved via dedicated training, as this could provide a route to improving performance in symbolic mathematics. However, current evidence regarding the trainability of the ANS comes largely from studies that have used short training durations, leaving open the question of whether improvements occur over a longer time span. To address this limitation, we utilized a perceptual learning approach to investigate the extent to which long-term (8,000+ trials) training modifies the ANS. Consistent with the general methodological approach common in the domain of perceptual learning (where learning specificity is commonly observed), we also examined whether ANS training generalizes to: (a) untrained locations in the visual field; (b) an enumeration task; (c) a higher-level ratio comparison task; and (d) arithmetic ability. In contrast to previous short-term training studies showing that ANS learning quickly asymptotes, our long-term training approach revealed that performance continued to improve even after thousands of trials. We further found that the training generalized to untrained visual locations. At post-test there was non-significant evidence for generalization to a low-level enumeration task, but not to our high-level tasks, including ratio comparison, multi-object tracking, and arithmetic performance. These results demonstrate the potential utility of long-term psychophysical training, but also suggest that ANS training alone (even long-duration training) may be insufficient to modify higher-level math skills.
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15
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Elliott L, Feigenson L, Halberda J, Libertus ME. Bidirectional, Longitudinal Associations Between Math Ability and Approximate Number System Precision in Childhood. JOURNAL OF COGNITION AND DEVELOPMENT 2018. [DOI: 10.1080/15248372.2018.1551218] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
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16
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Suárez-Pellicioni M, Booth JR. Fluency in symbolic arithmetic refines the approximate number system in parietal cortex. Hum Brain Mapp 2018; 39:3956-3971. [PMID: 30024084 DOI: 10.1002/hbm.24223] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2018] [Revised: 05/04/2018] [Accepted: 05/09/2018] [Indexed: 01/29/2023] Open
Abstract
The objective of this study was to investigate, using a brain measure of approximate number system (ANS) acuity, whether the precision of the ANS is crucial for the development of symbolic numerical abilities (i.e., scaffolding hypothesis) and/or whether the experience with symbolic number processing refines the ANS (i.e., refinement hypothesis). To this aim, 38 children solved a dot comparison task inside the scanner when they were approximately 10-years old (Time 1) and once again approximately 2 years later (Time 2). To study the scaffolding hypothesis, a regression analysis was carried out by entering ANS acuity at T1 as the predictor and symbolic math performance at T2 as the dependent measure. Symbolic math performance, visuospatial WM and full IQ (all at T1) were entered as covariates of no interest. In order to study the refinement hypothesis, the regression analysis included symbolic math performance at T1 as the predictor and ANS acuity at T2 as the dependent measure, while ANS acuity, visuospatial WM and full IQ (all at T1) were entered as covariates of no interest. Our results supported the refinement hypothesis, by finding that the higher the initial level of symbolic math performance, the greater the intraparietal sulcus activation was at T2 (i.e., more precise representation of quantity). To the best of our knowledge, our finding constitutes the first evidence showing that expertise in the manipulation of symbols, which is a cultural invention, has the power to refine the neural representation of quantity in the evolutionarily ancient, approximate system of quantity representation.
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Affiliation(s)
| | - James R Booth
- Department of Psychology and Human Development, Vanderbilt University, Nashville, Tennessee, 37203-5721
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17
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Abstract
AbstractLeibovich et al. argue persuasively that researchers should not assume that approximate number system (ANS) tasks harness an innate sense of number. However, some studies have reported a causal link between ANS tasks and mathematics performance, implicating the ANS in the development of numerical skills. Here we report a p-curve analysis, which indicates that these experimental studies do not contain evidential value.
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18
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Libertus ME, Forsman L, Adén U, Hellgren K. Deficits in Approximate Number System Acuity and Mathematical Abilities in 6.5-Year-Old Children Born Extremely Preterm. Front Psychol 2017; 8:1175. [PMID: 28744252 PMCID: PMC5504250 DOI: 10.3389/fpsyg.2017.01175] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2016] [Accepted: 06/27/2017] [Indexed: 01/29/2023] Open
Abstract
Preterm children are at increased risk for poor academic achievement, especially in math. In the present study, we examined whether preterm children differ from term-born children in their intuitive sense of number that relies on an unlearned, approximate number system (ANS) and whether there is a link between preterm children’s ANS acuity and their math abilities. To this end, 6.5-year-old extremely preterm (i.e., <27 weeks gestation, n = 82) and term-born children (n = 89) completed a non-symbolic number comparison (ANS acuity) task and a standardized math test. We found that extremely preterm children had significantly lower ANS acuity than term-born children and that these differences could not be fully explained by differences in verbal IQ, perceptual reasoning skills, working memory, or attention. Differences in ANS acuity persisted even when demands on visuo-spatial skills and attention were reduced in the ANS task. Finally, we found that ANS acuity and math ability are linked in extremely preterm children, similar to previous results from term-born children. These results suggest that deficits in the ANS may be at least partly responsible for the deficits in math abilities often observed in extremely preterm children.
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Affiliation(s)
- Melissa E Libertus
- Department of Psychology, Learning Research and Development Center, University of PittsburghPittsburgh, PA, United States
| | - Lea Forsman
- Department of Women's and Children's Health, Karolinska InstitutetStockholm, Sweden
| | - Ulrika Adén
- Department of Women's and Children's Health, Karolinska InstitutetStockholm, Sweden
| | - Kerstin Hellgren
- Department of Clinical Neuroscience, Karolinska InstitutetStockholm, Sweden
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Schwenk C, Sasanguie D, Kuhn JT, Kempe S, Doebler P, Holling H. (Non-)symbolic magnitude processing in children with mathematical difficulties: A meta-analysis. RESEARCH IN DEVELOPMENTAL DISABILITIES 2017; 64:152-167. [PMID: 28432933 DOI: 10.1016/j.ridd.2017.03.003] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2016] [Revised: 02/21/2017] [Accepted: 03/06/2017] [Indexed: 05/23/2023]
Abstract
Symbolic and non-symbolic magnitude representations, measured by digit or dot comparison tasks, are assumed to underlie the development of arithmetic skills. The comparison distance effect (CDE) has been suggested as a hallmark of the preciseness of mental magnitude representations. It implies that two magnitudes are harder to discriminate when the numerical distance between them is small, and may therefore differ in children with mathematical difficulties (MD), i.e. low mathematical achievement or dyscalculia. However, empirical findings on the CDE in children with MD are heterogeneous, and only few studies assess both symbolic and non-symbolic skills. This meta-analysis therefore integrates 44 symbolic and 48 non-symbolic response time (RT) outcomes reported in nineteen studies (N=1630 subjects, aged 6-14 years). Independent of age, children with MD show significantly longer mean RTs than typically achieving controls, particularly on symbolic (Hedges' g=0.75; 95% CI [0.51; 0.99]), but to a significantly lower extent also on non-symbolic (g=0.24; 95% CI [0.13; 0.36]) tasks. However, no group differences were found for the CDE. Extending recent work, these meta-analytical findings on children with MD corroborate the diagnostic importance of magnitude comparison speed in symbolic tasks. By contrast, the validity of CDE measures in assessing MD is questioned.
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Affiliation(s)
- Christin Schwenk
- Institute of Psychology, University of Münster, Fliednerstraße 21, 48149 Münster, Germany.
| | - Delphine Sasanguie
- Brain and Cognition, KU Leuven, Tiensestraat 102 - Box 3711, 3000 Leuven, Belgium; Faculty of Psychology and Educational Sciences@Kulak, KU Leuven Kulak, Etienne Sabbelaan 53, 8500 Kortrijk, Belgium.
| | - Jörg-Tobias Kuhn
- Institute of Psychology, University of Münster, Fliednerstraße 21, 48149 Münster, Germany.
| | - Sophia Kempe
- Institute of Psychology, University of Münster, Fliednerstraße 21, 48149 Münster, Germany.
| | - Philipp Doebler
- TU Dortmund University, Faculty of Statistics, Technische Universität Dortmund, 44221 Dortmund, Germany.
| | - Heinz Holling
- Institute of Psychology, University of Münster, Fliednerstraße 21, 48149 Münster, Germany.
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