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Xenidou-Dervou I, van Atteveldt N, Surducan IM, Reynvoet B, Rossi S, Gilmore C. Multiple number-naming associations: How the inversion property affects adults' two-digit number processing. Q J Exp Psychol (Hove) 2024; 77:856-872. [PMID: 37246891 PMCID: PMC10960323 DOI: 10.1177/17470218231181367] [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: 06/17/2022] [Revised: 05/19/2023] [Accepted: 05/23/2023] [Indexed: 05/30/2023]
Abstract
Some number-naming systems are less transparent than others. For example, in Dutch, 49 is named "negenenveertig," which translates to "nine and forty," i.e., the unit is named first, followed by the decade. This is known as the "inversion property," where the morpho-syntactic representation of the number name is incongruent with its written Arabic form. Number word inversion can hamper children's developing mathematical skills. But little is known about its effects on adults' numeracy, the underlying mechanism, and how a person's bilingual background influences its effects. In the present study, Dutch-English bilingual adults performed an audiovisual matching task, where they heard a number word and simultaneously saw two-digit Arabic symbols and had to determine whether these matched in quantity. We experimentally manipulated the morpho-syntactic structure of the number words to alter their phonological (dis)similarities and numerical congruency with the target Arabic two-digit number. Results showed that morpho-syntactic (in)congruency differentially influenced quantity match and non-match decisions. Although participants were faster when hearing traditional non-transparent Dutch number names, they made more accurate decisions when hearing artificial, but morpho-syntactically transparent number words. This pattern was partly influenced by the participants' bilingual background, i.e., their L2 proficiency in English, which involves more transparent number names. Our findings suggest that, within inversion number-naming systems, multiple associations are formed between two-digit Arabic symbols and number names, which can influence adults' numerical cognition.
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2
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Leonard SJ, Roche C, Durkan A, Gomides M, Santos FH. Children grow upwards, and so does the number line: Evidence from a directional number line paradigm. PROGRESS IN BRAIN RESEARCH 2023; 279:37-56. [PMID: 37661162 DOI: 10.1016/bs.pbr.2023.03.002] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/05/2023]
Abstract
Technological advancements give researchers the opportunity to explore the internal metric that allows to mentally place numbers in a spatial and ordered way to establish relationships between quantities. In this study, we implement the cMNL, an embodied number line paradigm to investigate the configuration of children's number space mappings under multiple conditions. A sample of 185 primary school children aged 8-10years old completed digitally an embodied number line task encompassing directionality and modality as variables. Contrary to the premise of a fixed internal number line moving from left to right in many Western scripts, our results suggest that children's number-space mapping is more robust along a vertical axis. In addition, children's embodied number line estimation differed depending on input modality. The findings provide insight into the variability in children's number line estimation, and the usability of digital assessment in understanding the mechanisms of the developing number-space system.
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Affiliation(s)
- Sophie J Leonard
- UCD School of Psychology, University College Dublin, Dublin, Ireland
| | - Ciara Roche
- UCD School of Psychology, University College Dublin, Dublin, Ireland
| | - Aoife Durkan
- UCD School of Psychology, University College Dublin, Dublin, Ireland
| | - Mariuche Gomides
- UCD School of Psychology, University College Dublin, Dublin, Ireland
| | - Flavia H Santos
- UCD School of Psychology, University College Dublin, Dublin, Ireland.
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3
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Nuraydin S, Stricker J, Ugen S, Martin R, Schneider M. The number line estimation task is a valid tool for assessing mathematical achievement: A population-level study with 6484 Luxembourgish ninth-graders. J Exp Child Psychol 2023; 225:105521. [PMID: 35973280 DOI: 10.1016/j.jecp.2022.105521] [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: 02/22/2021] [Revised: 07/15/2022] [Accepted: 07/15/2022] [Indexed: 01/29/2023]
Abstract
The number line estimation task is an often-used measure of numerical magnitude understanding. The task also correlates substantially with broader measures of mathematical achievement. This raises the question of whether the task would be a useful component of mathematical achievement tests and instruments to diagnose dyscalculia or mathematical giftedness and whether a stand-alone version of the task can serve as a short screener for mathematical achievement. Previous studies on the relation between number line estimation accuracy and broader mathematical achievement were limited in that they used relatively small nonrepresentative samples and usually did not account for potentially confounding variables. To close this research gap, we report findings from a population-level study with nearly all Luxembourgish ninth-graders (N = 6484). We used multilevel regressions to test how a standardized mathematical achievement test relates to the accuracy in number line estimation on bounded number lines with whole numbers and fractions. We also investigated how these relations were moderated by classroom characteristics, person characteristics, and trial characteristics. Mathematical achievement and number line estimation accuracy were associated even after controlling for potentially confounding variables. Subpopulations of students showed meaningful differences in estimation accuracy, which can serve as benchmarks in future studies. Compared with the number line estimation task with whole numbers, the number line estimation task with fractions was more strongly related to mathematical achievement in students across the entire mathematical achievement spectrum. These results show that the number line estimation task is a valid and useful tool for diagnosing and monitoring mathematical achievement.
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Affiliation(s)
| | | | - Sonja Ugen
- University of Luxembourg, L-4365 Esch-sur-Alzette, Luxembourg
| | - Romain Martin
- Ministry of Higher Education and Research, L-2327 Luxembourg, Luxembourg
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4
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Haman M, Patro K. More linear than log? Non-symbolic number-line estimation in 3- to 5-year-old children. Front Psychol 2022; 13:1003696. [PMID: 36389566 PMCID: PMC9659870 DOI: 10.3389/fpsyg.2022.1003696] [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: 07/26/2022] [Accepted: 10/03/2022] [Indexed: 11/04/2022] Open
Abstract
The number-line estimation task has become one of the most important methods in numerical cognition research. Originally applied as a direct measure of spatial number representation, it became also informative regarding various other aspects of number processing and associated strategies. However, most of this work and associated conclusions concerns processing numbers in a symbolic format, by school children and older subjects. Symbolic number system is formally taught and trained at school, and its basic mathematical properties (e.g., equidistance, ordinality) can easily be transferred into a spatial format of an oriented number line. This triggers the question on basic characteristics of number line estimation before children get fully familiar with the symbolic number system, i.e., when they mostly rely on approximate system for non-symbolic quantities. In our three studies, we examine therefore how preschool children (3–5-years old) estimate position of non-symbolic quantities on a line, and how this estimation is related to the developing symbolic number knowledge and cultural (left-to-right) directionality. The children were tested with the Give-a-number task, then they performed a computerized number-line task. In Experiment 1, lines bounded with sets of 1 and 20 elements going left-to-right or right-to-left were used. Even in the least numerically competent group, the linear model better fit the estimates than the logarithmic or cyclic power models. The line direction was irrelevant. In Experiment 2, a 1–9 left-to-right oriented line was used. Advantage of linear model was found at group level, and variance of estimates correlated with tested numerosities. In Experiment 3, a position-to-number procedure again revealed the advantage of the linear model, although the strategy of selecting an option more similar to the closer end of the line was prevalent. The precision of estimation increased with the mastery of counting principles in all three experiments. These results contradict the hypothesis of the log-to-linear shift in development of basic numerical representation, rather supporting the linear model with scalar variance. However, the important question remains whether the number-line task captures the nature of the basic numerical representation, or rather the strategies of mapping that representation to an external space.
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Affiliation(s)
- Maciej Haman
- Faculty of Psychology, University of Warsaw, Warsaw, Poland
- *Correspondence: Maciej Haman,
| | - Katarzyna Patro
- Faculty of Psychology, University of Warsaw, Warsaw, Poland
- Department of Psychology, University of Tuebingen, Tübingen, Germany
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5
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Altarriba J, Basnight-Brown D. The Psychology of Communication: The Interplay Between Language and Culture Through Time. JOURNAL OF CROSS-CULTURAL PSYCHOLOGY 2022. [DOI: 10.1177/00220221221114046] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Human behavior is often guided by the development and use of language as a means of communication and as a way to represent thoughts and knowledge. Notions of linguistic relativity and the Sapir-Whorf hypothesis indicate that language plays a role in structuring the worldview and perceptions of individuals. The current work will explore how those perceptions are not only guided by language but are also moderated by culture and the beliefs, mores, and ideas that are sanctioned and regulated by a given cultural group. Papers, chapters, and books that have demonstrated the ways in which culture moderates behavior by way of the language that is used to express that culture will be of primary focus. Moreover, a developmental view of language learning will frame this approach in learning how language, culture, and thought have been examined and assessed as a way of describing how, together, they moderate human behavior. Is there truly evidence of linguistic relativity? Does language serve as the primary moderator of thought, or do cultural influences play a more pressing role in cognitive thought processes for a given group? Developments in theory, methods, and data that help explore these concepts through their publication in the Journal of Cross-Cultural Psychology as well as other outlets will be presented and discussed as a framework that can be developed to generate future research questions, testing paradigms, and experimental approaches—both basic and applied.
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6
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Lê ML, Noël MP. Transparent Vietnamese number-naming system facilitates first graders transcoding – A cross-linguistic study with French. COGNITIVE DEVELOPMENT 2022. [DOI: 10.1016/j.cogdev.2021.101145] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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7
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Iturra-Osorio D, Vásquez F, Espinoza Pastén L, Ygual Fernández A. Habilidades matemáticas tempranas en niños chilenos con Trastorno del Desarrollo del Lenguaje: Un estudio comparativo. REVISTA DE INVESTIGACIÓN EN LOGOPEDIA 2021. [DOI: 10.5209/rlog.69580] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
En las últimas décadas se ha incrementado el interés de las investigaciones respecto a las dificultades académicas que presentan los niños con Trastorno del Desarrollo del Lenguaje (TDL). No obstante, su relación con las habilidades matemáticas es una de las menos estudiadas. El objetivo de este estudio consistió en determinar si existen diferencias relevantes entre las habilidades matemáticas tempranas de niños con TDL y con desarrollo típico (DT). Participaron 78 niños de 4 a 7 años 11 meses de edad, pertenecientes a colegios con programas de integración escolar de Santiago de Chile. Se conformó un grupo de 44 niños con TDL y un grupo de 34 con DT. Se establecieron comparaciones del rendimiento en tareas matemáticas pertenecientes a la versión en español del Test de Evaluación Matemática Temprana de Utrecht (TEMT-U): subtest relacionales (comparación, clasificación, correspondencia uno a uno y seriación), y subtest numérico (conteo verbal, conteo estructurado, conteo resultante y conocimiento general de los números); hallándose un rendimiento matemático significativamente menor en el grupo con TDL de educación infantil en ambos subtest. Los hallazgos sugieren que las dificultades propias de los niños con TDL impactan el aprendizaje matemático, especialmente en los niños más pequeños, por lo que resulta imperante disminuir las barreras que obstaculizan su proceso de aprendizaje.
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Barrett HC. Towards a Cognitive Science of the Human: Cross-Cultural Approaches and Their Urgency. Trends Cogn Sci 2020; 24:620-638. [DOI: 10.1016/j.tics.2020.05.007] [Citation(s) in RCA: 41] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2020] [Revised: 05/11/2020] [Accepted: 05/18/2020] [Indexed: 12/20/2022]
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9
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Cipora K, Haman M, Domahs F, Nuerk HC. Editorial: On the Development of Space-Number Relations: Linguistic and Cognitive Determinants, Influences, and Associations. Front Psychol 2020; 11:182. [PMID: 32116967 PMCID: PMC7033566 DOI: 10.3389/fpsyg.2020.00182] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2020] [Accepted: 01/27/2020] [Indexed: 11/13/2022] Open
Affiliation(s)
- Krzysztof Cipora
- Department of Psychology, University of Tübingen, Tübingen, Germany.,LEAD Research Network, University of Tübingen, Tübingen, Germany
| | - Maciej Haman
- Faculty of Psychology, University of Warsaw, Warsaw, Poland
| | - Frank Domahs
- Department of Linguistics, University of Erfurt, Erfurt, Germany
| | - Hans-Christoph Nuerk
- Department of Psychology, University of Tübingen, Tübingen, Germany.,LEAD Research Network, University of Tübingen, Tübingen, Germany
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10
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Lewis CA, Bahnmueller J, Wesierska M, Moeller K, Göbel SM. Inversion effects on mental arithmetic in English- and Polish-speaking adults. Q J Exp Psychol (Hove) 2019; 73:91-103. [PMID: 31561743 DOI: 10.1177/1747021819881983] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
In some languages the order of tens and units in number words is inverted compared with the symbolic digital notation (e.g., German 23 → "dreiundzwanzig," literally: "three-and-twenty"). In other languages only teen-numbers are inverted (e.g., English 17 → "seventeen"; Polish 17 → "siedemnaście" literally "seventeen"). Previous studies have focused on between group comparisons of inverted and non-inverted languages and showed that number word inversion impairs performance on basic numerical tasks and arithmetic. In two independent experiments, we investigated whether number word inversion affects addition performance within otherwise non-inverted languages (Exp. 1: English, Exp. 2: Polish). In particular, we focused on the influence of inverted (I; English: teen-numbers ⩾ 13, Polish: numbers 11-19) and non-inverted (N) summands with sums between 13 and 39. Accordingly, three categories of addition problems were created: N + N, N + I, and I + I with problem size matched across categories. Across both language groups, we observed that problems with results in the 20 and 30 number range were responded to faster when only non-inverted summands were part of the problems as opposed to problems with one or two inverted summands. In line with this, the cost of a carry procedure was the largest for two inverted summands. The results support the notion that both language-specific and language-invariant aspects contribute to addition problem-solving. In particular though, regarding language-specific aspects, the results indicate that inverted number word formation of teens influences place-value processing of Arabic digits even in otherwise non-inverted languages.
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Affiliation(s)
- Carolin Annette Lewis
- Leibniz-Institut für Wissensmedien, Tübingen, Germany.,Department of Neurology, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany.,Department of Psychiatry and Psychotherapy, University of Tuebingen, Tübingen, Germany
| | - Julia Bahnmueller
- Leibniz-Institut für Wissensmedien, Tübingen, Germany.,Department of Psychology and LEAD Graduate School and Research Network, University of Tuebingen, Tübingen, Germany
| | - Marta Wesierska
- Department of Psychology, University of York, York, UK.,Department of Human Communication Sciences, The University of Sheffield, Sheffield, UK
| | - Korbinian Moeller
- Leibniz-Institut für Wissensmedien, Tübingen, Germany.,Department of Psychology and LEAD Graduate School and Research Network, University of Tuebingen, Tübingen, Germany
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11
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Dowker A, Li AM. English and Chinese Children's Performance on Numerical Tasks. Front Psychol 2019; 9:2731. [PMID: 30804867 PMCID: PMC6370685 DOI: 10.3389/fpsyg.2018.02731] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2018] [Accepted: 12/18/2018] [Indexed: 11/13/2022] Open
Abstract
East Asian pupils have consistently outperformed Western pupils in international comparisons of mathematical performance at both primary and secondary school level. It has sometimes been suggested that a contributory factor is the transparent counting systems of East Asian languages, which may facilitate number representation. The present study compared 35 7-year-old second-year primary school children in Oxford, England and 40 children of similar age in Hong Kong, China on a standardized arithmetic test; on a two-digit number comparison test, including easy, misleading and reversible comparisons; and on a number line task, involving placing numbers in the appropriate position on four number lines: 1-10, 1-20, 1-100, and 1-1000. The Chinese children performed significantly better than the English children on the standardized arithmetic test. They were faster but not significantly more accurate on the Number Comparison and Number Line tasks. There were no interactions between language group and comparison type on the number comparison task, though the performance of both groups was faster on easy pairs than those where there was conflict between the relative magnitudes of the tens and the units. Similarly, there were no interactions between group and number line range, though the performance of both groups was influenced by the range of the number line. The study supports the view that counting systems affect aspects of numerical abilities, but cannot be the full explanation for international differences in mathematics performance.
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Affiliation(s)
- Ann Dowker
- Department of Experimental Psychology, Oxford University, Oxford, United Kingdom
| | - Anthony M Li
- Somerville College, Oxford University, Oxford, United Kingdom
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12
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Tosto MG, Garon-Carrier G, Gross S, Petrill SA, Malykh S, Malki K, Hart SA, Thompson L, Karadaghi RL, Yakovlev N, Tikhomirova T, Opfer JE, Mazzocco MMM, Dionne G, Brendgen M, Vitaro F, Tremblay RE, Boivin M, Kovas Y. The nature of the association between number line and mathematical performance: An international twin study. BRITISH JOURNAL OF EDUCATIONAL PSYCHOLOGY 2018; 89:787-803. [PMID: 30548254 DOI: 10.1111/bjep.12259] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2018] [Revised: 10/29/2018] [Indexed: 01/29/2023]
Abstract
BACKGROUND The number line task assesses the ability to estimate numerical magnitudes. People vary greatly in this ability, and this variability has been previously associated with mathematical skills. However, the sources of individual differences in number line estimation and its association with mathematics are not fully understood. AIMS This large-scale genetically sensitive study uses a twin design to estimate the magnitude of the effects of genes and environments on: (1) individual variation in number line estimation and (2) the covariation of number line estimation with mathematics. SAMPLES We used over 3,000 8- to 16-year-old twins from the United States, Canada, the United Kingdom, and Russia, and a sample of 1,456 8- to 18-year-old singleton Russian students. METHODS Twins were assessed on: (1) estimation of numerical magnitudes using a number line task and (2) two mathematics components: fluency and problem-solving. RESULTS Results suggest that environments largely drive individual differences in number line estimation. Both genes and environments contribute to different extents to the number line estimation and mathematics correlation, depending on the sample and mathematics component. CONCLUSIONS Taken together, the results suggest that in more heterogeneous school settings, environments may be more important in driving variation in number line estimation and its association with mathematics, whereas in more homogeneous school settings, genetic effects drive the covariation between number line estimation and mathematics. These results are discussed in the light of development and educational settings.
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Affiliation(s)
- Maria Grazia Tosto
- Laboratory for Cognitive Investigations and Behavioral Genetics, Department of Psychology, Institute of Genetic, Neurobiological, and Social Foundations of Child Development, Tomsk State University, Tomsk, Oblast, Russia
| | | | - Susan Gross
- Department of Psychological Sciences, Case Western Reserve University, Cleveland, Ohio, USA
| | - Stephen A Petrill
- Department of Psychology, The Ohio State University, Columbus, Ohio, USA
| | - Sergey Malykh
- Laboratory for Cognitive Investigations and Behavioral Genetics, Department of Psychology, Institute of Genetic, Neurobiological, and Social Foundations of Child Development, Tomsk State University, Tomsk, Oblast, Russia.,Psychological Institute, Russian Academy of Education, Moscow, Russia
| | - Karim Malki
- MRC Social, Genetic and Developmental Psychiatry Centre, Institute of Psychiatry, Psychology& Neuroscience, King's College London, UK
| | - Sara A Hart
- Department of Psychology, Florida Center for Reading Research, The Florida State University, Tallahassee, Florida, USA
| | - Lee Thompson
- Department of Psychological Sciences, Case Western Reserve University, Cleveland, Ohio, USA
| | - Rezhaw L Karadaghi
- MRC Social, Genetic and Developmental Psychiatry Centre, Institute of Psychiatry, Psychology& Neuroscience, King's College London, UK
| | - Nikita Yakovlev
- Laboratory for Cognitive Investigations and Behavioral Genetics, Department of Psychology, Institute of Genetic, Neurobiological, and Social Foundations of Child Development, Tomsk State University, Tomsk, Oblast, Russia
| | | | - John E Opfer
- Department of Psychology, The Ohio State University, Columbus, Ohio, USA
| | - Michèle M M Mazzocco
- Institute of Child Development, University of Minnesota, Minneapolis, Minnesota, USA
| | - Ginette Dionne
- School of Psychology, Université Laval, Québec City, Québec, Canada
| | - Mara Brendgen
- Department of Psychology, School of Psychology, Université du Québec à Montréal, Québec, Canada
| | - Frank Vitaro
- Department of Psychoeducation, Department of Pediatrics and Psychology, Université de Montréal, Québec, Canada
| | - Richard E Tremblay
- Laboratory for Cognitive Investigations and Behavioral Genetics, Department of Psychology, Institute of Genetic, Neurobiological, and Social Foundations of Child Development, Tomsk State University, Tomsk, Oblast, Russia.,Department of Psychoeducation, Department of Pediatrics and Psychology, Université de Montréal, Québec, Canada.,School of Public Health, Physiotherapy and Sports Science, University College Dublin, Belfield, Dublin 4, Ireland
| | - Michel Boivin
- Laboratory for Cognitive Investigations and Behavioral Genetics, Department of Psychology, Institute of Genetic, Neurobiological, and Social Foundations of Child Development, Tomsk State University, Tomsk, Oblast, Russia.,School of Psychology, Université Laval, Québec City, Québec, Canada
| | - Yulia Kovas
- Laboratory for Cognitive Investigations and Behavioral Genetics, Department of Psychology, Institute of Genetic, Neurobiological, and Social Foundations of Child Development, Tomsk State University, Tomsk, Oblast, Russia.,MRC Social, Genetic and Developmental Psychiatry Centre, Institute of Psychiatry, Psychology& Neuroscience, King's College London, UK.,Department of Psychology, University of London, UK
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13
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Weis T, Nuerk HC, Lachmann T. Attention allows the SNARC effect to operate on multiple number lines. Sci Rep 2018; 8:13778. [PMID: 30214027 PMCID: PMC6137054 DOI: 10.1038/s41598-018-32174-y] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2017] [Accepted: 08/30/2018] [Indexed: 02/04/2023] Open
Abstract
To investigate whether participants can activate only one spatially oriented number line at a time or multiple number lines simultaneously, they were asked to solve a unit magnitude comparison task (unit smaller/larger than 5) and a parity judgment task (even/odd) on two-digit numbers. In both these primary tasks, decades were irrelevant. After some of the primary task trials (randomly), participants were asked to additionally solve a secondary task based on the previously presented number. In Experiment 1, they had to decide whether the two-digit number presented for the primary task was larger or smaller than 50. Thus, for the secondary task decades were relevant. In contrast, in Experiment 2, the secondary task was a color judgment task, which means decades were irrelevant. In Experiment 1, decades' and units' magnitudes influenced the spatial association of numbers separately. In contrast, in Experiment 2, only the units were spatially associated with magnitude. It was concluded that multiple number lines (one for units and one for decades) can be activated if attention is focused on multiple, separate magnitude attributes.
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Affiliation(s)
- Tina Weis
- Cognitive and Developmental Psychology Unit, Center for Cognitive Science, University of Kaiserslautern, Kaiserslautern, Germany
| | - Hans-Christoph Nuerk
- Department of Psychology, University of Tuebingen, Tuebingen, Germany.,Leibniz-Institut für Wissensmedien IWM-KMRC, Tuebingen, Germany.,LEAD Graduate School and Research Network, University of Tuebingen, Tuebingen, Germany
| | - Thomas Lachmann
- Cognitive and Developmental Psychology Unit, Center for Cognitive Science, University of Kaiserslautern, Kaiserslautern, Germany. .,Department of Psychology, University of Leuven, Leuven, Belgium.
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14
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Bahnmueller J, Göbel SM, Pixner S, Dresen V, Moeller K. More than simple facts: cross-linguistic differences in place-value processing in arithmetic fact retrieval. PSYCHOLOGICAL RESEARCH 2018; 84:650-659. [PMID: 30171424 DOI: 10.1007/s00426-018-1083-7] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2017] [Accepted: 08/21/2018] [Indexed: 11/30/2022]
Abstract
Linguistic specificities such as the inversion property of number words (e.g., in German 43 is spoken dreiundvierzig, literally three and forty) moderate Arabic number processing. So far, cross-linguistic studies have mostly focused on inversion-related effects on simple (e.g., number comparison) and calculation-based (e.g., multi-digit addition) magnitude processing of numerical information. Despite the assumption that multiplication facts are represented in verbal format, not much attention has been paid to inversion-related influences on multiplication fact retrieval. Accordingly, the current study evaluated inversion-related effects on the processing of place-value information in multiplication. In a verification paradigm, the decade consistency effect (i.e., more errors when the decade of a solution probe shares the decade digit with the correct solution) was larger for English- than German-speaking participants for table-related probes. Processing of decade digits might be prioritised in English-speaking participants because the decade digit is named first in English number words, whereas in German number words the unit digit is named first. Our results indicate that (1) the influence of specificities of a verbal number word formation on place-value processing generalise to arithmetic fact retrieval and (2) inversion of number words might even be advantageous in specific cases.
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Affiliation(s)
- Julia Bahnmueller
- Junior Research Group Neuro-Cognitive Plasticity, Leibniz-Institut für Wissensmedien, Schleichstraße 6, 72076, Tübingen, Germany. .,Department of Psychology and LEAD Graduate School and Research Network, University of Tübingen, Tübingen, Germany.
| | - Silke M Göbel
- Department of Psychology, University of York, York, YO10 5DD, UK
| | - Silvia Pixner
- Learning and Learning Disorders Working Group, Department of Psychology, UMIT-The Health and Life Science University, Eduard-Wallnöfer-Zentrum 1, 6060, Hall, Austria
| | - Verena Dresen
- Learning and Learning Disorders Working Group, Department of Psychology, UMIT-The Health and Life Science University, Eduard-Wallnöfer-Zentrum 1, 6060, Hall, Austria
| | - Korbinian Moeller
- Junior Research Group Neuro-Cognitive Plasticity, Leibniz-Institut für Wissensmedien, Schleichstraße 6, 72076, Tübingen, Germany.,Department of Psychology and LEAD Graduate School and Research Network, University of Tübingen, Tübingen, Germany
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15
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Rodic M, Cui J, Malykh S, Zhou X, Gynku EI, Bogdanova EL, Zueva DY, Y. Bogdanova O, Kovas Y. Cognition, emotion, and arithmetic in primary school: A cross-cultural investigation. BRITISH JOURNAL OF DEVELOPMENTAL PSYCHOLOGY 2018; 36:255-276. [PMID: 29878517 PMCID: PMC6001455 DOI: 10.1111/bjdp.12248] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2016] [Revised: 04/14/2018] [Indexed: 11/26/2022]
Abstract
The study investigated cross-cultural differences in variability and average performance in arithmetic, mathematical reasoning, symbolic and non-symbolic magnitude processing, intelligence, spatial ability, and mathematical anxiety in 890 6- to 9-year-old children from the United Kingdom, Russia, and China. Cross-cultural differences explained 28% of the variance in arithmetic and 17.3% of the variance in mathematical reasoning, with Chinese children outperforming the other two groups. No cross-cultural differences were observed for spatial ability and mathematical anxiety. In all samples, symbolic magnitude processing and mathematical reasoning were independently related to early arithmetic. Other factors, such as non-symbolic magnitude processing, mental rotation, intelligence, and mathematical anxiety, produced differential patterns across the populations. The results are discussed in relation to potential influences of parental practice, school readiness, and linguistic factors on individual differences in early mathematics. Statement of contribution What is already known on this subject? Cross-cultural differences in mathematical ability are present in preschool children. Similar mechanisms of mathematical development operate in preschool children from the United Kingdom, Russia, and China. Tasks that require understanding of numbers are best predictors of arithmetic in preschool children. What does this study add? Cross-cultural differences in mathematical ability become greater with age/years of formal education. Similar mechanisms of mathematical development operate in early primary school children from the United Kingdom, Russia, and China. Symbolic number magnitude and mathematical reasoning are the main predictors of arithmetic in all three populations.
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Affiliation(s)
- Maja Rodic
- Laboratory for Cognitive Investigations and Behavioural GeneticsTomsk State UniversityTomskRussia
- InLabDepartment of PsychologyGoldsmiths, University of LondonUK
| | - Jiaxin Cui
- State Key Laboratory of Cognitive Neuroscience and Learning & IDG/McGovern Institute for Brain ResearchBeijing Normal UniversityBeijingChina
| | - Sergey Malykh
- Laboratory for Cognitive Investigations and Behavioural GeneticsTomsk State UniversityTomskRussia
- Psychological InstituteRussian Academy of EducationMoscowRussia
| | - Xinlin Zhou
- State Key Laboratory of Cognitive Neuroscience and Learning & IDG/McGovern Institute for Brain ResearchBeijing Normal UniversityBeijingChina
| | - Elena I. Gynku
- Laboratory for Cognitive Investigations and Behavioural GeneticsTomsk State UniversityTomskRussia
| | - Elena L. Bogdanova
- Unit of General and Educational PsychologyPsychology DepartmentTomsk State UniversityTomskRussia
| | - Dina Y. Zueva
- Laboratory for Cognitive Investigations and Behavioural GeneticsTomsk State UniversityTomskRussia
| | - Olga Y. Bogdanova
- Unit of General and Educational PsychologyPsychology DepartmentTomsk State UniversityTomskRussia
| | - Yulia Kovas
- Laboratory for Cognitive Investigations and Behavioural GeneticsTomsk State UniversityTomskRussia
- InLabDepartment of PsychologyGoldsmiths, University of LondonUK
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16
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Bassetti B, Clarke A, Trenkic D. The linguistic transparency of first language calendar terms affects calendar calculations in a second language. Acta Psychol (Amst) 2018; 186:81-89. [PMID: 29723774 DOI: 10.1016/j.actpsy.2018.04.006] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2017] [Revised: 04/12/2018] [Accepted: 04/15/2018] [Indexed: 11/28/2022] Open
Abstract
Calendar calculations - e.g., calculating the nth month after a certain month - are an important component of temporal cognition, and can vary cross-linguistically. English speakers rely on a verbal list representation-processing system. Chinese speakers - whose calendar terms are numerically transparent - rely on a more efficient numerical system. Does knowing a numerically transparent calendar lexicon facilitate calendar calculations in an opaque second language? Late Chinese-English bilinguals and English native speakers performed a Month and a Weekday Calculation Task in English. Directionality (forward/backward) and boundary-crossing (within/across the year/week boundary) were manipulated. English speakers relied on verbal list processing, and were slower in backward than forward calculations. In spite of the English calendar system's opaqueness, bilinguals relied on numerical processing, were slower in across- than within-boundary trials, and under some conditions had faster RTs than the native speakers. Results have implications for research on temporal cognition, linguistic relativity and bilingual cognition.
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17
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Cui J, Georgiou GK, Zhang Y, Li Y, Shu H, Zhou X. Examining the relationship between rapid automatized naming and arithmetic fluency in Chinese kindergarten children. J Exp Child Psychol 2016; 154:146-163. [PMID: 27883911 DOI: 10.1016/j.jecp.2016.10.008] [Citation(s) in RCA: 44] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2016] [Revised: 09/01/2016] [Accepted: 10/22/2016] [Indexed: 11/25/2022]
Abstract
Rapid automatized naming (RAN) has been found to predict mathematics. However, the nature of their relationship remains unclear. Thus, the purpose of this study was twofold: (a) to examine how RAN (numeric and non-numeric) predicts a subdomain of mathematics (arithmetic fluency) and (b) to examine what processing skills may account for the RAN-arithmetic fluency relationship. A total of 160 third-year kindergarten Chinese children (83 boys and 77 girls, mean age=5.11years) were assessed on RAN (colors, objects, digits, and dice), nonverbal IQ, visual-verbal paired associate learning, phonological awareness, short-term memory, speed of processing, approximate number system acuity, and arithmetic fluency (addition and subtraction). The results indicated first that RAN was a significant correlate of arithmetic fluency and the correlations did not vary as a function of type of RAN or arithmetic fluency tasks. In addition, RAN continued to predict addition and subtraction fluency even after controlling for all other processing skills. Taken together, these findings challenge the existing theoretical accounts of the RAN-arithmetic fluency relationship and suggest that, similar to reading fluency, multiple processes underlie the RAN-arithmetic fluency relationship.
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Affiliation(s)
- Jiaxin Cui
- State Key Laboratory of Cognitive Neuroscience and Learning & IDG/McGovern School of Brain and Cognitive Sciences, Beijing Normal University, Beijing 100875, People's Republic of China; Advanced Innovation Center for Future Education & Siegler Center for Innovative Learning, Beijing Normal University, Beijing 100875, China
| | - George K Georgiou
- Department of Educational Psychology, University of Alberta, Edmonton, Alberta T6G 2G5, Canada.
| | - Yiyun Zhang
- School of Psychology, Liaoning Normal University, Dalian 116029, China
| | - Yixun Li
- School of Psychology, Beijing Normal University, Beijing 100875, People's Republic of China
| | - Hua Shu
- State Key Laboratory of Cognitive Neuroscience and Learning & IDG/McGovern School of Brain and Cognitive Sciences, Beijing Normal University, Beijing 100875, People's Republic of China
| | - Xinlin Zhou
- State Key Laboratory of Cognitive Neuroscience and Learning & IDG/McGovern School of Brain and Cognitive Sciences, Beijing Normal University, Beijing 100875, People's Republic of China; Advanced Innovation Center for Future Education & Siegler Center for Innovative Learning, Beijing Normal University, Beijing 100875, China
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18
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Dowker A, Nuerk HC. Editorial: Linguistic Influences on Mathematics. Front Psychol 2016; 7:1035. [PMID: 27462286 PMCID: PMC4940406 DOI: 10.3389/fpsyg.2016.01035] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2016] [Accepted: 06/24/2016] [Indexed: 12/02/2022] Open
Affiliation(s)
- Ann Dowker
- Experimental Psychology, University of OxfordOxford, UK
| | - Hans-Christoph Nuerk
- Department of Psychology, University of TuebingenTuebingen, Germany
- Knowledge Media Research Center, University of TuebingenTuebingen, Germany
- LEAD Graduate School and Research NetworkTuebingen, Germany
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19
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Dietrich JF, Huber S, Dackermann T, Moeller K, Fischer U. Place-value understanding in number line estimation predicts future arithmetic performance. BRITISH JOURNAL OF DEVELOPMENTAL PSYCHOLOGY 2016; 34:502-517. [PMID: 27136923 DOI: 10.1111/bjdp.12146] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2015] [Revised: 01/22/2016] [Indexed: 11/29/2022]
Abstract
In multi-digit numbers, the value of each digit is determined by its position within the digit string. Children's understanding of this place-value structure constitutes a building block for later arithmetic skills. We investigated whether a number line estimation task can provide an assessment of place-value understanding in first grade. We hypothesized that estimating the position of two-digit numbers requires place-value understanding. Therefore, we fitted a linear function to children's estimates of two-digit numbers and considered the resulting slope as a measure of children's place-value understanding. We observed a significant correlation between this slope and children's performance in a transcoding task known to require place-value understanding. Additionally, the slope for two-digit numbers assessed at the beginning of grade 1 predicted children's arithmetic performance at the end of grade 1. These results indicate that the number line estimation task may indeed constitute a valid measure for first-graders' place-value understanding. Moreover, these findings are hard to reconcile with the view that number line estimation directly assesses a spatial representation of numbers. Instead, our results suggest that numerical processes involved in performing the task (such as place-value understanding) may drive the association between number line estimation and arithmetic performance.
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Affiliation(s)
- Julia F Dietrich
- Leibniz-Institut für Wissensmedien, Tuebingen, Germany. .,Department of Psychology, Eberhard Karls University, Tuebingen, Germany.
| | - Stefan Huber
- Leibniz-Institut für Wissensmedien, Tuebingen, Germany
| | | | - Korbinian Moeller
- Leibniz-Institut für Wissensmedien, Tuebingen, Germany.,Department of Psychology, Eberhard Karls University, Tuebingen, Germany.,LEAD Graduate School, Eberhard Karls University, Tuebingen, Germany
| | - Ursula Fischer
- Leibniz-Institut für Wissensmedien, Tuebingen, Germany.,University of Regensburg, Germany
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20
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Bahnmueller J, Huber S, Nuerk HC, Göbel SM, Moeller K. Processing multi-digit numbers: a translingual eye-tracking study. PSYCHOLOGICAL RESEARCH 2015; 80:422-33. [DOI: 10.1007/s00426-015-0729-y] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2015] [Accepted: 11/18/2015] [Indexed: 12/17/2022]
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21
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Koerte IK, Willems A, Muehlmann M, Moll K, Cornell S, Pixner S, Steffinger D, Keeser D, Heinen F, Kubicki M, Shenton ME, Ertl-Wagner B, Schulte-Körne G. Mathematical abilities in dyslexic children: a diffusion tensor imaging study. Brain Imaging Behav 2015; 10:781-91. [DOI: 10.1007/s11682-015-9436-y] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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22
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Bahnmueller J, Moeller K, Mann A, Nuerk HC. On the limits of language influences on numerical cognition - no inversion effects in three-digit number magnitude processing in adults. Front Psychol 2015; 6:1216. [PMID: 26322010 PMCID: PMC4532912 DOI: 10.3389/fpsyg.2015.01216] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2014] [Accepted: 07/31/2015] [Indexed: 11/13/2022] Open
Abstract
The inversion of number words influences numerical cognition even in seemingly non-verbal tasks, such as Arabic number comparison. However, it is an open question whether inversion of decades and units also influences number processing beyond the two-digit number range. The current study addresses this question by investigating compatibility effects in both German- (a language with inverted) and English-speaking (a language with non-inverted number words) university students (mean age 22 years) in a three-digit number comparison task. We observed reliable hundred-decade as well as hundred-unit compatibility effects for three-digit number comparison. This indicates that, comparable two-digit numbers, three-digit numbers are processed in a parallel decomposed fashion. However, in contrast to previous results on two-digit numbers as well as on children’s processing of three-digit numbers, no reliable modulation of these compatibility effects through language was observed in adults. The present data indicate that inversion-related differences in multi-digit number processing are limited. They seem to be restricted to the number range involving those digits being inverted (i.e., tens and units in two-digit numbers) but do not generalize to neighboring digits. Possible reasons for this lack of generalization are discussed.
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Affiliation(s)
- Julia Bahnmueller
- Knowledge Media Research Center Tuebingen, Germany ; Department of Psychology, Eberhard Karls University Tuebingen, Germany
| | - Korbinian Moeller
- Knowledge Media Research Center Tuebingen, Germany ; Department of Psychology, Eberhard Karls University Tuebingen, Germany ; LEAD Graduate School, Eberhard Karls University Tuebingen, Germany
| | - Anne Mann
- Department of Psychology, Eberhard Karls University Tuebingen, Germany
| | - Hans-Christoph Nuerk
- Knowledge Media Research Center Tuebingen, Germany ; Department of Psychology, Eberhard Karls University Tuebingen, Germany ; LEAD Graduate School, Eberhard Karls University Tuebingen, Germany
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23
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Moeller K, Zuber J, Olsen N, Nuerk HC, Willmes K. Intransparent German number words complicate transcoding - a translingual comparison with Japanese. Front Psychol 2015; 6:740. [PMID: 26113827 PMCID: PMC4462644 DOI: 10.3389/fpsyg.2015.00740] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2014] [Accepted: 05/18/2015] [Indexed: 11/13/2022] Open
Abstract
Superior early numerical competencies of children in several Asian countries have (amongst others) been attributed to the higher transparency of their number word systems. Here, we directly investigated this claim by evaluating whether Japanese children’s transcoding performance when writing numbers to dictation (e.g., “twenty five” → 25) was less error prone than that of German-speaking children – both in general as well as when considering language-specific attributes of the German number word system such as the inversion property, in particular. In line with this hypothesis we observed that German-speaking children committed more transcoding errors in general than their Japanese peers. Moreover, their error pattern reflected the specific inversion intransparency of the German number-word system. Inversion errors in transcoding represented the most prominent error category in German-speaking children, but were almost absent in Japanese-speaking children. We conclude that the less transparent German number-word system complicates the acquisition of the correspondence between symbolic Arabic numbers and their respective verbal number words.
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Affiliation(s)
- Korbinian Moeller
- Knowledge Media Research Center Tuebingen, Germany ; Department of Psychology, University of Tuebingen Tuebingen, Germany ; LEAD Graduate School, University of Tuebingen Tuebingen, Germany
| | - Julia Zuber
- Department of Psychology, University of Tuebingen Tuebingen, Germany
| | - Naoko Olsen
- Section Neuropsychology, Department of Neurology, RWTH Aachen University Tuebingen, Germany
| | - Hans-Christoph Nuerk
- Knowledge Media Research Center Tuebingen, Germany ; Department of Psychology, University of Tuebingen Tuebingen, Germany ; LEAD Graduate School, University of Tuebingen Tuebingen, Germany
| | - Klaus Willmes
- Section Neuropsychology, Department of Neurology, RWTH Aachen University Tuebingen, Germany
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24
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Professional mathematicians differ from controls in their spatial-numerical associations. PSYCHOLOGICAL RESEARCH 2015; 80:710-26. [PMID: 26063316 PMCID: PMC4889706 DOI: 10.1007/s00426-015-0677-6] [Citation(s) in RCA: 47] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2014] [Accepted: 05/22/2015] [Indexed: 11/25/2022]
Abstract
While mathematically impaired individuals have been shown to have deficits in all kinds of basic numerical representations, among them spatial-numerical associations, little is known about individuals with exceptionally high math expertise. They might have a more abstract magnitude representation or more flexible spatial associations, so that no automatic left/small and right/large spatial-numerical association is elicited. To pursue this question, we examined the Spatial Numerical Association of Response Codes (SNARC) effect in professional mathematicians which was compared to two control groups: Professionals who use advanced math in their work but are not mathematicians (mostly engineers), and matched controls. Contrarily to both control groups, Mathematicians did not reveal a SNARC effect. The group differences could not be accounted for by differences in mean response speed, response variance or intelligence or a general tendency not to show spatial-numerical associations. We propose that professional mathematicians possess more abstract and/or spatially very flexible numerical representations and therefore do not exhibit or do have a largely reduced default left-to-right spatial-numerical orientation as indexed by the SNARC effect, but we also discuss other possible accounts. We argue that this comparison with professional mathematicians also tells us about the nature of spatial-numerical associations in persons with much less mathematical expertise or knowledge.
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25
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Friso-van den Bos I, Kroesbergen EH, Van Luit JE, Xenidou-Dervou I, Jonkman LM, Van der Schoot M, Van Lieshout EC. Longitudinal development of number line estimation and mathematics performance in primary school children. J Exp Child Psychol 2015; 134:12-29. [DOI: 10.1016/j.jecp.2015.02.002] [Citation(s) in RCA: 52] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2014] [Revised: 02/02/2015] [Accepted: 02/04/2015] [Indexed: 10/23/2022]
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26
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Ganayim D, Ibrahim R. Number Processing in Arabic and Hebrew Bilinguals. JOURNAL OF CROSS-CULTURAL PSYCHOLOGY 2015. [DOI: 10.1177/0022022115573316] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
In the current study, a direct assessment of the effect of presentation language and format on the compatibility effect of two-digit numbers was made by contrasting performance of Arabic/Hebrew bilinguals in a digital (Hindi digits/Arabic digits) and verbal numerical comparison task (Arabic an inverted language: units-decades and Hebrew a non-inverted language: decades-units). Our data revealed in digital presentation format a regular compatibility effect in Hindi digits and Arabic digits characterized by lower reaction-time (RT) means for compatible number pairs than incompatible ones with no difference in the RT means of participants in the two languages, Arabic language–Hindi digits as a mother tongue and Hebrew language–Arabic digits as a second language. However, in verbal presentation format, different patterns of compatibility effect were found in Arabic and Hebrew verbal numbers. In Arabic number words, a regular compatibility effect was found, while in Hebrew number words, no compatibility effect was found. This reflects the influence and modulation of the lexical-syntactic structure of the language in two-digit numbers comparison. Evidently, these differences in the compatibility effect advocate and strengthen the claim that two-digit numbers comparison is influenced by the numbers presentation format. Different modes of presentation of two-digit numbers (digital vs. verbal) can lead to different number comparison styles. The parallel model accounts for the numerical comparison in digital presentation, while for the verbal numbers presentation, a revised sequential-syntactic model is preferable.
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Affiliation(s)
- Deia Ganayim
- The Arab Center for Mind, Brain & Behavior, Sakhnin, Israel
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27
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Pixner S, Leyrer M, Moeller K. Number processing and arithmetic skills in children with cochlear implants. Front Psychol 2014; 5:1479. [PMID: 25566152 PMCID: PMC4267190 DOI: 10.3389/fpsyg.2014.01479] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2014] [Accepted: 12/01/2014] [Indexed: 11/13/2022] Open
Abstract
Though previous findings report that hearing impaired children exhibit impaired language and arithmetic skills, our current understanding of how hearing and the associated language impairments may influence the development of arithmetic skills is still limited. In the current study numerical/arithmetic performance of 45 children with a cochlea implant were compared to that of controls matched for hearing age, intelligence and sex. Our main results were twofold disclosing that children with CI show general as well as specific numerical/arithmetic impairments. On the one hand, we found an increased percentage of children with CI with an indication of dyscalculia symptoms, a general slowing in multiplication and subtraction as well as less accurate number line estimations. On the other hand, however, children with CI exhibited very circumscribed difficulties associated with place-value processing. Performance declined specifically when subtraction required a borrow procedure and number line estimation required the integration of units, tens, and hundreds instead of only units and tens. Thus, it seems that despite initially atypical language development, children with CI are able to acquire arithmetic skills in a qualitatively similar fashion as their normal hearing peers. Nonetheless, when demands on place-value understanding, which has only recently been proposed to be language mediated, hearing impaired children experience specific difficulties.
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Affiliation(s)
- Silvia Pixner
- Institute of Applied Psychology, UMIT - The Health and Life Sciences University Hall in Tyrol, Austria
| | - Martin Leyrer
- Department of Otolaryngology, Paracelsus University Medical School Salzburg Salzburg, Austria ; Department of Linguistics, University of Salzburg Salzburg, Austria
| | - Korbinian Moeller
- Knowledge Media Research Center Tübingen, Germany ; Department of Psychology, University of Tübingen Tübingen, Germany
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28
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Moeller K, Shaki S, Göbel SM, Nuerk HC. Language influences number processing--a quadrilingual study. Cognition 2014; 136:150-5. [PMID: 25497523 DOI: 10.1016/j.cognition.2014.11.003] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2014] [Revised: 10/08/2014] [Accepted: 11/04/2014] [Indexed: 11/28/2022]
Abstract
Reading/writing direction or number word formation influence performance even in basic numerical tasks such as magnitude comparison. However, so far the interaction of these language properties has not been evaluated systematically. In this study we tested English, German, Hebrew, and Arab participants realizing a natural 2 × 2 design of reading/writing direction (left-to-right vs. right-to-left) and number word formation (non-inverted vs. inverted, i.e., forty-seven vs. seven-and-forty). Symbolic number magnitude comparison was specifically influenced by the interaction of reading/writing direction and number word formation: participants from cultures where reading direction and the order of tens and units in number words are incongruent (i.e., German and Hebrew) exhibited more pronounced unit interference in place-value integration. A within-group comparison indicated that this effect was not due to differences in education. Thus, basic cultural differences in numerical cognition were driven by natural language variables and their specific combination.
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Affiliation(s)
- Korbinian Moeller
- Knowledge Media Research Center, Tuebingen, Germany; Eberhard Karls University, Tuebingen, Germany.
| | | | | | - Hans-Christoph Nuerk
- Eberhard Karls University, Tuebingen, Germany; Knowledge Media Research Center, Tuebingen, Germany
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29
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Ebersbach M, Erz P. Symbolic versus non-symbolic magnitude estimations among children and adults. J Exp Child Psychol 2014; 128:52-68. [DOI: 10.1016/j.jecp.2014.06.005] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2013] [Revised: 06/11/2014] [Accepted: 06/23/2014] [Indexed: 10/25/2022]
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30
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Reexamining the language account of cross-national differences in base-10 number representations. J Exp Child Psychol 2014; 129:12-25. [PMID: 25240152 DOI: 10.1016/j.jecp.2014.08.004] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2014] [Revised: 08/18/2014] [Accepted: 08/18/2014] [Indexed: 01/29/2023]
Abstract
East Asian students consistently outperform students from other nations in mathematics. One explanation for this advantage is a language account; East Asian languages, unlike most Western languages, provide cues about the base-10 structure of multi-digit numbers, facilitating the development of base-10 number representations. To test this view, the current study examined how kindergartners represented two-digit numbers using single unit-blocks and ten-blocks. The participants (N=272) were from four language groups (Korean, Mandarin, English, and Russian) that vary in the extent of "transparency" of the base-10 structure. In contrast to previous findings with older children, kindergartners showed no cross-language variability in the frequency of producing base-10 representations. Furthermore, they showed a pattern of within-language variability that was not consistent with the language account and was likely attributable to experiential factors. These findings suggest that language might not play as critical a role in the development of base-10 representations as suggested in earlier research.
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31
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Link T, Nuerk HC, Moeller K. On the Relation between the Mental Number Line and Arithmetic Competencies. Q J Exp Psychol (Hove) 2014; 67:1597-613. [DOI: 10.1080/17470218.2014.892517] [Citation(s) in RCA: 57] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Abstract
In this study, we aimed at investigating whether it is indeed the spatial magnitude representation that links number line estimation performance to other basic numerical and arithmetic competencies. Therefore, estimations of 45 fourth-graders in both a bounded and a new unbounded number line estimation task (with only a start-point and a unit given) were correlated with their performance in a variety of tasks including addition, subtraction, and number magnitude comparison. Assuming that both number line tasks assess the same underlying mental number line representation, unbounded number line estimation should also be associated with other basic numerical and arithmetic competencies. However, results indicated that children's estimation performance in the bounded but not the unbounded number line estimation task was correlated significantly with numerical and arithmetic competencies. We conclude that unbounded and bounded number line estimation tasks do not assess the same underlying spatial–numerical representation. Rather, the observed association between bounded number line estimation and numerical/arithmetic competencies may be driven by additional numerical processes (e.g., proportion judgement, addition/subtraction) recruited to solve the task.
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Affiliation(s)
- Tanja Link
- Department of Psychology, Eberhard Karls University, Tuebingen, Germany
| | - Hans-Christoph Nuerk
- Department of Psychology, Eberhard Karls University, Tuebingen, Germany
- Knowledge Media Research Center, Tuebingen, Germany
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32
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Hochman Cohen H, Berger A, Rubinsten O, Henik A. Does the learning of two symbolic sets of numbers affect the automaticity of number processing in children? J Exp Child Psychol 2014; 121:96-110. [PMID: 24473470 DOI: 10.1016/j.jecp.2013.11.005] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2012] [Revised: 11/04/2013] [Accepted: 11/05/2013] [Indexed: 11/30/2022]
Abstract
We explored the effects of learning two different symbolic sets of numerals (Arabic and Indian) on the development of automatic number processing. Children in the school we examined learn Indian numerals between first and third grades. In third grade, they switch to a new set of numerals (i.e., Arabic numbers). Participants in this study performed a numerical Stroop-like task in which they assessed the numerical value or physical size of stimuli varying along these two dimensions. Each participant saw either Arabic or Indian numerals. The results of the size congruity effect in the physical task, for both Indian and Arabic numerals, suggest that studying two sets of numerals interferes with the acquisition of an automatic association of a numerical symbol and magnitude. This is true both for the first learned set of numerals (i.e., Indian numerals) and for the second one (i.e., Arabic numerals). Furthermore, we found an absence of the distance effect, which further supports this conclusion. This learning program gave us the unique opportunity to examine the connection between symbolic sets and the mental representation of numbers in a novel fashion.
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Affiliation(s)
- Hila Hochman Cohen
- Department of Psychology, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel.
| | - Andrea Berger
- Department of Psychology, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel
| | - Orly Rubinsten
- Department of Psychology, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel
| | - Avishai Henik
- Department of Psychology, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel
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Bos IFVD, Kolkman ME, Kroesbergen EH, Leseman PPM. Explaining Variability: Numerical Representations in 4- to 8-Year-Old Children. JOURNAL OF COGNITION AND DEVELOPMENT 2014. [DOI: 10.1080/15248372.2012.742900] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
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Multiplication facts and the mental number line: evidence from unbounded number line estimation. PSYCHOLOGICAL RESEARCH 2014; 79:95-103. [DOI: 10.1007/s00426-013-0538-0] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2013] [Accepted: 12/13/2013] [Indexed: 10/25/2022]
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Laski EV, Yu Q. Number line estimation and mental addition: Examining the potential roles of language and education. J Exp Child Psychol 2014; 117:29-44. [DOI: 10.1016/j.jecp.2013.08.007] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2013] [Revised: 08/13/2013] [Accepted: 08/13/2013] [Indexed: 01/29/2023]
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Ganayim D, Ibrahim R. Number processing of Arabic and Hebrew bilinguals: Evidence supporting the distance effect. JAPANESE PSYCHOLOGICAL RESEARCH 2013. [DOI: 10.1111/jpr.12035] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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Huber S, Moeller K, Nuerk HC. Dissociating number line estimations from underlying numerical representations. Q J Exp Psychol (Hove) 2013; 67:991-1003. [PMID: 24131386 DOI: 10.1080/17470218.2013.838974] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Estimation patterns in the number line task are usually interpreted to indicate the (logarithmic or linear) nature of the underlying mental number line. However, indicators of the to-be-achieved linear representation may also be confounded with task requirements or strategies to achieve optimal task performance. In this study, we dissociated correct task performance from indices of a linear representation. Therefore, we designed an experiment in which adults and first graders had to learn number-to-space mappings of nonlinear functions. For adults, we found better fits of the corresponding functions than a linear function after just a few minutes of training. For most first graders, estimation patterns were not fitted better by a logarithmic function when they had to learn a logarithmic layout. Thus, estimation patterns produced in the number line estimation task do not necessarily allow for valid inferences on the underlying representation of number magnitude.
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Affiliation(s)
- Stefan Huber
- a KMRC-Knowledge Media Research Center , Tuebingen , Germany
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Xu X, Chen C, Pan M, Li N. Development of numerical estimation in Chinese preschool children. J Exp Child Psychol 2013; 116:351-66. [PMID: 23933179 DOI: 10.1016/j.jecp.2013.06.009] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2012] [Revised: 06/19/2013] [Accepted: 06/19/2013] [Indexed: 01/29/2023]
Abstract
Although much is known about the development of mental representations of numbers, it is not clear how early children begin to represent numbers on a linear scale. The current study aimed to examine the development of numerical estimation of Chinese preschoolers. In total, 160 children of three age groups (51 3- and 4-year-olds, 50 5-year-olds, and 59 6-year-olds) were administered the numerical estimation task on three types of number lines (Arabic numbers, dots, and objects). All three age groups took the test on the 0-10 number lines, and the oldest group also took it on the 0-100 and 0-1000 Arabic number lines. Results showed that (a) linear representation of numbers increased with age, (b) representation of numbers was consistent across the three types of tasks, (c) Chinese participants generally showed earlier onset of various landmarks of attaining linear representations (e.g., linearity of various number ranges, accuracy, intercepts) than did their Western counterparts, as reported in previous studies, and (d) the estimates of older Chinese preschoolers on the 0-100 and 0-1000 symbolic number lines fitted the two-linear and linear models better than alternative models such as the one-cycle, two-cycle, and logarithmic models. These results extend the small but accumulating literature on the earlier development of number cognition among Chinese preschoolers compared with their Western counterparts, suggesting the importance of cultural factors in the development of early number cognition.
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Affiliation(s)
- Xiaohui Xu
- School of Preschool Education, Capital Normal University, Beijing 100048, China.
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Link T, Moeller K, Huber S, Fischer U, Nuerk HC. Walk the number line – An embodied training of numerical concepts. Trends Neurosci Educ 2013. [DOI: 10.1016/j.tine.2013.06.005] [Citation(s) in RCA: 50] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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