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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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Lachelin R, van Rinsveld A, Poncin A, Schiltz C. Number transcoding in bilinguals—A transversal developmental study. PLoS One 2022; 17:e0273391. [PMID: 36037234 PMCID: PMC9423630 DOI: 10.1371/journal.pone.0273391] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2021] [Accepted: 08/08/2022] [Indexed: 11/29/2022] Open
Abstract
Number transcoding is the cognitive task of converting between different numerical codes (i.e. visual “42”, verbal “forty-two”). Visual symbolic to verbal transcoding and vice versa strongly relies on language proficiency. We evaluated transcoding of German-French bilinguals from Luxembourg in 5th, 8th, 11th graders and adults. In the Luxembourgish educational system, children acquire mathematics in German (LM1) until the 7th grade, and then the language of learning mathematic switches to French (LM2). French `70s `80s `90s are less transparent than `30s `40s `50s numbers, since they have a base-20 structure, which is not the case in German. Transcoding was evaluated with a reading aloud and a verbal-visual number matching task. Results of both tasks show a cognitive cost for transcoding numbers having a base-20 structure (i.e. `70s, `80s and `90s), such that response times were slower in all age groups. Furthermore, considering only base-10 numbers (i.e. `30s `40s `50s), it appeared that transcoding in LM2 (French) also entailed a cost. While participants across age groups tended to read numbers slower in LM2, this effect was limited to the youngest age group in the matching task. In addition, participants made more errors when reading LM2 numbers. In conclusion, we observed an age-independent language effect with numbers having a base-20 structure in French, reflecting their reduced transparency with respect to the decimal system. Moreover, we find an effect of language of math acquisition such that transcoding is less well mastered in LM2. This effect tended to persist until adulthood in the reading aloud task, while in the matching task performance both languages become similar in older adolescents and young adults. This study supports the link between numbers and language, especially highlighting the impact of language on reading numbers aloud from childhood to adulthood.
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Affiliation(s)
- Rémy Lachelin
- Institute of Cognitive Science and Assessment, Department of Behavioural and Cognitive Sciences, University of Luxembourg, Esch-sur-Alzette, Luxembourg
- * E-mail:
| | - Amandine van Rinsveld
- Graduate School of Education, Stanford University, Stanford, CA, United States of America
| | - Alexandre Poncin
- Institute of Cognitive Science and Assessment, Department of Behavioural and Cognitive Sciences, University of Luxembourg, Esch-sur-Alzette, Luxembourg
| | - Christine Schiltz
- Institute of Cognitive Science and Assessment, Department of Behavioural and Cognitive Sciences, University of Luxembourg, Esch-sur-Alzette, Luxembourg
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3
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Silver AM, Libertus ME. Environmental influences on mathematics performance in early childhood. NATURE REVIEWS PSYCHOLOGY 2022; 1:407-418. [PMID: 36330081 PMCID: PMC9624502 DOI: 10.1038/s44159-022-00061-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/15/2022] [Indexed: 06/16/2023]
Abstract
Math skills relate to lifelong career, health, and financial outcomes. Individuals' own cognitive abilities predict math performance and there is growing recognition that environmental influences including differences in culture and variability in math engagement also impact math skills. In this Review, we summarize evidence indicating that differences between languages, exposure to math-focused language, socioeconomic status, attitudes and beliefs about math, and engagement with math activities influence young children's math performance. These influences play out at the community and individual level. However, research on the role of these environmental influences for foundational number skills, including understanding of number words, is limited. Future research is needed to understand individual differences in the development of early emerging math skills such as number word skills, examining to what extent different types of environmental input are necessary and how children's cognitive abilities shape the impact of environmental input.
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Affiliation(s)
- Alex M. Silver
- Department of Psychology, University of Pittsburgh, Pittsburgh, PA, USA
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4
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Transcoding counts: Longitudinal contribution of number writing to arithmetic in different languages. J Exp Child Psychol 2022; 223:105482. [PMID: 35785589 DOI: 10.1016/j.jecp.2022.105482] [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: 12/09/2021] [Revised: 05/24/2022] [Accepted: 05/26/2022] [Indexed: 11/21/2022]
Abstract
Number writing involves transcoding from number words (e.g., "thirty-two") to written digit strings (32) and is an important unique predictor of arithmetic. The existing longitudinal evidence about the relation between transcoding and arithmetic is mostly language specific. In languages with number word inversion (e.g., German), the order of tens and units is transposed in spoken number words compared with Arabic numbers. This makes transcoding more challenging than in languages without number word inversion (e.g., English). In the current study, we aimed to understand whether the contribution of number writing to the development of arithmetic is similar in languages with and without number word inversion. German-speaking children (n = 166) and English-speaking children (n = 201) were followed over the first 3 years of primary school. In a series of multiple linear regressions, we tested whether number writing of multi-digit numbers was a significant unique predictor of arithmetic after controlling for well-known non-numerical predictors (nonverbal reasoning and working memory) and numerical predictors (symbolic and nonsymbolic magnitude comparison). Number writing in Grade 1 predicted arithmetic in Grades 1, 2, and 3 over and above the other predictors. Crucially, number writing performance was of comparable importance for arithmetic development in German- and English-speaking children. Our findings extend previous evidence by showing that transcoding predicts the development of arithmetic skills during the first 3 years of primary school in languages with and without number word inversion.
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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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6
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Ganayim D, Ganayim S, Dowker A, Olkun S. Transcoding Errors of Two-Digit Numbers From Arabic Digits Into Verbal Numbers and From Verbal Numbers Into Arabic Digits by Arab First Graders. JOURNAL OF COGNITIVE EDUCATION AND PSYCHOLOGY 2021. [DOI: 10.1891/jcep-d-20-00007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Abstract
The study focuses on the effect of the lexical-syntactic structure on the patterns of errors by Arab first graders in tasks involving reading two-digit number and writing two-digit numbers to dictation. Children made few change or omission errors, indicating that they had little problem with the lexical aspects of the counting system. However, they made frequent substitution errors (e.g., 23 for 32), especially in the number reading task, and especially for numbers that depended strongly on the numerical syntactic structure. Such errors were less common for decade numbers and for the 11–19 number range than for other two-digit numbers. The results suggest particular difficulty with the syntactic rather than lexical aspects of the counting system. The syntactic aspects may be particularly difficult for Arabic-speaking children, due to the inversion feature of the Arabic counting system.
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Dotan D, Breslavskiy I, Copty-Diab H, Yousefi V. Syntactic priming reveals an explicit syntactic representation of multi-digit verbal numbers. Cognition 2021; 215:104821. [PMID: 34224979 DOI: 10.1016/j.cognition.2021.104821] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2021] [Revised: 06/16/2021] [Accepted: 06/21/2021] [Indexed: 01/01/2023]
Abstract
When we say or understand verbal numbers, a major challenge to the cognitive system is the need to process the number's syntactic structure. Several studies showed that number syntax is handled by dedicated processes, however, it is still unclear how precisely these processes operate, whether the number's syntactic structure is represented explicitly, and if it is - what this representation looks like. Here, we used a novel experimental paradigm, syntactic priming of numbers, which can examine in detail the syntactic representation of multi-digit verbal numbers. In each trial, the participants - Arabic-Hebrew bilinguals and Hebrew monolinguals - heard a multi-digit number and responded orally with a random number. The syntactic structure of their responses was similar to that of the targets, showing that they represented the verbal number's syntax. This priming effect was genuinely syntactic, and could not be explained as lexical - repeating words from the target; as phonological - responding with words phonologically-similar to the target; or as a numerical distance effect - producing responses numerically close to the target. The syntactic priming effect was stronger for earlier words in the verbal number and weaker for later words, suggesting that the syntactic representation is capped by working-memory limits. We propose that syntactic priming could become a useful method to examine various aspects of the syntactic representation of numbers.
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Affiliation(s)
- Dror Dotan
- Mathematical Thinking Lab, School of Education and the Sagol School of Neuroscience, Tel Aviv University, Tel Aviv 6997801, Israel.
| | - Ilya Breslavskiy
- Mathematical Thinking Lab, School of Education and the Sagol School of Neuroscience, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Haneen Copty-Diab
- Mathematical Thinking Lab, School of Education and the Sagol School of Neuroscience, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Vivian Yousefi
- Mathematical Thinking Lab, School of Education and the Sagol School of Neuroscience, Tel Aviv University, Tel Aviv 6997801, Israel
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8
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Huang HW, Nascimben M, Wang YY, Fong DY, Tzeng OJL, Huang CM. Which digit is larger? Brain responses to number and size interactions in a numerical Stroop task. Psychophysiology 2020; 58:e13744. [PMID: 33314155 DOI: 10.1111/psyp.13744] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2020] [Revised: 11/12/2020] [Accepted: 11/16/2020] [Indexed: 11/29/2022]
Abstract
When comparing the digits of different physical sizes, the processing of numerical value interacts with the processing of physical size. Given the universal use of Arabic numbers in mathematics and daily life, this study aims to elucidate the cognitive processes involved in the interactions of task-relevant and task-irrelevant features during information processing. We investigated this question by examining event-related potential (ERP) using a modified version of the size congruity comparison, which is a Stroop-like task. Numerical value and physical size were varied independently under task-relevant and task-irrelevant conditions. To better examine how the task-irrelevant features modulated the processing of the task-relevant attributes, a neutral condition was included in both tasks. For the physical task, congruent trials showed a less negative N200 response than neutral trials (indicating a facilitation effect), and incongruent trials elicited a larger N450 and smaller late positive complex (LPC) response than neutral trials (indicating an interference effect). For the numerical task, congruent trials showed a larger LPC response than neutral trials (indicating a facilitation effect). These ERP findings indicate that the sources of the facilitation and interference effects appear in different cognitive processes for each task. We further suggest that language characteristics may be a factor in the superior numerical processing exhibited in this study.
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Affiliation(s)
- Hsu-Wen Huang
- Department of Linguistics and Translation, City University of Hong Kong, Kowloon, Hong Kong
| | - Mauro Nascimben
- Department of Biological Science and Technology, National Chiao Tung University, Hsinchu, Taiwan
| | - Ya-Yi Wang
- Cognitive Neuroscience Laboratory, Institute of Linguistics Academia Sinica, Taipei, Taiwan
| | - Dong-Yang Fong
- Physical Education Office, National Taipei University of Technology, Taipei, Taiwan
| | - Ovid J-L Tzeng
- College of Humanities and Social Sciences, Taipei Medical University, Taipei, Taiwan.,Department of Educational Psychology and Counseling, National Taiwan Normal University, Taipei, Taiwan.,Hong Kong Institute for Advanced Study, City University of Hong Kong, Kowloon, Hong Kong.,Center for Intelligent Drug Systems and Smart Bio-devices (IDS2B), National Chiao Tung University, Hsinchu, Taiwan
| | - Chih-Mao Huang
- Department of Biological Science and Technology, National Chiao Tung University, Hsinchu, Taiwan.,Center for Intelligent Drug Systems and Smart Bio-devices (IDS2B), National Chiao Tung University, Hsinchu, Taiwan
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9
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Steiner AF, Banfi C, Finke S, Kemény F, Clayton FJ, Göbel SM, Landerl K. Twenty-four or four-and-twenty: Language modulates cross-modal matching for multidigit numbers in children and adults. J Exp Child Psychol 2020; 202:104970. [PMID: 33096369 DOI: 10.1016/j.jecp.2020.104970] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2019] [Revised: 07/29/2020] [Accepted: 07/29/2020] [Indexed: 11/18/2022]
Abstract
Does number-word structure have a long-lasting impact on transcoding? Contrary to English, German number words comprise decade-unit inversion (e.g., vierundzwanzig is literally translated as four-and-twenty). To investigate the mental representation of numbers, we tested the effect of visual and linguistic-morphological characteristics on the development of verbal-visual transcoding. In a longitudinal cross-linguistic design, response times (RTs) in a number-matching experiment were analyzed in Grade 2 (119 German-speaking and 179 English-speaking children) and in Grade 3 (131 German-speaking and 160 English-speaking children). To test for long-term effects, the same experiment was given to 38 German-speaking and 42 English-speaking adults. Participants needed to decide whether a spoken number matched a subsequent visual Arabic number. Systematic variation of digits in the nonmatching distractors allowed comparison of three different transcoding accounts (lexicalization, visual, and linguistic-morphological). German speakers were generally slower in rejecting inverted number distractors than English speakers. Across age groups, German speakers were more distracted by Arabic numbers that included the correct unit digit, whereas English speakers showed stronger distraction when the correct decade digit was included. These RT patterns reflect differences in number-word morphology. The individual cost of rejecting an inverted distractor (inversion effect) predicted arithmetic skills in German-speaking second-graders only. The moderate relationship between the efficiency to identify a matching number and arithmetic performance could be observed cross-linguistically in all age groups but was not significant in German-speaking adults. Thus, findings provide consistent evidence of a persistent impact of number-word structure on number processing, whereas the relationship with arithmetic performance was particularly pronounced in young children.
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Affiliation(s)
- Anna F Steiner
- Institute of Psychology, University of Graz, 8010 Graz, Austria.
| | - Chiara Banfi
- Institute of Psychology, University of Graz, 8010 Graz, Austria
| | - Sabrina Finke
- Institute of Psychology, University of Graz, 8010 Graz, Austria
| | - Ferenc Kemény
- Institute of Psychology, University of Graz, 8010 Graz, Austria
| | - Francina J Clayton
- Department of Psychology, University of York, Heslington, York YO10 5DD, UK
| | - Silke M Göbel
- Department of Psychology, University of York, Heslington, York YO10 5DD, UK; Department of Special Needs Education, University of Oslo, 0316 Oslo, Norway
| | - Karin Landerl
- Institute of Psychology, University of Graz, 8010 Graz, Austria; Department of Cognitive Science, Macquarie University, Sydney, New South Wales 2109, Australia
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10
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Clayton FJ, Copper C, Steiner AF, Banfi C, Finke S, Landerl K, Göbel SM. Two-digit number writing and arithmetic in Year 1 children: Does number word inversion matter? COGNITIVE DEVELOPMENT 2020. [DOI: 10.1016/j.cogdev.2020.100967] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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11
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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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12
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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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Bahnmueller J, Nuerk HC, Moeller K. A Taxonomy Proposal for Types of Interactions of Language and Place-Value Processing in Multi-Digit Numbers. Front Psychol 2018; 9:1024. [PMID: 29988596 PMCID: PMC6026795 DOI: 10.3389/fpsyg.2018.01024] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2018] [Accepted: 05/31/2018] [Indexed: 11/13/2022] Open
Abstract
Research on associations between language and number processing has seen growing interest in the last years – in particular with respect to place-value processing in multi-digit numbers. Recently, Dowker and Nuerk (2016) proposed a taxonomy of linguistic influences on number processing. However, this taxonomy does not address the generality or specificity of linguistic influences across different levels of number processing. In contrast, Nuerk et al. (2015) proposed different levels of place-value processing in multi-digit numbers. However, the authors did not specify if and how linguistic factors influence these levels of place-value processing. The present perspective aims at addressing this conceptual gap by suggesting an integrated taxonomy representing how different linguistic factors may influence different levels of place-value processing. We show that some effects of different linguistic levels have already been observed on different levels of place-value processing. Moreover, while some linguistic influences (e.g., lexical influences) have been studied for all levels of place-value processing, other influences have been studied for only one level or even none. Beyond categorizing existing research, we argue that the explicit consideration of research gaps may inspire new research paradigms complementing the picture of language influences on place-value processing. We conclude by outlining the importance of a differential approach for levels of both linguistic and number processing to evaluate linguistic obstacles and facilitators of different languages and their relevance for numerical development.
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Affiliation(s)
- Julia Bahnmueller
- Neuro-cognitive Plasticity Laboratory, Leibniz-Institut für Wissensmedien, Tübingen, Germany.,Department of Psychology, Eberhard Karls University of Tübingen, Tübingen, Germany.,LEAD Graduate School and Research Network, University of Tübingen, Tübingen, Germany
| | - Hans-Christoph Nuerk
- Neuro-cognitive Plasticity Laboratory, Leibniz-Institut für Wissensmedien, Tübingen, Germany.,Department of Psychology, Eberhard Karls University of Tübingen, Tübingen, Germany.,LEAD Graduate School and Research Network, University of Tübingen, Tübingen, Germany
| | - Korbinian Moeller
- Neuro-cognitive Plasticity Laboratory, Leibniz-Institut für Wissensmedien, Tübingen, Germany.,Department of Psychology, Eberhard Karls University of Tübingen, Tübingen, Germany.,LEAD Graduate School and Research Network, University of Tübingen, Tübingen, Germany
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14
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Artemenko C, Pixner S, Moeller K, Nuerk HC. Longitudinal development of subtraction performance in elementary school. BRITISH JOURNAL OF DEVELOPMENTAL PSYCHOLOGY 2017; 36:188-205. [PMID: 28980340 DOI: 10.1111/bjdp.12215] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2016] [Revised: 08/15/2017] [Indexed: 11/27/2022]
Abstract
A major goal of education in elementary mathematics is the mastery of arithmetic operations. However, research on subtraction is rather scarce, probably because subtraction is often implicitly assumed to be cognitively similar to addition, its mathematical inverse. To evaluate this assumption, we examined the relation between the borrow effect in subtraction and the carry effect in addition, and the developmental trajectory of the borrow effect in children using a choice reaction paradigm in a longitudinal study. In contrast to the carry effect in adults, carry and borrow effects in children were found to be categorical rather than continuous. From grades 3 to 4, children became more proficient in two-digit subtraction in general, but not in performing the borrow operation in particular. Thus, we observed no specific developmental progress in place-value computation, but a general improvement in subtraction procedures. Statement of contribution What is already known on this subject? The borrow operation increases difficulty in two-digit subtraction in adults. The carry effect in addition, as the inverse operation of borrowing, comprises categorical and continuous processing characteristics. What does this study add? In contrast to the carry effect in adults, the borrow and carry effects are categorical in elementary school children. Children generally improve in subtraction performance from grades 3 to 4 but do not progress in place-value computation in particular.
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Affiliation(s)
- Christina Artemenko
- LEAD Graduate School & Research Network, University of Tuebingen, Germany.,Department of Psychology, University of Tuebingen, Germany
| | - Silvia Pixner
- Institute for Psychology, UMIT - The Health and Life Sciences University, Hall in Tyrol, Austria
| | - Korbinian Moeller
- LEAD Graduate School & Research Network, University of Tuebingen, Germany.,Department of Psychology, University of Tuebingen, Germany.,Leibniz-Institut für Wissensmedien, Tuebingen, Germany
| | - Hans-Christoph Nuerk
- LEAD Graduate School & Research Network, University of Tuebingen, Germany.,Department of Psychology, University of Tuebingen, Germany.,Leibniz-Institut für Wissensmedien, Tuebingen, Germany
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15
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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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16
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Van Rinsveld A, Schiltz C. Sixty-twelve = Seventy-two? A cross-linguistic comparison of children's number transcoding. BRITISH JOURNAL OF DEVELOPMENTAL PSYCHOLOGY 2016; 34:461-8. [PMID: 27385154 DOI: 10.1111/bjdp.12151] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2015] [Revised: 06/08/2016] [Indexed: 11/29/2022]
Abstract
We compared French- and English-speaking fifth-grade (10-year-old) children's performance in number transcoding. Whereas English two-digit number names follow the decimal structure (base 10), the structure of French two-digit number words over 60 follow a vigesimal structure (base 20). Children undertook two number transcoding tasks. While children were generally successful at the tasks, English-speaking children significantly outperformed French-speaking children for numbers following a vigesimal structure in French compared to a decimal structure in English (i.e., numbers >60). Our findings show that verbal number name structures influence children's performance in numerical tasks, even though fifth-grade children have well passed the initial stage of acquiring transcoding skills for two-digit numbers. These findings highlight the importance of language specificities in children's number transcoding. Statement of contribution What is already known? Previous research reports that language influences number processing in young children. Number transcoding performances can be conditioned by the linguistic structure of number words. What does this study add? Our results show how the structure of French vigesimal number words impacts number transcoding. They demonstrate that these language influences also affect children who already master basic number competencies.
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Affiliation(s)
- Amandine Van Rinsveld
- Education, Culture, Cognition and Society Research Unit, Institute of Cognitive Science and Assessment, University of Luxembourg, Campus Belval, Esch-sur-Alzette, Luxembourg
| | - Christine Schiltz
- Education, Culture, Cognition and Society Research Unit, Institute of Cognitive Science and Assessment, University of Luxembourg, Campus Belval, Esch-sur-Alzette, Luxembourg
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Lopes-Silva JB, Moura R, Júlio-Costa A, Wood G, Salles JF, Haase VG. What Is Specific and What Is Shared Between Numbers and Words? Front Psychol 2016; 7:22. [PMID: 26869946 PMCID: PMC4735706 DOI: 10.3389/fpsyg.2016.00022] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2015] [Accepted: 01/07/2016] [Indexed: 01/10/2023] Open
Abstract
Reading and spelling performance have a significant correlation with number transcoding, which is the ability to establish a relationship between the verbal and Arabic representations of numbers, when a conversion of numerical symbols from one notation to the other is necessary. The aim of the present study is to reveal shared and non-shared mechanisms involved in reading and writing of words and Arabic numerals in Brazilian school-aged children. One hundred and seventy-two children from second to fourth grades were evaluated. All of them had normal intelligence. We conducted a series of hierarchical regression models using scores on word spelling and reading single words and Arabic numerals, as dependent variables. As predictor variables we investigated intelligence, the phonological and visuospatial components of working memory (WM) and phonemic awareness. All of the writing and reading tasks (single word spelling and reading as well as number reading and number writing) were significantly correlated to each other. In the regression models, phonological WM was specifically associated to word reading. Phonemic awareness was the only cognitive variable that systematically predicted all of the school skills investigated, both numerical and word tasks. This suggests that phonemic awareness is a modular cognitive ability shared by several school tasks and might be an important factor associated to the comorbidity between dyslexia and dyscalculia.
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Affiliation(s)
- Júlia B. Lopes-Silva
- Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas GeraisBelo Horizonte, Brazil
| | - Ricardo Moura
- Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas GeraisBelo Horizonte, Brazil
| | - Annelise Júlio-Costa
- Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas GeraisBelo Horizonte, Brazil
| | - Guilherme Wood
- Department of Neuropsychology, Institute of Psychology, Karl-Franzens University of GrazGraz, Austria
| | - Jerusa F. Salles
- Núcleo de Estudos em Neuropsicologia Cognitiva, Institute of Psychology, Universidade Federal do Rio Grande do SulPorto Alegre, Brazil
| | - Vitor G. Haase
- Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas GeraisBelo Horizonte, Brazil
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18
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Rodriguez M, Kratochvilova Z, Kuniss R, Vorackova V, Dorazilova A, Fajnerova I. Case report: Is verbal cognitive performance in bilingual neuropsychiatric patients test-language dependent? Psych J 2015; 4:208-17. [PMID: 26663627 DOI: 10.1002/pchj.118] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2015] [Accepted: 09/20/2015] [Indexed: 11/12/2022]
Abstract
Bilingualism (BL) is increasing around the world. Although BL has been shown to have a broad impact-both positive and negative-on language and cognitive functioning, cognitive models and standards are mainly based on monolinguals. If we take cognitive performance of monolinguals as a standard, then the performance of bilinguals might not be accurately estimated. The assessment of cognitive functions is an important part of both the diagnostic process and further treatment in neurological and neuropsychiatric patients. In order to identify the presence or absence of cognitive deficit in bilingual patients, it will be important to determine the positive and/or negative impact of BL properties on measured cognitive performance. However, research of the impact of BL on cognitive performance in neuropsychiatric patients is limited. This article aims to compare the influence of the language (dominant-L1, second-L2) used for assessment of verbal cognitive performance in two cases of bilingual neuropsychiatric patients (English/Czech). Despite the fact that the two cases have different diagnoses, similarities in working memory and verbal learning profiles for L1 and L2 were present in both patients. We expected L1 to have higher performance in all measures when compared with L2. This assumption was partially confirmed. As expected, verbal working memory performance was better when assessed in L1. In contrast, verbal learning showed the same or better performance in L2 when compared with L1. Verbal fluency and immediate recall results were comparable in both languages. In conclusion, the language of administration partially influenced verbal performance of bilingual patients. Whether the language itself influenced low performance in a given language or it was a result of a deficit requires further research. According to our results, we suggest that an assessment in both languages needs to be a component of reasonable cognitive assessment of bilingual patients.
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Affiliation(s)
- Mabel Rodriguez
- National Institute of Mental Health, Klecany, Czech Republic
| | | | - Renata Kuniss
- National Institute of Mental Health, Klecany, Czech Republic
| | | | | | - Iveta Fajnerova
- National Institute of Mental Health, Klecany, Czech Republic
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19
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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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20
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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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21
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Xenidou-Dervou I, Gilmore C, van der Schoot M, van Lieshout ECDM. The developmental onset of symbolic approximation: beyond nonsymbolic representations, the language of numbers matters. Front Psychol 2015; 6:487. [PMID: 25972822 PMCID: PMC4413728 DOI: 10.3389/fpsyg.2015.00487] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2014] [Accepted: 04/03/2015] [Indexed: 01/29/2023] Open
Abstract
Symbolic (i.e., with Arabic numerals) approximate arithmetic with large numerosities is an important predictor of mathematics. It was previously evidenced to onset before formal schooling at the kindergarten age (Gilmore et al., 2007) and was assumed to map onto pre-existing nonsymbolic (i.e., abstract magnitudes) representations. With a longitudinal study (Experiment 1), we show, for the first time, that nonsymbolic and symbolic arithmetic demonstrate different developmental trajectories. In contrast to Gilmore et al.’s (2007) findings, Experiment 1 showed that symbolic arithmetic onsets in grade 1, with the start of formal schooling, not earlier. Gilmore et al. (2007) had examined English-speaking children, whereas we assessed a large Dutch-speaking sample. The Dutch language for numbers can be cognitively more demanding, for example, due to the inversion property in numbers above 20. Thus, for instance, the number 48 is named in Dutch “achtenveertig” (eight and forty) instead of “forty eight.” To examine the effect of the language of numbers, we conducted a cross-cultural study with English- and Dutch-speaking children that had similar SES and math achievement skills (Experiment 2). Results demonstrated that Dutch-speaking kindergarteners lagged behind English-speaking children in symbolic arithmetic, not nonsymbolic and demonstrated a working memory overload in symbolic arithmetic, not nonsymbolic. Also, we show for the first time that the ability to name two-digit numbers highly correlates with symbolic approximate arithmetic not nonsymbolic. Our experiments empirically demonstrate that the symbolic number system is modulated more by development and education than the nonsymbolic system. Also, in contrast to the nonsymbolic system, the symbolic system is modulated by language.
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Affiliation(s)
- Iro Xenidou-Dervou
- Department of Educational Neuroscience and LEARN! Research Institute for Learning and Education, Faculty of Psychology and Education, VU University Amsterdam Amsterdam, Netherlands
| | - Camilla Gilmore
- Mathematics Education Centre, Loughborough University Loughborough, UK
| | - Menno van der Schoot
- Department of Educational Neuroscience and LEARN! Research Institute for Learning and Education, Faculty of Psychology and Education, VU University Amsterdam Amsterdam, Netherlands
| | - Ernest C D M van Lieshout
- Department of Educational Neuroscience and LEARN! Research Institute for Learning and Education, Faculty of Psychology and Education, VU University Amsterdam Amsterdam, Netherlands
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22
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Prior A, Katz M, Mahajna I, Rubinsten O. Number word structure in first and second language influences arithmetic skills. Front Psychol 2015; 6:266. [PMID: 25852591 PMCID: PMC4362083 DOI: 10.3389/fpsyg.2015.00266] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2014] [Accepted: 02/23/2015] [Indexed: 11/25/2022] Open
Abstract
Languages differ in how they represent numerical information, and specifically whether the verbal notation of numbers follows the same order as the symbolic notation (in non-inverted languages, e.g., Hebrew, “25, twenty-five”) or whether the two notations diverge (in inverted languages, e.g., Arabic, “25, five-and-twenty”). We examined how the structure of number–words affects how arithmetic operations are processed by bilingual speakers of an inverted and a non-inverted language. We examined Arabic–Hebrew bilinguals’ performance in the first language, L1 (inverted) and in the second language, L2 (non-inverted). Their performance was compared to that of Hebrew L1 speakers, who do not speak an inverted language. Participants judged the accuracy of addition problems presented aurally in L1, aurally in L2 or in visual symbolic notation. Problems were presented such that they matched or did not match the structure of number words in the language. Arabic–Hebrew bilinguals demonstrated both flexibility in processing and adaptation to the language of aural–verbal presentation – they were more accurate for the inverted order of presentation in Arabic, but more accurate for non-inverted order of presentation in Hebrew, thus exhibiting the same pattern found for native Hebrew speakers. In addition, whereas native Hebrew speakers preferred the non-inverted order in visual symbolic presentation as well, the Arabic–Hebrew bilinguals showed enhanced flexibility, without a significant preference for one order over the other, in either speed or accuracy. These findings suggest that arithmetic processing is sensitive to the linguistic representations of number words. Moreover, bilinguals exposed to inverted and non-inverted languages showed influence of both systems, and enhanced flexibility in processing. Thus, the L1 does not seem to have exclusive power in shaping numerical mental representations, but rather the system remains open to influences from a later learned L2.
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Affiliation(s)
- Anat Prior
- *Correspondence: Anat Prior, Edmond J. Safra Brain Research Center for the Study of Learning Disabilities, Faculty of Education, University of Haifa, Mount Carmel, Haifa 31905, Israel
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23
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Daroczy G, Wolska M, Meurers WD, Nuerk HC. Word problems: a review of linguistic and numerical factors contributing to their difficulty. Front Psychol 2015; 6:348. [PMID: 25883575 PMCID: PMC4381502 DOI: 10.3389/fpsyg.2015.00348] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2014] [Accepted: 03/11/2015] [Indexed: 11/13/2022] Open
Abstract
Word problems (WPs) belong to the most difficult and complex problem types that pupils encounter during their elementary-level mathematical development. In the classroom setting, they are often viewed as merely arithmetic tasks; however, recent research shows that a number of linguistic verbal components not directly related to arithmetic contribute greatly to their difficulty. In this review, we will distinguish three components of WP difficulty: (i) the linguistic complexity of the problem text itself, (ii) the numerical complexity of the arithmetic problem, and (iii) the relation between the linguistic and numerical complexity of a problem. We will discuss the impact of each of these factors on WP difficulty and motivate the need for a high degree of control in stimuli design for experiments that manipulate WP difficulty for a given age group.
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Affiliation(s)
- Gabriella Daroczy
- Diagnostics and Cognitive Neuropsychology, Department of Psychology, Eberhard Karls Universität Tübingen Tübingen, Germany ; LEAD Graduate School, Eberhard Karls Universität Tübingen Tübingen, Germany
| | - Magdalena Wolska
- LEAD Graduate School, Eberhard Karls Universität Tübingen Tübingen, Germany
| | - Walt Detmar Meurers
- LEAD Graduate School, Eberhard Karls Universität Tübingen Tübingen, Germany ; Department of Linguistics, Eberhard Karls Universität Tübingen Tübingen, Germany
| | - Hans-Christoph Nuerk
- Diagnostics and Cognitive Neuropsychology, Department of Psychology, Eberhard Karls Universität Tübingen Tübingen, Germany ; LEAD Graduate School, Eberhard Karls Universität Tübingen Tübingen, Germany ; Knowledge Media Research Center Tübingen, Germany
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24
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Van Rinsveld A, Brunner M, Landerl K, Schiltz C, Ugen S. The relation between language and arithmetic in bilinguals: insights from different stages of language acquisition. Front Psychol 2015; 6:265. [PMID: 25821442 PMCID: PMC4357777 DOI: 10.3389/fpsyg.2015.00265] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2014] [Accepted: 02/23/2015] [Indexed: 01/29/2023] Open
Abstract
Solving arithmetic problems is a cognitive task that heavily relies on language processing. One might thus wonder whether this language-reliance leads to qualitative differences (e.g., greater difficulties, error types, etc.) in arithmetic for bilingual individuals who frequently have to solve arithmetic problems in more than one language. The present study investigated how proficiency in two languages interacts with arithmetic problem solving throughout language acquisition in adolescents and young adults. Additionally, we examined whether the number word structure that is specific to a given language plays a role in number processing over and above bilingual proficiency. We addressed these issues in a German-French educational bilingual setting, where there is a progressive transition from German to French as teaching language. Importantly, German and French number naming structures differ clearly, as two-digit number names follow a unit-ten order in German, but a ten-unit order in French. We implemented a transversal developmental design in which bilingual pupils from grades 7, 8, 10, 11, and young adults were asked to solve simple and complex additions in both languages. The results confirmed that language proficiency is crucial especially for complex addition computation. Simple additions in contrast can be retrieved equally well in both languages after extended language practice. Additional analyses revealed that over and above language proficiency, language-specific number word structures (e.g., unit-ten vs. ten-unit) also induced significant modulations of bilinguals' arithmetic performances. Taken together, these findings support the view of a strong relation between language and arithmetic in bilinguals.
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Affiliation(s)
- Amandine Van Rinsveld
- Education, Culture, Cognition and Society, Institute of Cognitive Science and Assessment, University of Luxembourg Walferdange, Luxembourg
| | - Martin Brunner
- Berlin-Brandenburg Institute for School Quality, Free University of Berlin Berlin, Germany
| | - Karin Landerl
- Department of Psychology, University of Graz Graz, Austria
| | - Christine Schiltz
- Education, Culture, Cognition and Society, Institute of Cognitive Science and Assessment, University of Luxembourg Walferdange, Luxembourg
| | - Sonja Ugen
- Luxembourg Center for Educational Testing, University of Luxembourg Luxembourg, Luxembourg
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25
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Lonnemann J, Yan S. Does number word inversion affect arithmetic processes in adults? Trends Neurosci Educ 2015. [DOI: 10.1016/j.tine.2015.01.002] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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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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27
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Moura R, Lopes-Silva JB, Vieira LR, Paiva GM, Prado ACDA, Wood G, Haase VG. From "five" to 5 for 5 minutes: Arabic number transcoding as a short, specific, and sensitive screening tool for mathematics learning difficulties. Arch Clin Neuropsychol 2014; 30:88-98. [PMID: 25488062 DOI: 10.1093/arclin/acu071] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
Number transcoding (e.g., writing 29 when hearing "twenty-nine") is one of the most basic numerical abilities required in daily life and is paramount for mathematics achievement. The aim of this study is to investigate psychometric properties of an Arabic number-writing task and its capacity to identify children with mathematics difficulties. We assessed 786 children (55% girls) from first to fourth grades, who were classified as children with mathematics difficulties (n = 103) or controls (n = 683). Although error rates were low, the task presented adequate internal consistency (0.91). Analyses revealed effective diagnostic accuracy in first and second school grades (specificity equals to 0.67 and 0.76 respectively, and sensitivity equals to 0.70 and 0.88 respectively). Moreover, items tapping the understanding of place-value syntax were the most sensitive to mathematics achievement. Overall, we propose that number transcoding is a useful tool for the assessment of mathematics abilities in early elementary school.
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Affiliation(s)
- Ricardo Moura
- Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas Gerais, Minas Gerais, Brazil Programa de Pós-graduação em Neurociências, Universidade Federal de Minas Gerais, Minas Gerais, Brazil
| | - Júlia Beatriz Lopes-Silva
- Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas Gerais, Minas Gerais, Brazil
| | - Laura Rodrigues Vieira
- Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas Gerais, Minas Gerais, Brazil
| | - Giulia Moreira Paiva
- Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas Gerais, Minas Gerais, Brazil
| | - Ana Carolina de Almeida Prado
- Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas Gerais, Minas Gerais, Brazil
| | - Guilherme Wood
- Department of Psychology, Karl-Franzens-University of Graz, Graz, Austria BioTechMed-Graz, Graz, Austria
| | - Vitor Geraldi Haase
- Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas Gerais, Minas Gerais, Brazil Programa de Pós-graduação em Neurociências, Universidade Federal de Minas Gerais, Minas Gerais, Brazil
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Imbo I, Vanden Bulcke C, De Brauwer J, Fias W. Sixty-four or four-and-sixty? The influence of language and working memory on children's number transcoding. Front Psychol 2014; 5:313. [PMID: 24782811 PMCID: PMC3990049 DOI: 10.3389/fpsyg.2014.00313] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2013] [Accepted: 03/25/2014] [Indexed: 11/21/2022] Open
Abstract
Number transcoding (e.g., writing 64 when hearing “sixty-four”) is a basic numerical skill; rather faultlessly performed in adults, but difficult for children. In the present study, children speaking Dutch (an inversed number language) and French (a non-inversed number language) wrote Arabic digits to dictation. We also tested their IQ and their phonological, visuospatial, and executive working memory. Although the number of transcoding errors (e.g., hearing 46 but writing 56) was equal in both groups, the number of inversion errors (e.g., hearing 46 but writing 64) was significantly higher in Dutch-speaking than in French-speaking children. Regression analyses confirmed that language was the only significant predictor of inversion errors. Working-memory components, in contrast, were the only significant predictors of transcoding errors. Executive resources were important in all children. Less-skilled transcoders also differed from more-skilled transcoders in that they used semantic rather than asemantic transcoding routes. Given the observed relation between number transcoding and mathematics grades, current findings may provide useful information for educational and clinical settings.
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Affiliation(s)
- Ineke Imbo
- Department of Experimental Psychology, Ghent University Ghent, Belgium
| | | | - Jolien De Brauwer
- Code, Expertise Centre for Development and Learning and Department of Applied Psychology, Thomas More University College Antwerp, Belgium
| | - Wim Fias
- Department of Experimental Psychology, Ghent University Ghent, Belgium
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Haase VG, Júlio-Costa A, Lopes-Silva JB, Starling-Alves I, Antunes AM, Pinheiro-Chagas P, Wood G. Contributions from specific and general factors to unique deficits: two cases of mathematics learning difficulties. Front Psychol 2014; 5:102. [PMID: 24592243 PMCID: PMC3923187 DOI: 10.3389/fpsyg.2014.00102] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2013] [Accepted: 01/25/2014] [Indexed: 11/18/2022] Open
Abstract
Mathematics learning difficulties are a highly comorbid and heterogeneous set of disorders linked to several dissociable mechanisms and endophenotypes. Two of these endophenotypes consist of primary deficits in number sense and verbal numerical representations. However, currently acknowledged endophenotypes are underspecified regarding the role of automatic vs. controlled information processing, and their description should be complemented. Two children with specific deficits in number sense and verbal numerical representations and normal or above-normal intelligence and preserved visuospatial cognition illustrate this point. Child H.V. exhibited deficits in number sense and fact retrieval. Child G.A. presented severe deficits in orally presented problems and transcoding tasks. A partial confirmation of the two endophenotypes that relate to the number sense and verbal processing was obtained, but a much more clear differentiation between the deficits presented by H.V. and G.A. can be reached by looking at differential impairments in modes of processing. H.V. is notably competent in the use of controlled processing but has problems with more automatic processes, such as nonsymbolic magnitude processing, speeded counting and fact retrieval. In contrast, G.A. can retrieve facts and process nonsymbolic magnitudes but exhibits severe impairment in recruiting executive functions and the concentration that is necessary to accomplish transcoding tasks and word problem solving. These results indicate that typical endophenotypes might be insufficient to describe accurately the deficits that are observed in children with mathematics learning abilities. However, by incorporating domain-specificity and modes of processing into the assessment of the endophenotypes, individual deficit profiles can be much more accurately described. This process calls for further specification of the endophenotypes in mathematics learning difficulties.
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Affiliation(s)
- Vitor G Haase
- Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas Gerais Belo Horizonte, Brazil ; Programa de Pós-graduação em Saúde da Criança e do Adolescente, Faculdade de Medicina, Universidade Federal de Minas Gerais Belo Horizonte, Brazil
| | - Annelise Júlio-Costa
- Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas Gerais Belo Horizonte, Brazil ; Programa de Pós-graduação em Saúde da Criança e do Adolescente, Faculdade de Medicina, Universidade Federal de Minas Gerais Belo Horizonte, Brazil
| | - Júlia B Lopes-Silva
- Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas Gerais Belo Horizonte, Brazil ; Programa de Pós-graduação em Saúde da Criança e do Adolescente, Faculdade de Medicina, Universidade Federal de Minas Gerais Belo Horizonte, Brazil
| | - Isabella Starling-Alves
- Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas Gerais Belo Horizonte, Brazil
| | - Andressa M Antunes
- Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas Gerais Belo Horizonte, Brazil
| | - Pedro Pinheiro-Chagas
- INSERM, U992, Cognitive Neuroimaging Unit Gif sur Yvette, France ; CEA, DSV/I2BM, NeuroSpin Center Gif sur Yvette, France
| | - Guilherme Wood
- Department of Neuropsychology, Institute of Psychology, Karl-Franzens-University of Graz Graz, Austria
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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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Lopes-Silva JB, Moura R, Júlio-Costa A, Haase VG, Wood G. Phonemic awareness as a pathway to number transcoding. Front Psychol 2014; 5:13. [PMID: 24478744 PMCID: PMC3904123 DOI: 10.3389/fpsyg.2014.00013] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2013] [Accepted: 01/07/2014] [Indexed: 11/13/2022] Open
Abstract
Although verbal and numerical abilities have a well-established interaction, the impact of phonological processing on numeric abilities remains elusive. The aim of this study is to investigate the role of phonemic awareness in number processing and to explore its association with other functions such as working memory and magnitude processing. One hundred seventy-two children in 2nd grade to 4th grade were evaluated in terms of their intelligence, number transcoding, phonemic awareness, verbal and visuospatial working memory and number sense (non-symbolic magnitude comparison) performance. All of the children had normal intelligence. Among these measurements of magnitude processing, working memory and phonemic awareness, only the last was retained in regression and path models predicting transcoding ability. Phonemic awareness mediated the influence of verbal working memory on number transcoding. The evidence suggests that phonemic awareness significantly affects number transcoding. Such an association is robust and should be considered in cognitive models of both dyslexia and dyscalculia.
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Affiliation(s)
- Júlia B Lopes-Silva
- Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas Gerais Belo Horizonte, Brazil ; Programa de Pós-graduação em Saúde da Criança e do Adolescente, Universidade Federal de Minas Gerais Belo Horizonte, Brazil
| | - Ricardo Moura
- Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas Gerais Belo Horizonte, Brazil ; Programa de Pós-graduação em Neurociências, Universidade Federal de Minas Gerais Belo Horizonte, Brazil
| | - Annelise Júlio-Costa
- Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas Gerais Belo Horizonte, Brazil ; Programa de Pós-graduação em Neurociências, Universidade Federal de Minas Gerais Belo Horizonte, Brazil
| | - Vitor G Haase
- Developmental Neuropsychology Laboratory, Department of Psychology, Universidade Federal de Minas Gerais Belo Horizonte, Brazil ; Programa de Pós-graduação em Saúde da Criança e do Adolescente, Universidade Federal de Minas Gerais Belo Horizonte, Brazil ; Programa de Pós-graduação em Neurociências, Universidade Federal de Minas Gerais Belo Horizonte, Brazil
| | - Guilherme Wood
- Department of Neuropsychology, Institute of Psychology, Karl-Franzens-University of Graz Graz, Austria
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Transcoding abilities in typical and atypical mathematics achievers: The role of working memory and procedural and lexical competencies. J Exp Child Psychol 2013; 116:707-27. [DOI: 10.1016/j.jecp.2013.07.008] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2012] [Revised: 07/16/2013] [Accepted: 07/18/2013] [Indexed: 11/21/2022]
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Byrge L, Smith LB, Mix KS. Beginnings of place value: how preschoolers write three-digit numbers. Child Dev 2013; 85:437-43. [PMID: 24003873 DOI: 10.1111/cdev.12162] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Place value notation is essential to mathematics learning. This study examined young children's (4- to 6-year-olds, N = 172) understanding of place value prior to explicit schooling by asking them write spoken numbers (e.g., "six hundred and forty-two"). Children's attempts often consisted of "expansions" in which the proper digits were written in order but with 0s or other insertions marking place (e.g., "600402" or "610042"). This partial knowledge increased with age. Gender differences were also observed with older boys more likely than older girls to produce the conventional form (e.g., 642). Potential experiences contributing to expanded number writing and the observed gender differences are discussed.
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Klein E, Bahnmueller J, Mann A, Pixner S, Kaufmann L, Nuerk HC, Moeller K. Language influences on numerical development-Inversion effects on multi-digit number processing. Front Psychol 2013; 4:480. [PMID: 23935585 PMCID: PMC3733006 DOI: 10.3389/fpsyg.2013.00480] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2013] [Accepted: 07/09/2013] [Indexed: 11/27/2022] Open
Abstract
In early numerical development, children have to become familiar with the Arabic number system and its place-value structure. The present review summarizes and discusses evidence for language influences on the acquisition of the highly transparent structuring principles of digital-Arabic digits by means of its moderation through the transparency of the respective language's number word system. In particular, the so-called inversion property (i.e., 24 named as “four and twenty” instead of “twenty four”) was found to influence number processing in children not only in verbal but also in non-verbal numerical tasks. Additionally, there is first evidence suggesting that inversion-related difficulties may influence numerical processing longitudinally. Generally, language-specific influences in children's numerical development are most pronounced for multi-digit numbers. Yet, there is currently only one study on three-digit number processing for German-speaking children. A direct comparison of additional new data from Italian-speaking children further corroborates the assumption that language impacts on cognitive (number) processing as inversion-related interference was found most pronounced for German-speaking children. In sum, we conclude that numerical development may not be language-specific but seems to be moderated by language.
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Affiliation(s)
- E Klein
- Section Neuropsychology, Department of Neurology, University Hospital RWTH Aachen University Tuebingen, Germany ; IWM-KMRC Knowledge Media Research Center Tuebingen, Germany
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