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Artemenko C, Giannouli V, Nuerk HC. Age-related effects in magnitude and place-value processing. Sci Rep 2024; 14:13645. [PMID: 38871811 DOI: 10.1038/s41598-024-63298-z] [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: 06/01/2023] [Accepted: 05/27/2024] [Indexed: 06/15/2024] Open
Abstract
While general cognitive skills decline during aging, numerical skills seem to be mainly preserved. Such skills are essential for an independent life up to old age, e.g., when dealing with money or time. Operating with numbers usually requires number magnitude and place-value processing. The question is whether these processes are negatively affected by aging due to the general cognitive decline or positively affected due to lifelong experience with numbers. Therefore, we investigated age-related changes in the distance and compatibility effects in single-digit, two-digit, and four-digit number comparison. On the one hand, older adults took longer for number processing and showed a smaller distance effect, indicating altered number magnitude representations. On the other hand, older adults were better in place-value processing as indicated by a smaller compatibility effect than in younger adults. We conclude that aging differentially affects basic numerical skills.
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Affiliation(s)
- Christina Artemenko
- Department of Psychology, University of Tuebingen, Schleichstr. 4, 72076, Tuebingen, Germany.
- LEAD Graduate School and Research Network, University of Tuebingen, Tuebingen, Germany.
| | - Vaitsa Giannouli
- Department of Psychology, University of Western Macedonia, Florina, Greece
| | - Hans-Christoph Nuerk
- Department of Psychology, University of Tuebingen, Schleichstr. 4, 72076, Tuebingen, Germany
- LEAD Graduate School and Research Network, University of Tuebingen, Tuebingen, Germany
- German Centre for Mental Health (DZPG), Tuebingen, Germany
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Gilmore C. Understanding the complexities of mathematical cognition: A multi-level framework. Q J Exp Psychol (Hove) 2023; 76:1953-1972. [PMID: 37129432 PMCID: PMC10466984 DOI: 10.1177/17470218231175325] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2022] [Revised: 01/16/2023] [Accepted: 01/17/2023] [Indexed: 05/03/2023]
Abstract
Mathematics skills are associated with future employment, well-being, and quality of life. However, many adults and children fail to learn the mathematics skills they require. To improve this situation, we need to have a better understanding of the processes of learning and performing mathematics. Over the past two decades, there has been a substantial growth in psychological research focusing on mathematics. However, to make further progress, we need to pay greater attention to the nature of, and multiple elements involved in, mathematical cognition. Mathematics is not a single construct; rather, overall mathematics achievement is comprised of proficiency with specific components of mathematics (e.g., number fact knowledge, algebraic thinking), which in turn recruit basic mathematical processes (e.g., magnitude comparison, pattern recognition). General cognitive skills and different learning experiences influence the development of each component of mathematics as well as the links between them. Here, I propose and provide evidence for a framework that structures how these components of mathematics fit together. This framework allows us to make sense of the proliferation of empirical findings concerning influences on mathematical cognition and can guide the questions we ask, identifying where we are missing both research evidence and models of specific mechanisms.
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Affiliation(s)
- Camilla Gilmore
- Centre for Mathematical Cognition, Loughborough University, Loughborough, UK
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Park J, Im SH, Varma S. A language compatibility effect in fraction processing. Q J Exp Psychol (Hove) 2023; 76:596-605. [PMID: 35400219 DOI: 10.1177/17470218221095747] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
A language compatibility effect occurs when there is a match between what a language provides and what a mathematical task demands. Here, we investigated whether such an effect exists for fraction processing in English, which names the numerator first, versus Korean, which names the denominator first. We developed two new tasks: a fraction span task where participants view and then recall four fractions and a fraction identification task where they view one fraction and then another and judge whether the two fractions are the same or not. We generally found that English speakers were advantaged when the numerator drove task performance and Korean speakers were advantaged when the denominator was critical. These findings, particularly from the fraction identification task, were inconsistent with the attentional focus hypothesis, which proposes that the serialisation bias of a language guides which fraction component is attended to first. Rather, they were better explained by the verbal encoding hypothesis, which states that a necessary condition for observing language compatibility effects may be that the fraction components must be encoded in verbal working memory and rehearsed there.
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Affiliation(s)
- Jimin Park
- Department of Educational Psychology, University of Minnesota Twin Cities, Minneapolis, MN, USA
| | - Soo-Hyun Im
- Department of Education, Hanyang University, Seoul, Republic of Korea
| | - Sashank Varma
- Schools of Interactive Computing and Psychology, Georgia Institute of Technology, Atlanta, GA, USA
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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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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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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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Professional mathematicians do not differ from others in the symbolic numerical distance and size effects. Sci Rep 2020; 10:11531. [PMID: 32661271 PMCID: PMC7359336 DOI: 10.1038/s41598-020-68202-z] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2020] [Accepted: 06/11/2020] [Indexed: 01/29/2023] Open
Abstract
The numerical distance effect (it is easier to compare numbers that are further apart) and size effect (for a constant distance, it is easier to compare smaller numbers) characterize symbolic number processing. However, evidence for a relationship between these two basic phenomena and more complex mathematical skills is mixed. Previously this relationship has only been studied in participants with normal or poor mathematical skills, not in mathematicians. Furthermore, the prevalence of these effects at the individual level is not known. Here we compared professional mathematicians, engineers, social scientists, and a reference group using the symbolic magnitude classification task with single-digit Arabic numbers. The groups did not differ with respect to symbolic numerical distance and size effects in either frequentist or Bayesian analyses. Moreover, we looked at their prevalence at the individual level using the bootstrapping method: while a reliable numerical distance effect was present in almost all participants, the prevalence of a reliable numerical size effect was much lower. Again, prevalence did not differ between groups. In summary, the phenomena were neither more pronounced nor more prevalent in mathematicians, suggesting that extremely high mathematical skills neither rely on nor have special consequences for analogue processing of symbolic numerical magnitudes.
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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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