1
|
Ren X, Libertus ME. (Dis)similarities between non-symbolic and symbolic number representations: Insights from vector space models. Acta Psychol (Amst) 2024; 248:104374. [PMID: 38908226 DOI: 10.1016/j.actpsy.2024.104374] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2023] [Revised: 06/20/2024] [Accepted: 06/20/2024] [Indexed: 06/24/2024] Open
Abstract
Empirical evidence in support of a shared system for non-symbolic and symbolic number processing has been inconclusive. The current study aims to address this question in a novel way, specifically by testing whether the efficient coding principle based on co-occurrence of number symbols in natural language holds for both non-symbolic and symbolic number processing. The efficient coding principle postulates that perception is optimized when stimuli frequently co-occur in a natural environment. We hypothesized that both numerical ratios and co-occurrence frequencies of symbolic numbers would significantly influence participants' performance on a non-symbolic and symbolic number comparison task. To test this hypothesis, we employed latent semantic analysis on a TASA corpus to quantify number co-occurrence in natural language and calculate language similarity estimates. We engaged 73 native English speakers (mean age = 19.36, standard deviation = 1.83) with normal or corrected vision and no learning disorders in a number comparison task involving non-symbolic (dot arrays) and symbolic stimuli (Arabic numerals and English number words). Results showed that numerical ratios significantly predicted participants' performances across all number formats (ps < 0.001). Language similarity estimates derived from everyday language also predicted performance on the non-symbolic task and the symbolic task involving number words (ps < 0.007). Our results highlight the complex nature of numerical processing, pointing to the co-occurrence of number symbols in natural language as an auxiliary factor in understanding the shared characteristics between non-symbolic and symbolic number representations. Given that our study focused on a limited number range (5 to 16) and a specific task type, future studies should explore a wider range of tasks and numbers to further test the role of the efficient coding principle in number processing.
Collapse
Affiliation(s)
- Xueying Ren
- Department of Psychology, University of Pittsburgh, Pittsburgh 15260, PA, USA; Learning Research and Development Center, University of Pittsburgh, Pittsburgh 15260, PA, USA; Center for the Neural Basis of Cognition, Pittsburgh 15260, PA, USA.
| | - Melissa E Libertus
- Department of Psychology, University of Pittsburgh, Pittsburgh 15260, PA, USA; Learning Research and Development Center, University of Pittsburgh, Pittsburgh 15260, PA, USA; Center for the Neural Basis of Cognition, Pittsburgh 15260, PA, USA
| |
Collapse
|
2
|
Lunardon M, Cerni T, Rumiati RI. Field of Study and Gender Moderation of the Association of Personality and Math Anxiety with Numeracy. THE JOURNAL OF PSYCHOLOGY 2024:1-29. [PMID: 38805670 DOI: 10.1080/00223980.2024.2352706] [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: 06/17/2023] [Accepted: 04/30/2024] [Indexed: 05/30/2024] Open
Abstract
Math anxiety and personality influence numeracy, although the nature of their contribution has been overlooked. In the present study, we investigated whether their association with numeracy depended on field of study and gender in higher education. Participants were Italian undergraduates in either the humanities (N = 201) or Science, Technology, Engineering and Math (STEM; N = 209) fields of study. These participants remotely completed standardized tests assessing numeracy, math anxiety, personality, intelligence, and basic numerical skills. We tested whether math anxiety and personality interacted with field of study and gender in predicting numeracy. Results showed that math anxiety was negatively associated with numeracy independently of field of study and gender, while the effect of personality, especially neuroticism, on numeracy interacted with field of study over and above intelligence and basic numerical skills. Specifically, humanities undergraduates with higher neuroticism levels scored lower in numeracy than STEM undergraduates. These findings underscore the importance of emotional experience for a good performance in mathematics, beyond math anxiety and the other personality traits, in the students that are less familiar with mathematics. Finally, no robust gender moderation emerged, suggesting that its role may be overridden by differences associated with career choice.
Collapse
|
3
|
García-Orza J, Gutiérrez-Cordero I, Rodríguez-Montenegro I, Álvarez-Montesinos JA. Children's comparison of different-length numbers: Managing different attributes in multidigit number processing. J Exp Child Psychol 2024; 240:105827. [PMID: 38194820 DOI: 10.1016/j.jecp.2023.105827] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2023] [Revised: 11/08/2023] [Accepted: 11/09/2023] [Indexed: 01/11/2024]
Abstract
In everyday life the comparison of numbers usually occurs between numbers with different numbers of digits. However, experimental research here is scarce. Recent research has shown that adults respond faster to congruent pairs (the initial digit in the number with more digits is larger, e.g., 2384 vs. 107) than to incongruent pairs (the initial digit is larger in the number with fewer digits, e.g., 2675 vs. 398). This has been interpreted as support for the processing of multiple attributes in parallel and against serial accounts. The current research asked whether there is a change in the relevance of these attributes as school grades increase. School-age children from the second to sixth grades (N = 206) were presented with pairs of numbers that had either the same number of digits (3 vs. 3 or 4 vs. 4) or a different number of digits (3 vs. 4). In this latter condition, the stimuli, matched by distance, could be either length/digit congruent (e.g., 2384 vs. 107) or length/digit incongruent (e.g., 2675 vs. 398). Linear mixed models showed a length/digit congruity effect from second graders. Interestingly, in the response time measure, congruity interacted with school grade and the side in which the larger number of the pair was presented. Whereas these results support a model that considers number comparison as a process that weighs different attributes in parallel, it is also argued that developmental changes are associated with differences in the level of automatization of the componential skills involved in the comparison.
Collapse
Affiliation(s)
- Javier García-Orza
- Numerical Cognition Lab, Faculty of Psychology and Speech Therapy, Universidad de Málaga, 29010 Málaga, Spain; Instituto de Investigación Biomédica de Málaga (IBIMA), 29590 Málaga, Spain; Department of Basic Psychology, Faculty of Psychology and Speech Therapy, Universidad de Málaga, 29010 Málaga, Spain.
| | - Ismael Gutiérrez-Cordero
- Numerical Cognition Lab, Faculty of Psychology and Speech Therapy, Universidad de Málaga, 29010 Málaga, Spain; Department of Basic Psychology, Faculty of Psychology and Speech Therapy, Universidad de Málaga, 29010 Málaga, Spain; Cognitive Neurology and Aphasia Unit, Centro de Investigaciones Médico-Sanitarias, Universidad de Málaga, 29071 Málaga. Spain
| | - Ismael Rodríguez-Montenegro
- Numerical Cognition Lab, Faculty of Psychology and Speech Therapy, Universidad de Málaga, 29010 Málaga, Spain
| | | |
Collapse
|
4
|
Hofmann W, Kinder A, Pekár J. How learning influences non-symbolic numerical processing: effects of feedback in the dot comparison task. Front Psychol 2024; 14:1287429. [PMID: 38352965 PMCID: PMC10861774 DOI: 10.3389/fpsyg.2023.1287429] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2023] [Accepted: 12/18/2023] [Indexed: 02/16/2024] Open
Abstract
It has long been debated how humans estimate the numerosity of sets of elements and what role continuous visual properties play in this process. The dot comparison task, in which the more numerous of two dot arrays must be selected, is a dominant method to investigate this phenomenon. It has been shown that the visual properties of the two dot patterns strongly influence the comparison. This influence can be systematically investigated by manipulating visual properties congruently and incongruently with numerosity. However, it remains unclear how learning and prior experience affect the influence of the visual properties. To address this question, we introduced feedback into the classical dot comparison task: during the learning phase, participants in the experimental group received feedback after each trial indicating whether their answer was correct whereas participants in the control group did not. After the learning phase, neither group received feedback. The convex hull of the dot patterns and the average dot diameter were manipulated congruently and incongruently with numerosity. Our results show that feedback had no effect on overall performance. However, when manipulated separately, dot diameter no longer affected performance in the experimental group after the learning phase, but it did in the control group. Moreover, this effect remained visible even when diameter and convex hull were manipulated simultaneously. This pattern of results is consistent with the notion of sensory integration which proposes that weights are assigned to different visual cues and that numerical judgments depend on an additive combination of these weights. We also found a correlation between performance on an arithmetic task and performance on trials in which dot size was manipulated incongruently with numerosity. However, there were no correlations between an inhibition task and performance in the dot comparison task. Taken together, the current results suggest that learning with feedback may affect some visual properties but not others. Future studies should further investigate a wider range of visual properties to examine which of them can be influenced by learning and under what conditions learning occurs.
Collapse
Affiliation(s)
- Wiebke Hofmann
- Institute of Psychology of Learning, Department of Education and Psychology, Free University of Berlin, Berlin, Germany
- Department of Psychiatry and Neurosciences, Charité – Universitätsmedizin Berlin, Corporate Member of Freie Universität Berlin and Humboldt Universität Zu Berlin, Charité Campus Mitte (CCM), Berlin, Germany
| | - Annette Kinder
- Institute of Psychology of Learning, Department of Education and Psychology, Free University of Berlin, Berlin, Germany
| | - Judit Pekár
- Institute of Psychology of Learning, Department of Education and Psychology, Free University of Berlin, Berlin, Germany
| |
Collapse
|
5
|
Walker K, Carrigan E, Coppola M. Early access to language supports number mapping skills in deaf children. JOURNAL OF DEAF STUDIES AND DEAF EDUCATION 2023; 29:1-18. [PMID: 38124681 DOI: 10.1093/deafed/enad045] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2022] [Revised: 08/31/2023] [Accepted: 09/03/2023] [Indexed: 12/23/2023]
Abstract
The ability to associate different types of number representations referring to the same quantity (symbolic Arabic numerals, signed/spoken number words, and nonsymbolic quantities), is an important predictor of overall mathematical success. This foundational skill-mapping-has not been examined in deaf and hard-of-hearing (DHH) children. To address this gap, we studied 188 4 1/2 to 9-year-old DHH and hearing children and systematically examined the relationship between their language experiences and mapping skills. We asked whether the timing of children's language exposure (early vs. later), the modality of their language (signed vs. spoken), and their rote counting abilities related to mapping performance. We found that language modality did not significantly relate to mapping performance, but timing of language exposure and counting skills did. These findings suggest that early access to language, whether spoken or signed, supports the development of age-typical mapping skills and that knowledge of number words is critical for this development.
Collapse
Affiliation(s)
- Kristin Walker
- Department of Psychology, Stony Brook University, Stony Brook, NY, United States
| | - Emily Carrigan
- Department of Psychological Sciences, University of Connecticut, Storrs, CT, United States
| | - Marie Coppola
- Department of Psychological Sciences, University of Connecticut, Storrs, CT, United States
- Department of Linguistics, University of Connecticut, Storrs, CT, United States
| |
Collapse
|
6
|
Weiers H, Inglis M, Gilmore C. Learning artificial number symbols with ordinal and magnitude information. ROYAL SOCIETY OPEN SCIENCE 2023; 10:220840. [PMID: 37293367 PMCID: PMC10245205 DOI: 10.1098/rsos.220840] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Accepted: 05/18/2023] [Indexed: 06/10/2023]
Abstract
The question of how numerical symbols gain semantic meaning is a key focus of mathematical cognition research. Some have suggested that symbols gain meaning from magnitude information, by being mapped onto the approximate number system, whereas others have suggested symbols gain meaning from their ordinal relations to other symbols. Here we used an artificial symbol learning paradigm to investigate the effects of magnitude and ordinal information on number symbol learning. Across two experiments, we found that after either magnitude or ordinal training, adults successfully learned novel symbols and were able to infer their ordinal and magnitude meanings. Furthermore, adults were able to make relatively accurate judgements about, and map between, the novel symbols and non-symbolic quantities (dot arrays). Although both ordinal and magnitude training was sufficient to attach meaning to the symbols, we found beneficial effects on the ability to learn and make numerical judgements about novel symbols when combining small amounts of magnitude information for a symbol subset with ordinal information about the whole set. These results suggest that a combination of magnitude and ordinal information is a plausible account of the symbol learning process.
Collapse
Affiliation(s)
- Hanna Weiers
- Centre for Mathematical Cognition, Loughborough University, Loughborough LE11 3TU, UK
| | - Matthew Inglis
- Centre for Mathematical Cognition, Loughborough University, Loughborough LE11 3TU, UK
| | - Camilla Gilmore
- Centre for Mathematical Cognition, Loughborough University, Loughborough LE11 3TU, UK
| |
Collapse
|
7
|
Reinert RM, Gashaj V, Hartmann M, Moeller K. A potential dissociation between perception and production version for bounded but not unbounded number line estimation. Trends Neurosci Educ 2023; 31:100202. [PMID: 37308259 DOI: 10.1016/j.tine.2023.100202] [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: 11/16/2022] [Revised: 04/05/2023] [Accepted: 04/12/2023] [Indexed: 06/14/2023]
Abstract
BACKGROUND What, exactly, do number line estimation (NLE) tasks measure? Different versions of the task were observed to have different effects on performance. METHOD We investigated associations between the production (indicating the location) and perception version (indicating the number) of the bounded and unbounded NLE task and their relationship to arithmetic. RESULTS A stronger correlation was observed between the production and perception version of the unbounded than the bounded NLE task, indicating that both versions of the unbounded-but not the bounded-NLE task measure the same construct. Moreover, overall low but significant associations between NLE performance and arithmetic were only observed for the production version of the bounded NLE task. CONCLUSION These results substantiate that the production version of bounded NLE seems to rely on proportion judgment strategies, whereas both unbounded versions and the perception version of the bounded NLE task may rely more on magnitude estimation.
Collapse
Affiliation(s)
| | - Venera Gashaj
- University of Tübingen, Tübingen, Germany; Centre for Mathematical Cognition, School of Science, Loughborough University, United Kingdom.
| | - Matthias Hartmann
- Department of Psychology, University of Bern, Bern, Switzerland; Faculty of Psychology, UniDistance Suisse, Brig, Switzerland
| | - Korbinian Moeller
- Centre for Mathematical Cognition, School of Science, Loughborough University, United Kingdom; Leibniz-Institut für Wissensmedien, Tübingen, Germany; LEAD Graduate School and Research Network, University of Tübingen, Germany; Individual Development and Adaptive Education Center for Children at Risk, Frankfurt am Main, Germany
| |
Collapse
|
8
|
Xu X, Chen C, Wang L, Zhao M, Xin Z, Liu H. Longitudinal relationship between number line estimation and other mathematical abilities in Chinese preschool children. J Exp Child Psychol 2023; 228:105619. [PMID: 36592578 DOI: 10.1016/j.jecp.2022.105619] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2022] [Revised: 12/11/2022] [Accepted: 12/15/2022] [Indexed: 01/02/2023]
Abstract
Many cross-sectional studies have shown that number line estimation is associated with other mathematical skills, but there has been limited longitudinal research. To systematically examine such associations longitudinally at the earliest stage of mathematical learning, the current study tested 40 Chinese preschoolers (mean age = 4.97 years, SD = 0.18) and followed them up 8 months later. For both waves of data collection, children were administered six tasks: number line estimation, dot counting, comparison of two dot arrays, comparison of triple dot arrays, symbolic number comparison, and simple addition. Results of two-wave cross-lagged panel analysis showed that (a) dot counting and non-symbolic numerical comparison at Time 1 had significant longitudinal associations with number line estimation at Time 2, (b) number line estimation had bidirectional associations with symbolic number comparison, and (c) number line estimation at Time 1 had a marginally significant longitudinal association with simple addition at Time 2. These results extend the small but accumulating literature on the longitudinal relations between number line estimation and other mathematical skills and specify the important role of number line estimation in the early development of mathematical skills.
Collapse
Affiliation(s)
- Xiaohui Xu
- School of Preschool Education, Capital Normal University, Beijing 100048, China
| | - Chuansheng Chen
- Department of Psychological Science, University of California, Irvine, Irvine, CA 92697, USA
| | - Lan Wang
- School of Education, Capital Normal University, Beijing 100048, China
| | - Mengmeng Zhao
- School of Education, Capital Normal University, Beijing 100048, China
| | - Zhiyong Xin
- School of Sociology and Psychology, Central University of Finance and Economics, Beijing 100081, China
| | - Hongyun Liu
- Faculty of Psychology, Beijing Normal University, Beijing 100875, China.
| |
Collapse
|
9
|
Asakawa A, Sugimura S. Mediating process between fine motor skills, finger gnosis, and calculation abilities in preschool children. Acta Psychol (Amst) 2022; 231:103771. [PMID: 36327667 DOI: 10.1016/j.actpsy.2022.103771] [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: 10/30/2021] [Revised: 09/01/2022] [Accepted: 10/11/2022] [Indexed: 11/05/2022] Open
Abstract
Previous studies have found a relationship between fine motor skills, finger gnosis, and calculation skill. However, what mediates this association remains unclear. Therefore, this study investigated whether fine motor skills and finger gnosis are selectively associated with counting and symbolic comparison, and whether fine motor skills and finger gnosis are associated with calculation skills through numerical concepts to which they are selectively associated. We measured the counting, symbolic comparison, fine motor skills, finger gnosis, and working memory in preschool children (N = 48). The hierarchical multiple regression analysis results demonstrated that fine motor skills were selectively associated with counting, and finger gnosis with symbolic comparison. Moreover, based on the results of the mediation analysis, counting mediated the relationship between fine motor and calculation skills. However, the direct effects of fine motor skills and finger gnosis on calculation skills were also maintained. The findings were that fine motor skills and finger gnosis were related to numerical abilities, including counting, symbolic comparison, and calculations. Therefore, the findings were discussed in terms of the functional view and redeployment views, suggesting that the two views were complementary rather than exclusive.
Collapse
Affiliation(s)
| | - Shinichiro Sugimura
- Graduate School of Humanities and Social Sciences, Hiroshima University, Japan.
| |
Collapse
|
10
|
Fang S, Zhou X. Form perception speed is critical for the relationship between non-verbal number sense and arithmetic fluency. INTELLIGENCE 2022. [DOI: 10.1016/j.intell.2022.101704] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
|
11
|
Haman M, Patro K. More linear than log? Non-symbolic number-line estimation in 3- to 5-year-old children. Front Psychol 2022; 13:1003696. [PMID: 36389566 PMCID: PMC9659870 DOI: 10.3389/fpsyg.2022.1003696] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2022] [Accepted: 10/03/2022] [Indexed: 11/04/2022] Open
Abstract
The number-line estimation task has become one of the most important methods in numerical cognition research. Originally applied as a direct measure of spatial number representation, it became also informative regarding various other aspects of number processing and associated strategies. However, most of this work and associated conclusions concerns processing numbers in a symbolic format, by school children and older subjects. Symbolic number system is formally taught and trained at school, and its basic mathematical properties (e.g., equidistance, ordinality) can easily be transferred into a spatial format of an oriented number line. This triggers the question on basic characteristics of number line estimation before children get fully familiar with the symbolic number system, i.e., when they mostly rely on approximate system for non-symbolic quantities. In our three studies, we examine therefore how preschool children (3–5-years old) estimate position of non-symbolic quantities on a line, and how this estimation is related to the developing symbolic number knowledge and cultural (left-to-right) directionality. The children were tested with the Give-a-number task, then they performed a computerized number-line task. In Experiment 1, lines bounded with sets of 1 and 20 elements going left-to-right or right-to-left were used. Even in the least numerically competent group, the linear model better fit the estimates than the logarithmic or cyclic power models. The line direction was irrelevant. In Experiment 2, a 1–9 left-to-right oriented line was used. Advantage of linear model was found at group level, and variance of estimates correlated with tested numerosities. In Experiment 3, a position-to-number procedure again revealed the advantage of the linear model, although the strategy of selecting an option more similar to the closer end of the line was prevalent. The precision of estimation increased with the mastery of counting principles in all three experiments. These results contradict the hypothesis of the log-to-linear shift in development of basic numerical representation, rather supporting the linear model with scalar variance. However, the important question remains whether the number-line task captures the nature of the basic numerical representation, or rather the strategies of mapping that representation to an external space.
Collapse
Affiliation(s)
- Maciej Haman
- Faculty of Psychology, University of Warsaw, Warsaw, Poland
- *Correspondence: Maciej Haman,
| | - Katarzyna Patro
- Faculty of Psychology, University of Warsaw, Warsaw, Poland
- Department of Psychology, University of Tuebingen, Tübingen, Germany
| |
Collapse
|
12
|
Marlair C, Crollen V, Lochy A. A shared numerical magnitude representation evidenced by the distance effect in frequency-tagging EEG. Sci Rep 2022; 12:14559. [PMID: 36028649 PMCID: PMC9418351 DOI: 10.1038/s41598-022-18811-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Accepted: 08/19/2022] [Indexed: 11/09/2022] Open
Abstract
Humans can effortlessly abstract numerical information from various codes and contexts. However, whether the access to the underlying magnitude information relies on common or distinct brain representations remains highly debated. Here, we recorded electrophysiological responses to periodic variation of numerosity (every five items) occurring in rapid streams of numbers presented at 6 Hz in randomly varying codes—Arabic digits, number words, canonical dot patterns and finger configurations. Results demonstrated that numerical information was abstracted and generalized over the different representation codes by revealing clear discrimination responses (at 1.2 Hz) of the deviant numerosity from the base numerosity, recorded over parieto-occipital electrodes. Crucially, and supporting the claim that discrimination responses reflected magnitude processing, the presentation of a deviant numerosity distant from the base (e.g., base “2” and deviant “8”) elicited larger right-hemispheric responses than the presentation of a close deviant numerosity (e.g., base “2” and deviant “3”). This finding nicely represents the neural signature of the distance effect, an interpretation further reinforced by the clear correlation with individuals’ behavioral performance in an independent numerical comparison task. Our results therefore provide for the first time unambiguously a reliable and specific neural marker of a magnitude representation that is shared among several numerical codes.
Collapse
Affiliation(s)
- Cathy Marlair
- Institute of Psychology (IPSY) and Institute of Neuroscience (IoNS), Université Catholique de Louvain, Place Cardinal Mercier 10, 1348, Louvain-la-Neuve, Belgium.
| | - Virginie Crollen
- Institute of Psychology (IPSY) and Institute of Neuroscience (IoNS), Université Catholique de Louvain, Place Cardinal Mercier 10, 1348, Louvain-la-Neuve, Belgium
| | - Aliette Lochy
- Institute of Psychology (IPSY) and Institute of Neuroscience (IoNS), Université Catholique de Louvain, Place Cardinal Mercier 10, 1348, Louvain-la-Neuve, Belgium.,Department of Behavioral and Cognitive Sciences, Faculty of Humanities, Social and Educational Sciences, Institute of Cognitive Science and Assessment, Université du Luxembourg, Esch-sur-Alzette, Luxembourg
| |
Collapse
|
13
|
Zhang Y, An N, Chen J, Zhou X, Cui Z. Numerosity sense correlates with fluent mathematical abilities. Acta Psychol (Amst) 2022; 228:103655. [DOI: 10.1016/j.actpsy.2022.103655] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2021] [Revised: 05/11/2022] [Accepted: 06/20/2022] [Indexed: 01/29/2023] Open
|
14
|
Numerical estrangement and integration between symbolic and non-symbolic numerical information: Task-dependence and its link to math abilities in adults. Cognition 2022; 224:105067. [DOI: 10.1016/j.cognition.2022.105067] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2021] [Revised: 01/20/2022] [Accepted: 02/15/2022] [Indexed: 11/20/2022]
|
15
|
Zhang Y, Ma Y, Zhou X. The association between non-symbolic number comparison and mathematical abilities depends on fluency. Cogn Process 2022; 23:423-439. [PMID: 35704131 DOI: 10.1007/s10339-022-01098-x] [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: 10/05/2021] [Accepted: 05/19/2022] [Indexed: 11/03/2022]
Abstract
Numerous studies have explored the correlation between non-symbolic number comparison and mathematical abilities in children, but the results have been inconsistent. The underlying mental processing featuring fluency may affect the correlation. The current study tested the fluency hypothesis that non-symbolic number comparison is associated with mathematical fluency in the development of mathematical ability. Non-symbolic number comparison, arithmetic computation, mathematical reasoning, non-symbolic number estimation, symbolic number comparison, and a series of basic cognitive processing tasks, including mental rotation, non-verbal matrix reasoning, and choice reaction time, were administered to 1072 first- to fourth-grade children. The results show that non-symbolic number comparison (measured via numerosity comparison) was the only independent predictor of arithmetic computation in higher grades, even after controlled for age, gender, basic cognitive processing, non-symbolic number estimation (measured via numerosity estimation), and symbolic number comparison (measured via digit comparison). However, it did not correlate with mathematical reasoning in any grade. These findings support the fluency hypothesis for developmental correlation between non-symbolic number comparison and mathematical abilities. That is, non-symbolic number comparison correlates with mathematical ability featuring fluency.
Collapse
Affiliation(s)
- Yiyun Zhang
- School of Psychology, Liaoning Normal University, Liaoning, China.,State Key Laboratory of Cognitive Neuroscience and Learning and IDG, McGovern Institute for Brain Research, Beijing Normal University, Beijing, 100875, China
| | - Yuanyuan Ma
- School of Psychology, Liaoning Normal University, Liaoning, China
| | - Xinlin Zhou
- State Key Laboratory of Cognitive Neuroscience and Learning and IDG, McGovern Institute for Brain Research, Beijing Normal University, Beijing, 100875, China. .,Research Associationion for Brain and Mathematical Learning, Beijing Normal University, Beijing, China.
| |
Collapse
|
16
|
Lee SH, Kim D, Opfer JE, Pitt MA, Myung JI. A number-line task with a Bayesian active learning algorithm provides insights into the development of non-symbolic number estimation. Psychon Bull Rev 2022; 29:971-984. [PMID: 34918270 DOI: 10.3758/s13423-021-02041-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 11/11/2021] [Indexed: 01/29/2023]
Abstract
To characterize numerical representations, the number-line task asks participants to estimate the location of a given number on a line flanked with zero and an upper-bound number. An open question is whether estimates for symbolic numbers (e.g., Arabic numerals) and non-symbolic numbers (e.g., number of dots) rely on common processes with a common developmental pathway. To address this question, we explored whether well-established findings in symbolic number-line estimation generalize to non-symbolic number-line estimation. For exhaustive investigations without sacrificing data quality, we applied a novel Bayesian active learning algorithm, dubbed Gaussian process active learning (GPAL), that adaptively optimizes experimental designs. The results showed that the non-symbolic number estimation in participants of diverse ages (5-73 years old, n = 238) exhibited three characteristic features of symbolic number estimation.
Collapse
Affiliation(s)
- Sang Ho Lee
- Department of Psychology, The Ohio State University, 212 Psychology Building, 1835 Neil Avenue, Columbus, OH, 43210, USA.
| | - Dan Kim
- Department of Psychology, The Ohio State University, 212 Psychology Building, 1835 Neil Avenue, Columbus, OH, 43210, USA
| | - John E Opfer
- Department of Psychology, The Ohio State University, 212 Psychology Building, 1835 Neil Avenue, Columbus, OH, 43210, USA
| | - Mark A Pitt
- Department of Psychology, The Ohio State University, 212 Psychology Building, 1835 Neil Avenue, Columbus, OH, 43210, USA
| | - Jay I Myung
- Department of Psychology, The Ohio State University, 212 Psychology Building, 1835 Neil Avenue, Columbus, OH, 43210, USA
| |
Collapse
|
17
|
Predicting mathematics achievement from subdomains of early number competence: Differences by grade and achievement level. J Exp Child Psychol 2022; 217:105354. [DOI: 10.1016/j.jecp.2021.105354] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2021] [Revised: 11/09/2021] [Accepted: 12/14/2021] [Indexed: 11/16/2022]
|
18
|
Kuzmina Y, Antipkina I. The Association between Approximate Number Sense (ANS) and Math Achievement Depends on the Format of the ANS Test. JOURNAL OF COGNITION AND DEVELOPMENT 2022. [DOI: 10.1080/15248372.2022.2063293] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
|
19
|
Ching BHH, Kong KHC. Understanding additive composition is important for symbolic numerical magnitude processing. COGNITIVE DEVELOPMENT 2022. [DOI: 10.1016/j.cogdev.2022.101170] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
|
20
|
Mathematics and Numerosity but Not Visuo-Spatial Working Memory Correlate with Mathematical Anxiety in Adults. Brain Sci 2022; 12:brainsci12040422. [PMID: 35447954 PMCID: PMC9029128 DOI: 10.3390/brainsci12040422] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2022] [Revised: 03/15/2022] [Accepted: 03/20/2022] [Indexed: 12/04/2022] Open
Abstract
Many individuals, when faced with mathematical tasks or situations requiring arithmetic skills, experience exaggerated levels of anxiety. Mathematical anxiety (MA), in addition to causing discomfort, can lead to avoidance behaviors and then to underachievement. However, the factors inducing MA and how MA deploys its detrimental effects are still largely debated. There is evidence suggesting that MA affects working memory capacity by further diminishing its limited processing resources. An alternative account postulates that MA originates from a coarse early numerical cognition capacity, the perception of numerosity. In the current study, we measured MA, math abilities, numerosity perception and visuo-spatial working memory (VSWM) in a sample of neurotypical adults. Correlational analyses confirmed previous studies showing that high MA was associated with lower math scores and worse numerosity estimation precision. Conversely, MA turned out to be unrelated to VSWM capacities. Finally, partial correlations revealed that MA fully accounted for the relationship between numerosity estimation precision and math abilities, suggesting a key role for MA as a mediating factor between these two domains.
Collapse
|
21
|
Feldman A, Berger A. Development of the Mental Number Line Representation of Numbers 0–10 and Its Relationship to Mental Arithmetic. Brain Sci 2022; 12:brainsci12030335. [PMID: 35326291 PMCID: PMC8946762 DOI: 10.3390/brainsci12030335] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2022] [Revised: 02/23/2022] [Accepted: 02/26/2022] [Indexed: 12/04/2022] Open
Abstract
The internal representation of numbers on the mental number line (MNL) was demonstrated by performing the computerized version of the number-to-position (CNP) task on a touchscreen while restricting response time. We found that the estimation pattern is best fit by a sigmoid function, further denoted as the “sigmoidal model”. Two developmental leaps occurring during elementary school were recognized: (1) the division of the number line into two segments and (2) consistent use of different anchor points on the number line—the left endpoint in first grade, the right endpoint in second grade, and finally the midpoint in third grade. Additionally, when examining the differences between the breakpoints, we found that first graders demonstrated a breakpoint close to 6, which linearly decreased over the years until stabilizing close to 5. The relation between the ability to place individual numbers on a number line and performance of mental arithmetic showed that the consistent use of anchor points correlated significantly with faster responses in mental arithmetic.
Collapse
|
22
|
Kamphorst E, Cantell M, Van Der Veer G, Minnaert A, Houwen S. Emerging School Readiness Profiles: Motor Skills Matter for Cognitive- and Non-cognitive First Grade School Outcomes. Front Psychol 2022; 12:759480. [PMID: 35027900 PMCID: PMC8751626 DOI: 10.3389/fpsyg.2021.759480] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2021] [Accepted: 11/01/2021] [Indexed: 11/24/2022] Open
Abstract
A promising approach for studying school readiness involves a person-centered approach, aimed at exploring how functioning in diverse developmental domains conjointly affects children’s school outcomes. Currently, however, a systematic understanding lacks of how motor skills, in conjunction with other school readiness skills, affect a child’s school outcomes. Additionally, little is known about longitudinal associations of school readiness with non-academic (e.g., socioemotional) school outcomes. Therefore, we examined the school readiness skills of a sample of Dutch children (N = 91) with a mean age of 3 years and 4 months (46% girls). We used a multi-informant test battery to assess children’s school readiness in terms of executive functions (EFs), language and emergent literacy, motor skills, and socioemotional behavior. During the spring term of a child’s first grade year, we collected academic and non-academic (i.e., EFs, motor skills, socioemotional- and classroom behavior, and creative thinking) school outcomes. A latent profile analysis revealed four distinct profiles. Children in the “Parent Positive” (29%) profile were rated positively by their parents, and performed variably on motor and language/emergent literacy skills tests. The second profile–“Multiple Strengths” (13%)–consisted of children showing strengths in multiple domains, especially with respect to motor skills. Children from the third profile–“Average Performers” (50%)–did not show any distinct strengths or weaknesses, rather displayed school readiness skill levels close to, or just below the sample mean. Finally, the “Parental Concern” (8%) profile was characterized by high levels of parental concerns, while displaying slightly above average performance on specific motor and language skills. Motor skills clearly distinguished between profiles, next to parent-rated EFs and socioemotional behavior, and to a lesser extent emergent literacy skills. School readiness profiles were found to differ in mean scores on first grade academic achievement, parent- and teacher-rated EFs, motor skills, parent-rated socioemotional functioning, and pre-requisite learning skills. The pattern of mean differences was complex, suggesting that profiles could not be ranked from low to high in terms of school outcomes. Longitudinal studies are needed to disentangle the interaction between emerging school readiness of the child and the surrounding context.
Collapse
Affiliation(s)
- Erica Kamphorst
- Faculty of Behavioural and Social Sciences, Inclusive and Special Needs Education Unit, University of Groningen, Groningen, Netherlands
| | - Marja Cantell
- Faculty of Behavioural and Social Sciences, Inclusive and Special Needs Education Unit, University of Groningen, Groningen, Netherlands
| | - Gerda Van Der Veer
- Faculty of Behavioural and Social Sciences, Inclusive and Special Needs Education Unit, University of Groningen, Groningen, Netherlands
| | - Alexander Minnaert
- Faculty of Behavioural and Social Sciences, Inclusive and Special Needs Education Unit, University of Groningen, Groningen, Netherlands
| | - Suzanne Houwen
- Faculty of Behavioural and Social Sciences, Inclusive and Special Needs Education Unit, University of Groningen, Groningen, Netherlands
| |
Collapse
|
23
|
Kim D, Opfer JE. Dynamics Versus Development in Numerosity Estimation: A Computational Model Accurately Predicts a Developmental Reversal. Cogn Sci 2021; 45:e13049. [PMID: 34647341 DOI: 10.1111/cogs.13049] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2020] [Revised: 08/06/2021] [Accepted: 08/27/2021] [Indexed: 01/29/2023]
Abstract
Perceptual judgments result from a dynamic process, but little is known about the dynamics of number-line estimation. A recent study proposed a computational model that combined a model of trial-to-trial changes with a model for the internal scaling of discrete numbers. Here, we tested a surprising prediction of the model-a situation in which children's estimates of numerosity would be better than those of adults. Consistent with the model simulations, task contexts led to a clear developmental reversal: children made more adult-like, linear estimates when to-be-estimated numbers were descending over trials (i.e., backward condition), whereas adults became more like children with logarithmic estimates when numbers were ascending (i.e., forward condition). In addition, adults' estimates were subject to inter-trial differences regardless of stimulus order. In contrast, children were not able to use the trial-to-trial dynamics unless stimuli varied systematically, indicating the limited cognitive capacity for dynamic updates. Together, the model adequately predicts both developmental and trial-to-trial changes in number-line tasks.
Collapse
Affiliation(s)
- Dan Kim
- Department of Psychology, The Ohio State University
| | - John E Opfer
- Department of Psychology, The Ohio State University
| |
Collapse
|
24
|
Rebholz F, Golle J, Moeller K. The association of basic numerical abilities and math achievement: The mediating role of visuospatial and arithmetical abilities. Q J Exp Psychol (Hove) 2021; 75:841-853. [PMID: 34344247 PMCID: PMC8958554 DOI: 10.1177/17470218211040060] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Abstract
Basic numerical abilities such as number line estimation have been observed repeatedly to be associated with mathematical achievement. Recently, it was argued that the association between basic numerical abilities and mathematical achievement is fully mediated by visuospatial abilities. However, arithmetical abilities have not yet been considered as influencing this association, even though solution strategies in number line estimation as well as mathematical achievement often involve arithmetical procedures. Therefore, we investigated the mediating role of arithmetical and visuospatial abilities on the association between number line estimation and mathematical achievement in a sample of n = 599 German elementary school students. The results indicated that arithmetical abilities as well as visuospatial abilities mediated the association between number line estimation and mathematical achievement. However, neither visuospatial nor arithmetical abilities fully mediated the association between number line estimation and mathematical achievement when considered in isolation. This substantiates the relevance of the intertwined development of visuospatial and arithmetical abilities as well as basic numerical abilities such as number line estimation (i.e., the combination of domain-specific numerical and domain-general abilities) driving mathematical achievement.
Collapse
Affiliation(s)
- Franziska Rebholz
- Hector Research Institute of Education Sciences and Psychology, University of Tübingen, Tübingen, Germany.,LEAD Graduate School & Research Network, University of Tübingen, Tübingen, Germany
| | - Jessika Golle
- Hector Research Institute of Education Sciences and Psychology, University of Tübingen, Tübingen, Germany.,LEAD Graduate School & Research Network, University of Tübingen, Tübingen, Germany
| | - Korbinian Moeller
- LEAD Graduate School & Research Network, University of Tübingen, Tübingen, Germany.,Centre for Mathematical Cognition, School of Science, Loughborough University, Loughborough, UK.,Leibniz-Institut für Wissensmedien, Tübingen, Germany.,Department of Psychology, University of Tübingen, Tübingen, Germany
| |
Collapse
|
25
|
Gilmore C, Batchelor S. Verbal count sequence knowledge underpins numeral order processing in children. Acta Psychol (Amst) 2021; 216:103294. [PMID: 33838444 DOI: 10.1016/j.actpsy.2021.103294] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2020] [Revised: 02/24/2021] [Accepted: 03/02/2021] [Indexed: 10/21/2022] Open
Abstract
Recent research has suggested that numeral order processing - the speed and accuracy with which individuals can determine whether a set of digits is in numerical order or not - is related to arithmetic and mathematics outcomes. It has therefore been proposed that ordinal relations are a fundamental property of symbolic numeral representations. However, order information is also inherent in the verbal count sequence, and thus verbal count sequence knowledge may instead explain the relationship between performance on numeral order tasks and arithmetic. We explored this question with 62 children aged 6- to 8-years-old. We found that performance on a verbal count sequence knowledge task explained the relationship between numeral order processing and arithmetic. Moreover many children appeared to explicitly base their judgments of numerical order on count sequence information. This suggests that insufficient attention may have been paid to verbal number knowledge in understanding the sources of information that give meaning to numbers.
Collapse
|
26
|
Wang J, Liu RD, Star J, Zhen R, Liu Y, Hong W. Do Students Respond Faster to Inequalities with a Greater than Sign or to Inequalities with a Less than Sign: Spatial-Numerical Association in Inequalities. JOURNAL OF COGNITION AND DEVELOPMENT 2021. [DOI: 10.1080/15248372.2021.1916499] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
| | | | | | - Rui Zhen
- Hangzhou Normal University, China
| | | | - Wei Hong
- Beijing Normal University, China
| |
Collapse
|
27
|
Long-term relevance and interrelation of symbolic and non-symbolic abilities in mathematical-numerical development: Evidence from large-scale assessment data. COGNITIVE DEVELOPMENT 2021. [DOI: 10.1016/j.cogdev.2021.101008] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
|
28
|
van ‘t Noordende JE, Kroesbergen EH, Leseman PPM, Volman M(CJM. The Role of Non-symbolic and Symbolic Skills in the Development of Early Numerical Cognition from Preschool to Kindergarten Age. JOURNAL OF COGNITION AND DEVELOPMENT 2020. [DOI: 10.1080/15248372.2020.1858835] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
|
29
|
Li M, Cheng D, Lu Y, Zhou X. Neural association between non-verbal number sense and arithmetic fluency. Hum Brain Mapp 2020; 41:5128-5140. [PMID: 32937010 PMCID: PMC7670642 DOI: 10.1002/hbm.25179] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2020] [Revised: 06/18/2020] [Accepted: 08/04/2020] [Indexed: 11/29/2022] Open
Abstract
Non‐verbal number sense has been shown to significantly correlate with arithmetic fluency. Accumulated behavioral evidence indicates that the cognitive mechanism relies on visual perception. However, few studies have investigated the neural mechanism underlying this association. Following the visual perception account, we hypothesized that there would be a neural association in occipital areas of the brain between non‐verbal number sense, arithmetic fluency, and visual perception. We analyzed event‐related potentials that are sensitive to neural responses while participants performed five cognitive tasks: simple addition, simple subtraction, numerosity comparison, figure matching, and character rhyming. The single‐trial ERP‐behavior correlation approach was used to enhance the statistical power. The results showed that the N1 component significantly correlated with reaction time at occipital electrodes on all tasks except for character rhyming. The N1 component for arithmetic fluency (simple addition and subtraction) and character rhyming correlated with the reaction time for numerosity comparison and figure matching. The results suggest that there are neural associations between arithmetic fluency, non‐verbal number sense, and visual perception in the occipital cortex, and that visual perception is the shared mechanism for both non‐verbal number sense and arithmetic fluency.
Collapse
Affiliation(s)
- Mengyi Li
- State Key Laboratory of Cognitive Neuroscience and Learning, IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China.,Advanced Innovation Center for Future Education, Beijing Normal University, Beijing, China.,Siegler Center for Innovative Learning, Beijing Normal University, Beijing, China
| | - Dazhi Cheng
- State Key Laboratory of Cognitive Neuroscience and Learning, IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China.,Advanced Innovation Center for Future Education, Beijing Normal University, Beijing, China.,Department of Pediatric Neurology, Capital Institute of Pediatrics, Beijing, China
| | - Yujie Lu
- State Key Laboratory of Cognitive Neuroscience and Learning, IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China.,Advanced Innovation Center for Future Education, Beijing Normal University, Beijing, China.,Siegler Center for Innovative Learning, Beijing Normal University, Beijing, China
| | - Xinlin Zhou
- State Key Laboratory of Cognitive Neuroscience and Learning, IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China.,Advanced Innovation Center for Future Education, Beijing Normal University, Beijing, China.,Siegler Center for Innovative Learning, Beijing Normal University, Beijing, China
| |
Collapse
|
30
|
Fuhs MW, Tavassolie N, Wang Y, Bartek V, Sheeks NA, Gunderson EA. Children’s Flexible Attention to Numerical and Spatial Magnitudes in Early Childhood. JOURNAL OF COGNITION AND DEVELOPMENT 2020. [DOI: 10.1080/15248372.2020.1844712] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
|
31
|
Gomez A, Huron C. Subitizing and counting impairments in children with developmental coordination disorder. RESEARCH IN DEVELOPMENTAL DISABILITIES 2020; 104:103717. [PMID: 32585441 DOI: 10.1016/j.ridd.2020.103717] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2020] [Revised: 06/03/2020] [Accepted: 06/10/2020] [Indexed: 06/11/2023]
Abstract
Developmental coordination disorder (DCD) interferes with academic achievement and daily life, and is associated with persistent academic difficulties, in particular within mathematical learning. In the present study, we aimed to study numerical cognition using an approach that taps very basic numerical processes such as subitizing and counting abilities in DCD. We used a counting task and a subitizing task in forty 7-10 years-old children with or without DCD. In both tasks, children were presented with arrays of one to eight dots and asked to name aloud the number of dots as accurately and quickly as possible. In the subitizing task, dots were presented during 250 ms whereas in the counting task they stayed on the screen until the participants gave a verbal response. The results showed that children with DCD were less accurate and slower in the two enumeration tasks (with and without a time limit), providing evidence that DCD impairs both counting and subitizing. These impairments might have a deleterious impact on the ability to improve the acuity of the Approximate Number System through counting, and thus could play a role in the underachievement of children with DCD in mathematics.
Collapse
Affiliation(s)
- Alice Gomez
- Institute of Cognitive Science Marc Jeannerod, CNRS, UMR 5229, Bron, France; Université Claude Bernard Lyon 1, Inspé, France; INSERM, U992, Cognitive Neuroimaging Unit, CEA/SAC/DSV/DRM/NeuroSpin, Bat 145, Point Courrier 156, F-91191 Gif/Yvette, France; CEA, DSV/I2BM, NeuroSpin Center, Bât 145, Point Courrier 156, F-91191 Gif/Yvette, France; Univ Paris-Sud, Cognitive Neuroimaging Unit, Bât 300, 91405 Orsay Cedex, France; INSERM U1284, France.
| | - Caroline Huron
- INSERM, U992, Cognitive Neuroimaging Unit, CEA/SAC/DSV/DRM/NeuroSpin, Bat 145, Point Courrier 156, F-91191 Gif/Yvette, France; CEA, DSV/I2BM, NeuroSpin Center, Bât 145, Point Courrier 156, F-91191 Gif/Yvette, France; Univ Paris-Sud, Cognitive Neuroimaging Unit, Bât 300, 91405 Orsay Cedex, France; Center for Research and Interdisciplinarity (CRI), France; Université de Paris, France; INSERM U1284, France
| |
Collapse
|
32
|
Haman M, Lipowska K. Moving attention along the mental number line in preschool age: Study of the operational momentum in 3- to 5-year-old children's non-symbolic arithmetic. Dev Sci 2020; 24:e13007. [PMID: 32567767 DOI: 10.1111/desc.13007] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2018] [Revised: 05/03/2020] [Accepted: 06/02/2020] [Indexed: 01/29/2023]
Abstract
People tend to underestimate subtraction and overestimate addition outcomes and to associate subtraction with the left side and addition with the right side. These two phenomena are collectively labeled 'operational momentum' (OM) and thought to have their origins in the same mechanism of 'moving attention along the mental number line'. OM in arithmetic has never been tested in children at the preschool age, which is critical for numerical development. In this study, 3-5 years old were tested with non-symbolic addition and subtraction tasks. Their level of understanding of counting principles (CP) was assessed using the give-a-number task. When the second operand's cardinality was 5 or 6 (Experiment 1), the child's reaction time was shorter in addition/subtraction tasks after cuing attention appropriately to the right/left. Adding/subtracting one element (Experiment 2) revealed a more complex developmental pattern. Before acquiring CP, the children showed generalized overestimation bias. Underestimation in addition and overestimation in subtraction emerged only after mastering CP. No clear spatial-directional OM pattern was found, however, the response time to rightward/leftward cues in addition/subtraction again depended on stage of mastering CP. Although the results support the hypothesis about engagement of spatial attention in early numerical processing, they point to at least partial independence of the spatial-directional and magnitude OM. This undermines the canonical version of the number line-based hypothesis. Mapping numerical magnitudes to space may be a complex process that undergoes reorganization during the period of acquisition of symbolic representations of numbers. Some hypotheses concerning the role of spatial-numerical associations in numerical development are proposed.
Collapse
Affiliation(s)
- Maciej Haman
- Faculty of Psychology, University of Warsaw, Warszawa, Poland
| | | |
Collapse
|
33
|
Aragón E, Cerda G, Aguilar M, Mera C, Navarro JI. Modulation of general and specific cognitive precursors to early mathematical competencies in preschool children. EUROPEAN JOURNAL OF PSYCHOLOGY OF EDUCATION 2020. [DOI: 10.1007/s10212-020-00483-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
34
|
Marchand E, Wade S, Sullivan J, Barner D. Language-specific numerical estimation in bilingual children. J Exp Child Psychol 2020; 197:104860. [PMID: 32445950 DOI: 10.1016/j.jecp.2020.104860] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2019] [Revised: 03/05/2020] [Accepted: 03/24/2020] [Indexed: 01/29/2023]
Abstract
We tested 5- to 7-year-old bilingual learners of French and English (N = 91) to investigate how language-specific knowledge of verbal numerals affects numerical estimation. Participants made verbal estimates for rapidly presented random dot arrays in each of their two languages. Estimation accuracy differed across children's two languages, an effect that remained when controlling for children's familiarity with number words across their two languages. In addition, children's estimates were equivalently well ordered in their two languages, suggesting that differences in accuracy were due to how children represented the relative distance between number words in each language. Overall, these results suggest that bilingual children have different mappings between their verbal and nonverbal counting systems across their two languages and that those differences in mappings are likely driven by an asymmetry in their knowledge of the structure of the count list across their languages. Implications for bilingual math education are discussed.
Collapse
Affiliation(s)
- Elisabeth Marchand
- Department of Psychology, University of California, San Diego, La Jolla, CA 92093, USA.
| | - Shirlene Wade
- Department of Brain and Cognitive Sciences, University of Rochester, Rochester, NY 14627, USA; Department of Psychology, University of California, Berkeley, Berkeley, CA 94720, USA
| | - Jessica Sullivan
- Department of Psychology, Skidmore College, Saratoga Springs, NY 12866, USA
| | - David Barner
- Department of Psychology, University of California, San Diego, La Jolla, CA 92093, USA
| |
Collapse
|
35
|
Lambert K, Wortha SM, Moeller K. Time Reading in Middle and Secondary School Students: The Influence of Basic-Numerical Abilities. The Journal of Genetic Psychology 2020; 181:255-277. [PMID: 32406334 DOI: 10.1080/00221325.2020.1760778] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Abstract
Time reading skills are central for the management of personal and professional life. However, little is known about the differential influence of basic numerical abilities on analog and digital time reading in general and in middle and secondary school students in particular. The present study investigated the influence of basic numerical skills separately for analog and digital time reading in N = 709 students from 5th to 8th grade. The present findings suggest that the development of time reading skills is not completed by the end of primary school. Results indicated that aspects of magnitude manipulation and arithmetic fact knowledge predicted analog time reading significantly over and above the influence of age. Furthermore, results showed that spatial representations of number magnitude, magnitude manipulation, arithmetic fact knowledge, and conceptual knowledge were significant predictors of digital time reading beyond general cognitive ability and sex. To the best of our knowledge, the present study is the first to show differential effects of basic numerical abilities on analog and digital time reading skills in middle and secondary school students. As time readings skills are crucial for everyday life, these results are highly relevant to better understand basic numerical processes underlying time reading.
Collapse
Affiliation(s)
- Katharina Lambert
- Hector Research Institute of Education Sciences and Psychology, University of Tuebingen, Tuebingen, Germany.,LEAD Graduate School & Research Network, University of Tuebingen, Tuebingen, Germany
| | - Silke M Wortha
- LEAD Graduate School & Research Network, University of Tuebingen, Tuebingen, Germany.,Leibniz-Institut für Wissensmedien, Tuebingen, Germany
| | - Korbinian Moeller
- LEAD Graduate School & Research Network, University of Tuebingen, Tuebingen, Germany.,Leibniz-Institut für Wissensmedien, Tuebingen, Germany.,Department of Psychology, University of Tuebingen, Tuebingen, Germany
| |
Collapse
|
36
|
Kang I, Ratcliff R. Modeling the interaction of numerosity and perceptual variables with the diffusion model. Cogn Psychol 2020; 120:101288. [PMID: 32325289 DOI: 10.1016/j.cogpsych.2020.101288] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2020] [Accepted: 02/25/2020] [Indexed: 10/24/2022]
Abstract
Ratcliff and McKoon (2018) proposed integrated diffusion models for numerosity judgments in which a numerosity representation provides evidence used to drive the decision process. We extend this modeling framework to examine the interaction of non-numeric perceptual variables with numerosity by assuming that drift rate and non-decision time are functions of those variables. Four experiments were conducted with two different types of stimuli: a single array of intermingled blue and yellow dots in which both numerosity and dot area vary over trials and two side-by-side arrays of dots in which numerosity, dot area, and convex hull vary over trials. The tasks were to decide whether there were more blue or yellow dots (two experiments), more dots on which side, or which dots have a larger total area. Development of models started from the principled models in Ratcliff and McKoon (2018) and became somewhat ad hoc as we attempted to capture unexpected patterns induced by the conflict between numerosity and perceptual variables. In the three tasks involving numerosity judgments, the effects of the non-numeric variables were moderated by the number of dots. Under a high conflict, judgments were dominated by perceptual variables and produced an unexpected shift in the leading edge of the reaction time (RT) distributions. Although the resulting models were able to predict most of the accuracy and RT patterns, the models were not able to completely capture this shift in the RT distributions. However, when subjects judged area, numerosity affected perceptual judgments but there was no leading edge effect. Based on the results, it appears that the integrated diffusion models provide an effective framework to study the role of numerical and perceptual variables in numerosity tasks and their context-dependency.
Collapse
Affiliation(s)
- Inhan Kang
- The Ohio State University, 291 Psychology Building, 1835 Neil Avenue, Columbus, OH 43210, United States.
| | - Roger Ratcliff
- The Ohio State University, 291 Psychology Building, 1835 Neil Avenue, Columbus, OH 43210, United States.
| |
Collapse
|
37
|
Caviola S, Colling LJ, Mammarella IC, Szűcs D. Predictors of mathematics in primary school: Magnitude comparison, verbal and spatial working memory measures. Dev Sci 2020; 23:e12957. [DOI: 10.1111/desc.12957] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2019] [Revised: 11/15/2019] [Accepted: 02/10/2020] [Indexed: 11/28/2022]
Affiliation(s)
- Sara Caviola
- School of Psychology University of Leeds Leeds UK
- Department of Psychology Centre for Neuroscience in Education University of Cambridge Cambridge UK
| | - Lincoln J. Colling
- Department of Psychology Centre for Neuroscience in Education University of Cambridge Cambridge UK
- School of Psychology University of Sussex Brighton UK
| | | | - Dénes Szűcs
- Department of Psychology Centre for Neuroscience in Education University of Cambridge Cambridge UK
| |
Collapse
|
38
|
Numerals do not need numerosities: robust evidence for distinct numerical representations for symbolic and non-symbolic numbers. PSYCHOLOGICAL RESEARCH 2020; 85:764-776. [DOI: 10.1007/s00426-019-01286-z] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2019] [Accepted: 12/30/2019] [Indexed: 10/25/2022]
|
39
|
Canto-López MC, Aguilar M, García-Sedeño MA, Navarro JI, Aragón E, Delgado C, Mera C. Numerical Estimation and Mathematical Learning Methodology in Preschoolers. Psychol Rep 2019; 124:438-458. [PMID: 31875765 DOI: 10.1177/0033294119892880] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
One of the means for representing quantities/magnitudes is the mental number line. It is still a nonsolved question as to whether the method of learning mathematics in the early years could improve this type of estimating. A total of 233 students, aged four and five years, who learned mathematics with a new method called Open Algorithm Based on Number or the more traditional Closed Based on Ciphers approach, were evaluated with a reliable estimation on the number line test. Results revealed significant differences in participants' estimation functions based on the learning method used. Students who learned mathematics through the Open Algorithm Based on Number method used a linear representation more efficiently than those who were taught with the Closed Based on Ciphers methodology. This group exhibited a logarithmic function in their approach. We discussed whether these differences can be attributed to a recurrent practice in estimation tasks at school, characterized by the Open Algorithm Based on Number methodology.
Collapse
Affiliation(s)
- M C Canto-López
- Department of Psychology, 16727University of Cadiz, Puerto Real, Spain
| | - M Aguilar
- Department of Psychology, 16727University of Cadiz, Puerto Real, Spain
| | - M A García-Sedeño
- Department of Psychology, 16727University of Cadiz, Puerto Real, Spain
| | - J I Navarro
- Department of Psychology, 16727University of Cadiz, Puerto Real, Spain
| | - E Aragón
- Department of Psychology, 16727University of Cadiz, Puerto Real, Spain
| | - C Delgado
- Department of Psychology, 16727University of Cadiz, Puerto Real, Spain
| | - C Mera
- Department of Psychology, 16727University of Cadiz, Puerto Real, Spain
| |
Collapse
|
40
|
Tikhomirova T, Kuzmina Y, Lysenkova I, Malykh S. The Relationship Between Non-symbolic and Symbolic Numerosity Representations in Elementary School: The Role of Intelligence. Front Psychol 2019; 10:2724. [PMID: 31866910 PMCID: PMC6906201 DOI: 10.3389/fpsyg.2019.02724] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2019] [Accepted: 11/18/2019] [Indexed: 01/29/2023] Open
Abstract
This study aimed to estimate the extent to which the development of symbolic numerosity representations relies on pre-existing non-symbolic numerosity representations that refer to the Approximate Number System. To achieve this aim, we estimated the longitudinal relationships between accuracy in the Number Line (NL) test and “blue–yellow dots” test across elementary school children. Data from a four-wave longitudinal study involving schoolchildren in grades 1–4 in Russia and Kyrgyzstan (N = 490, mean age 7.65 years in grade 1) were analyzed. We applied structural equation modeling and tested several competing models. The results revealed that at the start of schooling, the accuracy in the NL test predicted subsequent accuracy in the “blue–yellow dots” test, whereas subsequently, non-symbolic representation in grades 2 and 3 predicted subsequent symbolic representation. These results indicate that the effect of non-symbolic representation on symbolic representation emerges after a child masters the basics of symbolic number knowledge, such as counting in the range of twenty and simple arithmetic. We also examined the extent to which the relationships between non-symbolic and symbolic representations might be explained by fluid intelligence, which was measured by Raven’s Standard Progressive Matrices test. The results revealed that the effect of symbolic representation on non-symbolic representation was explained by fluid intelligence, whereas at the end of elementary school, non-symbolic representation predicted subsequent symbolic representation independently of fluid intelligence.
Collapse
Affiliation(s)
- Tatiana Tikhomirova
- Department of Psychology, Lomonosov Moscow State University, Moscow, Russia.,Psychological Institute of Russian Academy of Education, Moscow, Russia
| | - Yulia Kuzmina
- Department of Psychology, Lomonosov Moscow State University, Moscow, Russia.,Psychological Institute of Russian Academy of Education, Moscow, Russia
| | - Irina Lysenkova
- Department of Psychology, Kyrgyz-Russian Slavic University, Bishkek, Kyrgyzstan
| | - Sergey Malykh
- Department of Psychology, Lomonosov Moscow State University, Moscow, Russia.,Psychological Institute of Russian Academy of Education, Moscow, Russia
| |
Collapse
|
41
|
Goffin C, Vogel SE, Slipenkyj M, Ansari D. A comes before B, like 1 comes before 2. Is the parietal cortex sensitive to ordinal relationships in both numbers and letters? An fMRI-adaptation study. Hum Brain Mapp 2019; 41:1591-1610. [PMID: 31854024 PMCID: PMC7268023 DOI: 10.1002/hbm.24897] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2019] [Revised: 11/13/2019] [Accepted: 12/03/2019] [Indexed: 12/02/2022] Open
Abstract
How are number symbols (e.g., Arabic digits) represented in the brain? Functional resonance imaging adaptation (fMRI‐A) research has indicated that the intraparietal sulcus (IPS) exhibits a decrease in activation with the repeated presentation of the same number, that is followed by a rebound effect with the presentation of a new number. This rebound effect is modulated by the numerical ratio or difference between presented numbers. It has been suggested that this ratio‐dependent rebound effect is reflective of a link between the symbolic numerical representation system and an approximate magnitude system. Experiment 1 used fMRI‐A to investigate an alternative hypothesis: that the rebound effect observed in the IPS is related to the ordinal relationships between symbols (e.g., 3 comes before 4; C after B). In Experiment 1, adult participants exhibited the predicted distance‐dependent parametric rebound effect bilaterally in the IPS for number symbols during a number adaptation task, however, the same effect was not found anywhere in the brain in response to letters. When numbers were contrasted with letters (numbers > letters), the left intraparietal lobule remained significant. Experiment 2 demonstrated that letter stimuli used in Experiment 1 generated a behavioral distance effect during an active ordinality task, despite the lack of a neural distance effect using fMRI‐A. The current study does not support the hypothesis that general ordinal mechanisms underpin the neural parametric recovery effect in the IPS in response to number symbols. Additional research is needed to further our understanding of mechanisms underlying symbolic numerical representation in the brain.
Collapse
Affiliation(s)
- Celia Goffin
- Numerical Cognition Laboratory, Department of Psychology and Brain and Mind Institute, The University of Western Ontario, London, Ontario, Canada
| | - Stephan E Vogel
- Educational Neuroscience, Institute of Psychology, University of Graz, Graz, Austria
| | - Michael Slipenkyj
- Numerical Cognition Laboratory, Department of Psychology and Brain and Mind Institute, The University of Western Ontario, London, Ontario, Canada
| | - Daniel Ansari
- Numerical Cognition Laboratory, Department of Psychology and Brain and Mind Institute, The University of Western Ontario, London, Ontario, Canada
| |
Collapse
|
42
|
Yuan L, Prather R, Mix KS, Smith LB. Number Representations Drive Number-Line Estimates. Child Dev 2019; 91:e952-e967. [PMID: 31657470 DOI: 10.1111/cdev.13333] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
The number-line task has been extensively used to study the mental representation of numbers in children. However, studies suggest that proportional reasoning provides a better account of children's performance. Ninety 4- to 6-year-olds were given a number-line task with symbolic numbers, with clustered dot arrays that resembled a perceptual scaling task, or with spread-out dot arrays that involved numerical estimation. Children performed well with clustered dot arrays, but poorly with symbolic numbers and spread-out dot arrays. Performances with symbolic numbers and spread-out dot arrays were highly correlated and were related to counting skill; neither was true for clustered dot arrays. Overall, results provide evidence for the role of mental representation of numbers in the symbolic number-line task.
Collapse
|
43
|
Ramani GB, Daubert EN, Lin GC, Kamarsu S, Wodzinski A, Jaeggi SM. Racing dragons and remembering aliens: Benefits of playing number and working memory games on kindergartners' numerical knowledge. Dev Sci 2019; 23:e12908. [PMID: 31587470 DOI: 10.1111/desc.12908] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2018] [Revised: 08/21/2019] [Accepted: 09/27/2019] [Indexed: 11/28/2022]
Abstract
Sources that contribute to variation in mathematical achievement include both numerical knowledge and general underlying cognitive processing abilities. The current study tested the benefits of tablet-based training games that targeted each of these areas for improving the mathematical knowledge of kindergarten-age children. We hypothesized that playing a number-based game targeting numerical magnitude knowledge would improve children's broader numerical skills. We also hypothesized that the benefits of playing a working memory (WM) game would transfer to children's numerical knowledge given its important underlying role in mathematics achievement. Kindergarteners from diverse backgrounds (n = 148; 52% girls; Mage = 71.87 months) were randomly assigned to either play a number-based game, a WM game, or a control game on a tablet for 10 sessions. Structural equation modeling was used to model children's learning gains in mathematics and WM across time. Overall, our results suggest that playing the number game improved kindergarten children's numerical knowledge at the latent level, and these improvements remained stable as assessed 1 month later. However, children in the WM group did not improve their numerical knowledge compared to children in the control condition. Playing both the number game and WM game improved children's WM at the latent level. Importantly, the WM group continued to improve their WM for at least a month after playing the games. The results demonstrate that computerized games that target both domain-specific and domain-general skills can benefit a broad range of kindergarten-aged children.
Collapse
Affiliation(s)
- Geetha B Ramani
- Department of Human Development and Quantitative Methodology, University of Maryland, College Park, MD, USA
| | - Emily N Daubert
- Department of Human Development and Quantitative Methodology, University of Maryland, College Park, MD, USA
| | - Grace C Lin
- School of Education, University of California, Irvine, Irvine, CA, USA
| | - Snigdha Kamarsu
- School of Education, University of California, Irvine, Irvine, CA, USA
| | - Alaina Wodzinski
- Department of Human Development and Quantitative Methodology, University of Maryland, College Park, MD, USA
| | - Susanne M Jaeggi
- School of Education, University of California, Irvine, Irvine, CA, USA
| |
Collapse
|
44
|
Pappas MA, Polychroni F, Drigas AS. Assessment of Mathematics Difficulties for Second and Third Graders: Cognitive and Psychological Parameters. Behav Sci (Basel) 2019; 9:bs9070076. [PMID: 31336844 PMCID: PMC6681099 DOI: 10.3390/bs9070076] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2019] [Revised: 07/09/2019] [Accepted: 07/10/2019] [Indexed: 11/16/2022] Open
Abstract
Mathematical achievement during the first years of primary school seems to be a reliable predictor of students’ later performance. In addition, cognitive, metacognitive, and psychological parameters are considered to be factors related to mathematical achievement. However, in the Greek educational system, there is a shortage of valid and reliable tools for the assessment of mathematics difficulties and as a consequence, identification of children with these difficulties does not take place before the last years of primary school. This study aims to investigate the relationship between working memory, sustained attention, executive functions, and math anxiety with mathematical achievement in 2nd and 3rd graders. The design of the study was based on the parameters of mathematics difficulties, as they arise from the literature review. Ninety-one Year 2 and Year 3 primary school students (mean age 8.06 years) from three public schools situated in Attica, Greece participated in the study. The students completed three different scales including educational, cognitive, and psychological tasks. Results showed that mathematical skills were significantly correlated with sustained attention, inductive reasoning, math anxiety, and working memory. Moreover, mental arithmetic ability, sustained attention, and working memory predicted mathematical achievement of second and third graders. The study’s outcomes verify that sustained attention, inductive reasoning, working memory, and math anxiety are correlated with young students’ mathematical performance. The implications of the results for the development of an assessment tool for early detection of mathematics difficulties will be discussed.
Collapse
Affiliation(s)
- Marios A Pappas
- Department of Psychology, National and Kapodistrian University of Athens, 157 84 Athens, Greece.
| | - Fotini Polychroni
- Department of Psychology, National and Kapodistrian University of Athens, 157 84 Athens, Greece
| | - Athanasios S Drigas
- Net Media Lab-Mind & Brain R&D, I.I.T., N.C.S.R. 'Demokritos', 153 41 Agia Paraskevi, Greece
| |
Collapse
|
45
|
Matejko AA, Ansari D. The neural association between arithmetic and basic numerical processing depends on arithmetic problem size and not chronological age. Dev Cogn Neurosci 2019; 37:100653. [PMID: 31102959 PMCID: PMC6969316 DOI: 10.1016/j.dcn.2019.100653] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2018] [Revised: 04/16/2019] [Accepted: 04/26/2019] [Indexed: 11/30/2022] Open
Abstract
The intraparietal sulcus (IPS) is thought to be an important region for basic number processing (e.g. symbol-quantity associations) and arithmetic (e.g. addition). Evidence for shared circuitry within the IPS is largely based on comparisons across studies, and little research has investigated number processing and arithmetic in the same individuals. It is also unclear how the neural overlap between number processing and arithmetic is influenced by age and arithmetic problem difficulty. This study investigated these unresolved questions by examining basic number processing (symbol-quantity matching) and arithmetic (addition) networks in 26 adults and 42 children. Number processing and arithmetic elicited overlapping activity in the IPS in children and adults, however, the overlap was influenced by arithmetic problem size (i.e. which modulated the need to use procedural strategies). The IPS was recruited for number processing, and for arithmetic problems more likely to be solved using procedural strategies. We also found that the overlap between number processing and small-problem addition in children was comparable to the overlap between number processing and large-problem addition in adults. This finding suggests that the association between number processing and arithmetic in the IPS is related to the cognitive operation being performed rather than age.
Collapse
Affiliation(s)
- Anna A Matejko
- Numerical Cognition Laboratory, Department of Psychology and Brain & Mind Institute, Western University, London, ON, Canada; Center for the Study of Learning, Department of Pediatrics, Building D, Georgetown University, Washington DC, USA.
| | - Daniel Ansari
- Numerical Cognition Laboratory, Department of Psychology and Brain & Mind Institute, Western University, London, ON, Canada.
| |
Collapse
|
46
|
Zhang Y, Liu T, Chen C, Zhou X. Visual form perception supports approximate number system acuity and arithmetic fluency. LEARNING AND INDIVIDUAL DIFFERENCES 2019. [DOI: 10.1016/j.lindif.2019.02.008] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
|
47
|
Chew CS, Forte JD, Reeve RA. Implications of Change/Stability Patterns in Children's Non-symbolic and Symbolic Magnitude Judgment Abilities Over One Year: A Latent Transition Analysis. Front Psychol 2019; 10:441. [PMID: 30890984 PMCID: PMC6411817 DOI: 10.3389/fpsyg.2019.00441] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2018] [Accepted: 02/13/2019] [Indexed: 11/17/2022] Open
Abstract
Non-symbolic magnitude abilities are often claimed to support the acquisition of symbolic magnitude abilities, which, in turn, are claimed to support emerging math abilities. However, not all studies find links between non-symbolic and symbolic magnitude abilities, or between them and math ability. To investigate possible reasons for these different findings, recent research has analyzed differences in non-symbolic/symbolic magnitude abilities using latent class modeling and has identified four different magnitude ability profiles residing within the general magnitude ability distribution that were differentially related to cognitive and math abilities. These findings may help explain the different patterns of findings observed in previous research. To further investigate this possibility, we (1) attempted to replicate earlier findings, (2) determine whether magnitude ability profiles remained stable or changed over 1 year; and (3) assessed the degree to which stability/change in profiles were related to cognitive and math abilities. We used latent transition analysis to investigate stability/changes in non-symbolic and symbolic magnitude abilities of 109 5- to 6-year olds twice in 1 year. At Time 1 and 2, non-symbolic and symbolic magnitude abilities, number transcoding and single-digit addition abilities were assessed. Visuospatial working memory (VSWM), naming numbers, non-verbal IQ, basic RT was also assessed at Time 1. Analysis showed stability in one profile and changes in the three others over 1 year. VSWM and naming numbers predicted profile membership at Time 1 and 2, and profile membership predicted math abilities at both time points. The findings confirm the existence of four different non-symbolic-symbolic magnitude ability profiles; we suggest the changes over time in them potentially reflect deficit, delay, and normal math developmental pathways.
Collapse
Affiliation(s)
| | | | - Robert A. Reeve
- Melbourne School of Psychological Sciences, University of Melbourne, Parkville, VIC, Australia
| |
Collapse
|
48
|
Gimbert F, Camos V, Gentaz E, Mazens K. What predicts mathematics achievement? Developmental change in 5- and 7-year-old children. J Exp Child Psychol 2019; 178:104-120. [DOI: 10.1016/j.jecp.2018.09.013] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2017] [Revised: 07/06/2018] [Accepted: 09/20/2018] [Indexed: 01/29/2023]
|
49
|
Daker RJ, Lyons IM. Numerical and Non-numerical Predictors of First Graders' Number-Line Estimation Ability. Front Psychol 2018; 9:2336. [PMID: 30555374 PMCID: PMC6283913 DOI: 10.3389/fpsyg.2018.02336] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2018] [Accepted: 11/07/2018] [Indexed: 11/23/2022] Open
Abstract
Children’s ability to map numbers into a spatial context has been shown to be a powerful predictor of math performance. Here, we investigate how three types of cognitive abilities – approximate number processing ability, symbolic number processing ability, and non-numerical cognitive abilities – predict 0–100 number-line estimation performance in first graders. While each type of measure predicts number-line performance when considered individually, when considered together, only symbolic number comparison and non-verbal reasoning predicted unique variance in number-line estimation. Moreover, the relation between symbolic number comparison and number-line ability was stronger for male students than for female students, suggesting potential gender differences in the way boys and girls accomplish mapping numbers into space. These results suggest that number-line estimation ability is largely reflective of the precision with which symbolic magnitudes are represented (at least among boys). Our findings therefore suggest that promoting children’s understanding of symbolic, rather than non-symbolic, numerical magnitudes may help children learn better from number-lines in the classroom.
Collapse
Affiliation(s)
- Richard J Daker
- Department of Psychology, Georgetown University, Washington, DC, United States
| | - Ian M Lyons
- Department of Psychology, Georgetown University, Washington, DC, United States
| |
Collapse
|
50
|
Kim D, Opfer JE. Dynamics and development in number-to-space mapping. Cogn Psychol 2018; 107:44-66. [PMID: 30439563 DOI: 10.1016/j.cogpsych.2018.10.001] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2017] [Revised: 05/17/2018] [Accepted: 10/11/2018] [Indexed: 01/29/2023]
Abstract
Young children's estimates of numerical magnitude increase approximately logarithmically with actual magnitude. The conventional interpretation of this finding is that children's estimates reflect an innate logarithmic encoding of number. A recent set of findings, however, suggests that logarithmic number-line estimates emerge via a dynamic encoding mechanism that is sensitive to previously encountered stimuli. Here we examine trial-to-trial changes in logarithmicity of numerosity estimates to test an alternative dynamic model (D-MLLM) with both a strong logarithmic component and a weak response to previous stimuli. In support of D-MLLM, first-trial numerosity estimates in both adults (Study 1, 2, 3, and 4) and children (Study 4) were strongly logarithmic, despite zero previous stimuli. Additionally, although numerosity of a previous trial affected adults' estimates, the influence of previous numbers always accompanied the logarithmic-to-linear shift predicted by D-MLLM. We conclude that a dynamic encoding mechanism is not necessary for compressive mapping, but sequential effects on response scaling are a possible source of linearity in adults' numerosity estimation.
Collapse
Affiliation(s)
- Dan Kim
- The Ohio State University, 255 Psychology Building, Columbus, OH 43210, USA.
| | - John E Opfer
- The Ohio State University, 255 Psychology Building, Columbus, OH 43210, USA.
| |
Collapse
|