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Spiller J, Clayton S, Cragg L, Johnson S, Simms V, Gilmore C. Higher level domain specific skills in mathematics; The relationship between algebra, geometry, executive function skills and mathematics achievement. PLoS One 2023; 18:e0291796. [PMID: 37931003 PMCID: PMC10627446 DOI: 10.1371/journal.pone.0291796] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2022] [Accepted: 09/06/2023] [Indexed: 11/08/2023] Open
Abstract
Algebra and geometry are important components of mathematics that are often considered gatekeepers for future success. However, most studies that have researched the cognitive skills required for success in mathematics have only considered the domain of arithmetic. We extended models of mathematical skills to consider how executive function skills play both a direct role in secondary-school-level mathematical achievement as well as an indirect role via algebra and geometry, alongside arithmetic. We found that verbal and visuospatial working memory were indirectly associated with mathematical achievement via number fact knowledge, calculation skills, algebra and geometry. Inhibition was also indirectly associated with mathematical achievement via number fact knowledge and calculation skills. These findings highlight that there are multiple mechanisms by which executive function skills may be involved in mathematics outcomes. Therefore, using specific measures of mathematical processes as well as context-rich assessments of mathematical achievement is important to understand these mechanisms.
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Affiliation(s)
- Jayne Spiller
- Centre for Mathematical Cognition, Loughborough University, Loughborough, United Kingdom
- School of Psychology and Vision Sciences, University of Leicester, Leicester, United Kingdom
| | - Sarah Clayton
- Department of Health Sciences, University of Leicester, Leicester, United Kingdom
| | - Lucy Cragg
- School of Psychology, University of Nottingham, Nottingham, United Kingdom
| | - Samantha Johnson
- Department of Health Sciences, University of Leicester, Leicester, United Kingdom
| | - Victoria Simms
- School of Psychology, Ulster University, Coleraine, United Kingdom
| | - Camilla Gilmore
- Centre for Mathematical Cognition, Loughborough University, Loughborough, United Kingdom
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2
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Poletti C, Díaz-Barriga Yáñez A, Prado J, Thevenot C. The development of simple addition problem solving in children: Reliance on automatized counting or memory retrieval depends on both expertise and problem size. J Exp Child Psychol 2023; 234:105710. [PMID: 37285761 DOI: 10.1016/j.jecp.2023.105710] [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: 01/29/2023] [Revised: 04/05/2023] [Accepted: 05/11/2023] [Indexed: 06/09/2023]
Abstract
In an experiment, 98 children aged 8 to 9, 10 to 12, and 13 to 15 years solved addition problems with a sum up to 10. In another experiment, the same children solved the same calculations within a sign priming paradigm where half the additions were displayed with the "+" sign 150 ms before the addends. Therefore, size effects and priming effects could be considered conjointly within the same populations. Our analyses revealed that small problems, constructed with addends from 1 to 4, presented a linear increase of solution times as a function of problem sums (i.e., size effect) in all age groups. However, an operator priming effect (i.e., facilitation of the solving process with the anticipated presentation of the "+" sign) was observed only in the group of oldest children. These results support the idea that children use a counting procedure that becomes automatized (as revealed by the priming effect) around 13 years of age. For larger problems and whatever the age group, no size or priming effects were observed, suggesting that the answers to these problems were already retrieved from memory at 8 to 9 years of age. For this specific category of large problems, negative slopes in solution times demonstrate that retrieval starts from the largest problems during development. These results are discussed in light of a horse race model in which procedures can win over retrieval.
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Affiliation(s)
- Céline Poletti
- Institut de Psychologie, Université de Lausanne, CH-1015 Lausanne, Switzerland
| | - Andrea Díaz-Barriga Yáñez
- Lyon Neuroscience Research Center (CRNL), INSERM U1028-CNRS UMR5292, University of Lyon, 69675 Bron Cedex, France
| | - Jérôme Prado
- Lyon Neuroscience Research Center (CRNL), INSERM U1028-CNRS UMR5292, University of Lyon, 69675 Bron Cedex, France.
| | - Catherine Thevenot
- Institut de Psychologie, Université de Lausanne, CH-1015 Lausanne, Switzerland.
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Gilmore C. Understanding the complexities of mathematical cognition: A multi-level framework. Q J Exp Psychol (Hove) 2023; 76:1953-1972. [PMID: 37129432 PMCID: PMC10466984 DOI: 10.1177/17470218231175325] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2022] [Revised: 01/16/2023] [Accepted: 01/17/2023] [Indexed: 05/03/2023]
Abstract
Mathematics skills are associated with future employment, well-being, and quality of life. However, many adults and children fail to learn the mathematics skills they require. To improve this situation, we need to have a better understanding of the processes of learning and performing mathematics. Over the past two decades, there has been a substantial growth in psychological research focusing on mathematics. However, to make further progress, we need to pay greater attention to the nature of, and multiple elements involved in, mathematical cognition. Mathematics is not a single construct; rather, overall mathematics achievement is comprised of proficiency with specific components of mathematics (e.g., number fact knowledge, algebraic thinking), which in turn recruit basic mathematical processes (e.g., magnitude comparison, pattern recognition). General cognitive skills and different learning experiences influence the development of each component of mathematics as well as the links between them. Here, I propose and provide evidence for a framework that structures how these components of mathematics fit together. This framework allows us to make sense of the proliferation of empirical findings concerning influences on mathematical cognition and can guide the questions we ask, identifying where we are missing both research evidence and models of specific mechanisms.
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Affiliation(s)
- Camilla Gilmore
- Centre for Mathematical Cognition, Loughborough University, Loughborough, UK
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Thevenot C, Tazouti Y, Billard C, Dewi J, Fayol M. Acquisition of new arithmetic skills based on prior arithmetic skills: A cross-sectional study in primary school from grade 2 to grade 5. BRITISH JOURNAL OF EDUCATIONAL PSYCHOLOGY 2023; 93:727-741. [PMID: 36740227 DOI: 10.1111/bjep.12588] [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: 02/18/2022] [Revised: 01/06/2023] [Accepted: 01/18/2023] [Indexed: 02/07/2023]
Abstract
BACKGROUND In several countries, children's math skills have been declining at an alarming rate in recent years and decades, and one of the explanations for this alarming situation is that children have difficulties in establishing the relations between arithmetical operations. AIM In order to address this question, our goal was to determine the predictive power of previously taught operations on newly taught ones above general cognitive skills and basic numerical skills. SAMPLES More than one hundred children in each school level from Grades 2 to 5 from various socio-cultural environments (N = 435, 229 girls) were tested. METHODS Children were assessed on their abilities to solve the four basic arithmetic operations. They were also tested on their general cognitive abilities, including working memory, executive functions (i.e., inhibition and flexibility), visual attention and language. Finally, their basic numerical skills were measured through a matching task between symbolic and nonsymbolic numerosity representations. Additions and subtractions were presented to children from Grade 2, multiplications from Grade 3 and divisions from Grade 4. RESULTS AND CONCLUSIONS We show that addition predicts subtraction and multiplication performance in all grades. Moreover, multiplication predicts division performance in both Grades 4 and 5. Finally, addition predicts division in Grade 4 but not in Grade 5 and subtraction and division are not related whatever the school grade. These results are examined considering the existing literature, and their implications in terms of instruction are discussed.
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Affiliation(s)
- Catherine Thevenot
- Institut de Psychologie, Batiment Géopolis, University of Lausanne, Lausanne, Switzerland
| | | | - Catherine Billard
- Centre de Référence sur les Troubles des Apprentissages, Bicêtre Hospital, Le Kremlin-Bicêtre, Paris, France
| | - Jasinta Dewi
- Institut de Psychologie, Batiment Géopolis, University of Lausanne, Lausanne, Switzerland
| | - Michel Fayol
- Université de Clermont Auvergne (LAPSCO, UMR 6024 UCA-CNRS), Clermont-Ferrand, France
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Lafay A, Osana HP, Levin JR. Does Conceptual Transparency in Manipulatives Afford Place-Value Understanding in Children at Risk for Mathematics Learning Disabilities? LEARNING DISABILITY QUARTERLY : JOURNAL OF THE DIVISION FOR CHILDREN WITH LEARNING DISABILITIES 2023; 46:92-105. [PMID: 37168325 PMCID: PMC10164236 DOI: 10.1177/07319487221124088] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
We investigated the effect of conceptual transparency in the physical structure of manipulatives on place-value understanding in typically developing children and those at risk for mathematics learning disabilities. Second graders were randomly assigned to one of three manipulatives conditions: (a) attachable beads that did not make the denominations or ones in the denominations transparent, (b) pipe cleaners that made only the denominations transparent, and (c) string beads that made both the denominations and the ones in the denominations transparent. Participants used the manipulatives to represent double- and triple-digit numerals. Statistical analyses indicated that the transparency of the denominations, but not the transparency of the ones in the denominations, is responsible for children's number representation and place-value understanding. Descriptive analyses of their responses revealed that the at-risk children were at a greater disadvantage than their typically developing peers with the attachable beads, failing to use place-value concepts to interpret their representations.
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Affiliation(s)
- Anne Lafay
- Université Savoie Mont-Blanc, CNRS, LPNC UMR 5105, Chambéry, France
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Dotan D, Zviran-Ginat S. Elementary math in elementary school: the effect of interference on learning the multiplication table. Cogn Res Princ Implic 2022; 7:101. [PMID: 36459276 PMCID: PMC9716515 DOI: 10.1186/s41235-022-00451-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Accepted: 11/13/2022] [Indexed: 12/04/2022] Open
Abstract
Memorizing the multiplication table is a major challenge for elementary school students: there are many facts to memorize, and they are often similar to each other, which creates interference in memory. Here, we examined whether learning would improve if the degree of interference is reduced, and which memory processes are responsible for this improvement. In a series of 16 short training sessions over 4 weeks, first-grade children learned 16 multiplication facts-4 facts per week. In 2 weeks the facts were dissimilar from each other (low interference), and in 2 control weeks the facts were similar (high interference). Learning in the low-similarity, low-interference weeks was better than in the high-similarity weeks. Critically, this similarity effect originated in the specific learning context, i.e., the grouping of facts to weeks, and could not be explained as an intrinsic advantage of certain facts over others. Moreover, the interference arose from the similarity between facts in a given week, not from the similarity to previously learned facts. Similarity affected long-term memory-its effect persisted 7 weeks after training has ended; and it operated on long-term memory directly, not via the mediation of working memory. Pedagogically, the effectiveness of the low-interference training method, which is dramatically different from currently used pedagogical methods, may pave the way to enhancing how we teach the multiplication table in school.
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Affiliation(s)
- Dror Dotan
- Mathematical Thinking Lab, School of Education and the Sagol School of Neuroscience, Tel Aviv University, 6997801, Tel Aviv, Israel.
| | - Sharon Zviran-Ginat
- Mathematical Thinking Lab, School of Education and the Sagol School of Neuroscience, Tel Aviv University, 6997801, Tel Aviv, Israel
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7
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Buyle M, Crollen V. Deafness and early language deprivation influence arithmetic performances. Front Hum Neurosci 2022; 16:1000598. [DOI: 10.3389/fnhum.2022.1000598] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2022] [Accepted: 11/07/2022] [Indexed: 12/02/2022] Open
Abstract
It has been consistently reported that deaf individuals experience mathematical difficulties compared to their hearing peers. However, the idea that deafness and early language deprivation might differently affect verbal (i.e., multiplication) vs. visuospatial (i.e., subtraction) arithmetic performances is still under debate. In the present paper, three groups of 21 adults (i.e., deaf signers, hearing signers, and hearing controls) were therefore asked to perform, as fast and as accurately as possible, subtraction and multiplication operations. No significant group effect was found for accuracy performances. However, reaction time results demonstrated that the deaf group performed both arithmetic operations slower than the hearing groups. This group difference was even more pronounced for multiplication problems than for subtraction problems. Weaker language-based phonological representations for retrieving multiplication facts, and sensitivity to interference are two hypotheses discussed to explain the observed dissociation.
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Mosbacher JA, Halverscheid S, Pustelnik K, Danner M, Prassl C, Brunner C, Vogel SE, Nitsche MA, Grabner RH. Theta Band Transcranial Alternating Current Stimulation Enhances Arithmetic Learning: A Systematic Comparison of Different Direct and Alternating Current Stimulations. Neuroscience 2021; 477:89-105. [PMID: 34648868 DOI: 10.1016/j.neuroscience.2021.10.006] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2021] [Revised: 10/01/2021] [Accepted: 10/04/2021] [Indexed: 11/17/2022]
Abstract
Over the last decades, interest in transcranial electrical stimulation (tES) has grown, as it might allow for causal investigations of the associations between cortical activity and cognition as well as to directly influence cognitive performance. The main objectives of the present work were to assess whether tES can enhance the acquisition and application of arithmetic abilities, and whether it enables a better assessment of underlying neurophysiological processes. To this end, the present, double-blind, sham-controlled study assessed the effects of six active stimulations (three tES protocols: anodal transcranial direct current stimulation (tDCS), alpha band transcranial alternating current stimulation (tACS), and theta band tACS; targeting the left dorsolateral prefrontal cortex or the left posterior parietal cortex) on the acquisition of an arithmetic procedure, arithmetic facts, and event-related synchronization/desynchronization (ERS/ERD) patterns. 137 healthy adults were randomly assigned to one of seven groups, each receiving one of the tES-protocols during learning. Results showed that frontal theta band tACS reduced the repetitions needed to learn novel facts and both, frontal and parietal theta band tACS accelerated the decrease in calculation times in fact learning problems. The beneficial effect of frontal theta band tACS may reflect enhanced executive functions, allowing for better control and inhibition processes and hence, a faster acquisition and integration of novel fact knowledge. However, there were no significant effects of the stimulations on procedural learning or ERS/ERD patterns. Overall, theta band tACS appears promising as a support for arithmetic fact training, but effects on procedural calculations and neurophysiological processes remain ambiguous.
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Affiliation(s)
- Jochen A Mosbacher
- Section of Educational Neuroscience, Institute of Psychology, University of Graz, Graz, Austria.
| | | | - Kolja Pustelnik
- Mathematics Institute, University of Göttingen, Göttingen, Germany
| | - Martina Danner
- Section of Educational Neuroscience, Institute of Psychology, University of Graz, Graz, Austria
| | - Christina Prassl
- Section of Educational Neuroscience, Institute of Psychology, University of Graz, Graz, Austria
| | - Clemens Brunner
- Section of Educational Neuroscience, Institute of Psychology, University of Graz, Graz, Austria
| | - Stephan E Vogel
- Section of Educational Neuroscience, Institute of Psychology, University of Graz, Graz, Austria
| | - Michael A Nitsche
- Department of Psychology and Neurosciences, Leibniz Research Centre for Working Environment and Human Factors, Dortmund, Germany; Department of Neurology, University Medical Hospital Bergmannsheil, Ruhr-University Bochum, Bochum, Germany
| | - Roland H Grabner
- Section of Educational Neuroscience, Institute of Psychology, University of Graz, Graz, Austria; BioTechMed Graz, Graz, Austria
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Kanevski M, Booth JN, Oldridge J, McDougal E, Stewart TM, McGeown S, Rhodes SM. The relationship between cognition and mathematics in children with attention-deficit/hyperactivity disorder: a systematic review. Child Neuropsychol 2021; 28:394-426. [PMID: 34724883 DOI: 10.1080/09297049.2021.1985444] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Abstract
Cognitive processes play an imperative role in children's mathematics learning. Difficulties in cognitive functioning are a core feature of Attention Deficit Hyperactivity Disorder (ADHD) in children, who also tend to show lower levels of mathematics attainment than their typically developing peers. This review (registration number: CRD42020169708) sought to aggregate findings from studies assessing the relationship between cognition and mathematics in children with a clinical ADHD diagnosis aged 4-12 years. A total of 11,799 studies published between 1992 and August 2020 were screened for eligibility using various database (PsycINFO, PubMed, SCOPUS, EMBASE, ERIC, Web of Science, and additional sources), from which four studies met inclusion criteria. A narrative synthesis was conducted on the correlations between mathematics and cognitive domains, including an evaluation of the risk of bias within the studies. Across four studies meeting inclusion criteria, memory, inhibitory control, and processing speed were assessed. The results showed a positive association between cognition and mathematics performance in this population. The strength of associations across these studies varied as a function of the cognitive domain in question, means by which mathematics performance was assessed, as well as whether confounding factors such as age and IQ were controlled for. Collectively, this review demonstrates a lack of research in this area and points to various methodological considerations for identifying the association between cognition and mathematics performance in ADHD.
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Affiliation(s)
- Margarita Kanevski
- Child Life and Health, Clinical Brain Sciences, University of Edinburgh, Edinburgh, UK
| | - Josephine N Booth
- Institute of Education, Community and Society, Moray House School of Education and Sport, University of Edinburgh, Edinburgh, UK
| | - Jessica Oldridge
- Child Life and Health, Clinical Brain Sciences, University of Edinburgh, Edinburgh, UK
| | - Emily McDougal
- Child Life and Health, Clinical Brain Sciences, University of Edinburgh, Edinburgh, UK
| | - Tracy M Stewart
- Institute of Education, Community and Society, Moray House School of Education and Sport, University of Edinburgh, Edinburgh, UK
| | - Sarah McGeown
- Institute of Education, Community and Society, Moray House School of Education and Sport, University of Edinburgh, Edinburgh, UK
| | - Sinead M Rhodes
- Child Life and Health, Clinical Brain Sciences, University of Edinburgh, Edinburgh, UK
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Bagnoud J, Mathieu R, Dewi J, Masson S, Gonzalez-Monge S, Kasikci Z, Thevenot C. An investigation of the possible causes of arithmetic difficulties in children with dyscalculia. ANNEE PSYCHOLOGIQUE 2021. [DOI: 10.3917/anpsy1.213.0217] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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Abstract
Strong foundational skills in mathematical problem solving, acquired in early childhood, are critical not only for success in the science, technology, engineering, and mathematical (STEM) fields but also for quantitative reasoning in everyday life. The acquisition of mathematical skills relies on protracted interactive specialization of functional brain networks across development. Using a systems neuroscience approach, this review synthesizes emerging perspectives on neurodevelopmental pathways of mathematical learning, highlighting the functional brain architecture that supports these processes and sources of heterogeneity in mathematical skill acquisition. We identify the core neural building blocks of numerical cognition, anchored in the posterior parietal and ventral temporal-occipital cortices, and describe how memory and cognitive control systems, anchored in the medial temporal lobe and prefrontal cortex, help scaffold mathematical skill development. We highlight how interactive specialization of functional circuits influences mathematical learning across different stages of development. Functional and structural brain integrity and plasticity associated with math learning can be examined using an individual differences approach to better understand sources of heterogeneity in learning, including cognitive, affective, motivational, and sociocultural factors. Our review emphasizes the dynamic role of neurodevelopmental processes in mathematical learning and cognitive development more generally.
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Affiliation(s)
- Vinod Menon
- Department of Psychiatry and Behavioral Sciences, Stanford University School of Medicine, Stanford, California, USA
- Department of Neurology and Neurological Sciences, Stanford University School of Medicine, Stanford, California, USA
- Stanford Neuroscience Institute, Stanford University School of Medicine, Stanford, California, USA
- Symbolic Systems Program, Stanford University School of Medicine, Stanford, California, USA
| | - Hyesang Chang
- Department of Psychiatry and Behavioral Sciences, Stanford University School of Medicine, Stanford, California, USA
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12
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Can the interference effect in multiplication fact retrieval be modulated by an arithmetic training? An fMRI study. Neuropsychologia 2021; 157:107849. [PMID: 33857529 DOI: 10.1016/j.neuropsychologia.2021.107849] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2020] [Revised: 02/27/2021] [Accepted: 03/27/2021] [Indexed: 11/20/2022]
Abstract
Single-digit multiplications are thought to be associated with different levels of interference because they show different degrees of feature overlap (i.e., digits) with previously learnt problems. Recent behavioral and neuroimaging studies provided evidence for this interference effect and showed that individual differences in arithmetic fact retrieval are related to differences in sensitivity to interference (STI). The present study investigated whether and to what extent competence-related differences in STI and its neurophysiological correlates can be modulated by a multiplication facts training. Participants were 23 adults with high and 23 adults with low arithmetic competencies who underwent a five-day multiplication facts training in which they intensively practiced sets of low- and high-interfering multiplication problems. In a functional magnetic resonance imaging (fMRI) test session after the training, participants worked on a multiplication verification task that comprised trained and untrained problems. Analyses of the behavioral data revealed an interference effect only in the low competence group, which could be reduced but not resolved by training. On the neural level, competence-related differences in the interference effect were observed in the left supramarginal gyrus (SMG), showing activation differences between low- and high-interfering problems only in the low competent group. These findings support the idea that individuals' low arithmetic skills are related to the development of insufficient memory representations because of STI. Further, our results indicate that a short training by drill (i.e., learning associations between operands and solutions) was not fully effective to resolve existing interference effects in arithmetic fact knowledge.
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13
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Bagnoud J, Dewi J, Thevenot C. Differences in event-related potential (ERP) responses to small tie, non-tie and 1-problems in addition and multiplication. Neuropsychologia 2021; 153:107771. [PMID: 33548248 DOI: 10.1016/j.neuropsychologia.2021.107771] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2020] [Revised: 01/25/2021] [Accepted: 01/30/2021] [Indexed: 10/22/2022]
Abstract
Using ERP, we investigated the cause of the tie advantage according to which problems with repeated operands are solved faster and more accurately than non-tie problems. We found no differences in early or N400 ERP components between problems, suggesting that tie problems are not encoded faster or suffer from less interference than non-tie problems. However, a lesser negative amplitude of the N2 component was found for tie than non-tie problems. This suggests more working-memory and attentional resource requirements for non-tie problems and therefore more frequent use of retrieval for tie than non-tie problems. The possible peculiarity of problems involving a 1 was also investigated. We showed less negative N2 amplitudes for these problems than for other non-tie problems, suggesting less working-memory resources for 1-problems than other non-tie problems. This could be explained either by higher reliance on memory retrieval for 1-problems than non-1 problems or by the application of non-arithmetical rules for 1-problems.
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Affiliation(s)
- Jeanne Bagnoud
- University of Lausanne, Institute of Psychology, Switzerland.
| | - Jasinta Dewi
- University of Lausanne, Institute of Psychology, Switzerland
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14
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Katzoff A, Zigdon NM, Ashkenazi S. Difficulties in retrieval multiplication facts: The case of interference to reconsolidation. Trends Neurosci Educ 2020; 20:100137. [PMID: 32917304 DOI: 10.1016/j.tine.2020.100137] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2019] [Revised: 07/30/2020] [Accepted: 07/31/2020] [Indexed: 11/17/2022]
Abstract
OBJECTIVES Many students have difficulties in retrieving multiplication facts from memory. The aim of the present study was to test the difficulty in retrieval of multiplication facts from the perspective of the reconsolidation of long-term memory phase, which has been found to be sensitive to interferences. METHODS Students learned multiplication facts and then received a reminder, which led to reactivation and reconsolidation. After the reminder, additional multiplication facts (interference) were learned and memory was tested. RESULTS Students who received both a reminder and interference during reconsolidation showed no significant improvement in retrieving multiplication facts from memory, whereas Students who received either a reminder or additional multiplication facts (interference) exhibited a better performance in retrieval. CONCLUSIONS These results indicate, for the first time, that the reconsolidation phase is sensitive to interferences in mathematical declarative memory content. The findings indicate additional possible causes for difficulties in retrieval of multiplication facts in class.
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Affiliation(s)
| | - Nitza Mark Zigdon
- Levinsky College of Education, Tel Aviv, Israel; Tel Aviv University, Tel Aviv, Israel
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Mathematical Profile Test: A Preliminary Evaluation of an Online Assessment for Mathematics Skills of Children in Grades 1-6. Behav Sci (Basel) 2020; 10:bs10080126. [PMID: 32759837 PMCID: PMC7463740 DOI: 10.3390/bs10080126] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2020] [Revised: 07/29/2020] [Accepted: 07/31/2020] [Indexed: 11/22/2022] Open
Abstract
The domain of numerical cognition still lacks an assessment tool that is theoretically driven and that covers a wide range of key numerical processes with the aim of identifying the learning profiles of children with difficulties in mathematics (MD) or dyscalculia. This paper is the first presentation of an online collectively administered tool developed to meet these goals. The Mathematical Profile Test (MathPro Test) includes 18 subtests that assess numerical skills related to the core number domain or to the visual-spatial, memory or reasoning domains. The specific aim of this paper is to present the preliminary evaluation both of the sensitivity and the psychometric characteristics of the individual measures of the MathPro Test, which was administered to 622 primary school children (grades 1–6) in Belgium. Performance on the subtests increased across all grades and varied along the level of difficulty of the items, supporting the sensitivity of the test. The MathPro Test also showed satisfactory internal consistency and significant and stable correlation with a standardized test in mathematics across all grades. In particular, the achievement in mathematics was strongly associated with the performance on the subtests assessing the reasoning and the visuospatial domains throughout all school grades, whereas associations with the core number and memory tasks were found mainly in the younger children. MD children performed significantly lower than their peers; these differences in performance on the MathPro subtests also varied according to the school grades, informing us about the developmental changes of the weaknesses of children with MD. These results suggest that the MathPro Test is a very promising tool for conducting large scale research and for clinicians to sketch out the mathematical profile of children with MD or dyscalculia.
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Attout L, Noël MP, Rousselle L. Magnitude processing in populations with spina-bifida: The role of visuospatial and working memory processes. RESEARCH IN DEVELOPMENTAL DISABILITIES 2020; 102:103655. [PMID: 32413584 DOI: 10.1016/j.ridd.2020.103655] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2019] [Revised: 03/30/2020] [Accepted: 04/05/2020] [Indexed: 06/11/2023]
Abstract
People with Spina Bifida usually experience difficulties with mathematics. In a series of other developmental disorders, a magnitude processing deficit was considered to be the main source of subsequent difficulties in mathematics. The processing of magnitude could be numerical (which is the larger number) or non-numerical such as spatial (e.g., which is the longer?) or temporal (which one last longer?) for instance. However, no study yet has examined directly magnitude processes in a population with Spina Bifida. On the other hand, recent studies in people with genetic syndromes have suggested that visuospatial and working memory processes play an important role in magnitude processing, including number magnitude. Therefore, in this study we explored for the first time magnitude representation using several tasks with different visuospatial and working memory processing requirements, cognitive skills frequently impaired in Spina Bifida. Results showed children with SB presented a global magnitude processing deficit for non-numerical and numerical comparison tasks, but not in symbolic number magnitude tasks compared to controls. Importantly, visuospatial skills and working memory abilities could partially explain the differences between groups in comparison and estimation tasks. This study proposes that magnitude processing difficulties in children with SB could be due to higher cognitive factors such as visuospatial and working memory processes.
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Affiliation(s)
- Lucie Attout
- Research Unit "Enfances", University of Liège, Belgium; Psychological Sciences Research Institute, UCLouvain, Louvain-la-Neuve, Belgium.
| | - Marie-Pascale Noël
- Psychological Sciences Research Institute, UCLouvain, Louvain-la-Neuve, Belgium
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17
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Chu FW, vanMarle K, Hoard MK, Nugent L, Scofield JE, Geary DC. Preschool deficits in cardinal knowledge and executive function contribute to longer-term mathematical learning disability. J Exp Child Psychol 2019; 188:104668. [PMID: 31430570 DOI: 10.1016/j.jecp.2019.104668] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2018] [Revised: 06/25/2019] [Accepted: 07/13/2019] [Indexed: 11/26/2022]
Abstract
In a preschool through first grade longitudinal study, we identified groups of children with persistently low mathematics achievement (n = 14) and children with low achievement in preschool but average achievement in first grade (n = 23). The preschool quantitative developments of these respective groups of children with mathematical learning disability (MLD) and recovered children and a group of typically achieving peers (n = 35) were contrasted, as were their intelligence, executive function, and parental education levels. The core characteristics of the children with MLD were poor executive function and delayed understanding of the cardinal value of number words throughout preschool. These compounded into even more substantive deficits in number and arithmetic at the beginning of first grade. The recovered group had poor executive function and cardinal knowledge during the first year of preschool but showed significant gains during the second year. Despite these gains and average mathematics achievement, the recovered children had subtle deficits with accessing magnitudes associated with numerals and addition combinations (e.g., 5 + 6 = ?) in first grade. The study provides unique insight into domain-general and quantitative deficits in preschool that increase risk for long-term mathematical difficulties.
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Affiliation(s)
- Felicia W Chu
- Department of Psychological Sciences, University of Missouri, Columbia, MO 65211, USA
| | - Kristy vanMarle
- Department of Psychological Sciences, University of Missouri, Columbia, MO 65211, USA
| | - Mary K Hoard
- Department of Psychological Sciences, University of Missouri, Columbia, MO 65211, USA
| | - Lara Nugent
- Department of Psychological Sciences, University of Missouri, Columbia, MO 65211, USA
| | - John E Scofield
- Department of Psychological Sciences, University of Missouri, Columbia, MO 65211, USA
| | - David C Geary
- Department of Psychological Sciences, University of Missouri, Columbia, MO 65211, USA; Interdisciplinary Neuroscience Program, University of Missouri, Columbia, MO 65211, USA.
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18
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Heidekum AE, Grabner RH, De Smedt B, De Visscher A, Vogel SE. Interference during the retrieval of arithmetic and lexico-semantic knowledge modulates similar brain regions: Evidence from functional magnetic resonance imaging (fMRI). Cortex 2019; 120:375-393. [PMID: 31408755 PMCID: PMC6853793 DOI: 10.1016/j.cortex.2019.06.007] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2019] [Revised: 04/14/2019] [Accepted: 06/07/2019] [Indexed: 12/13/2022]
Abstract
Single-digit multiplications are mainly solved by memory retrieval. However, these problems are also prone to errors due to systematic interference (i.e., co-activation of interconnected but incorrect solutions). Semantic control processes are crucial to overcome this type of interference and to retrieve the correct information. Previous research suggests the importance of several brain regions such as the left inferior frontal cortex and the intraparietal sulcus (IPS) for semantic control. But, this evidence is mainly based on tasks measuring interference during the processing of lexico-semantic information (e.g., pictures or words). Here, we investigated whether semantic control during arithmetic problem solving (i.e., multiplication fact retrieval) draws upon similar or different brain mechanisms as in other semantic domains (i.e., lexico-semantic). The brain activity of 46 students was measured with fMRI while participants performed an operand-related-lure (OR) and a picture-word (PW) task. In the OR task participants had to verify the correctness of a given solution to a single-digit multiplication. Similarly, in the PW task, participants had to judge whether a presented word matches the concept displayed in a picture or not. Analyses showed that resolving interference in these two tasks modulates the activation of a widespread fronto-parietal network (e.g., left/right IFG, left insula lobe, left IPS). Importantly, conjunction analysis revealed a neural overlap in the left inferior frontal gyrus (IFG) pars triangularis and left IPS. Additional Bayesian analyses showed that regions that are thought to store lexico-semantic information (e.g., left middle temporal gyrus) did not show evidence for an arithmetic interference effect. Overall, our findings not only indicate that semantic control plays an important role in arithmetic problem solving but also that it is supported by common brain regions across semantic domains. Additionally, by conducting Bayesian analysis we confirmed the hypothesis that the semantic control network contributes differently to semantic tasks of various domains.
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Affiliation(s)
| | - Roland H Grabner
- Educational Neuroscience, Institute of Psychology, University of Graz, Austria
| | - Bert De Smedt
- Faculty of Psychology and Educational Sciences, KU Leuven, University of Leuven, Belgium
| | | | - Stephan E Vogel
- Educational Neuroscience, Institute of Psychology, University of Graz, Austria.
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19
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Polspoel B, De Visscher A, Vandermosten M, Vogel SE, Grabner RH, De Smedt B. The neural substrates of the problem size and interference effect in children's multiplication: An fMRI study. Brain Res 2019; 1714:147-157. [PMID: 30836066 DOI: 10.1016/j.brainres.2019.03.002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2018] [Revised: 02/28/2019] [Accepted: 03/01/2019] [Indexed: 11/19/2022]
Abstract
Within children's multiplication fact retrieval, performance can be influenced by various effects, such as the well-known problem size effect (i.e., smaller problems are solved faster and more accurately) and the more recent interference effect (i.e., the quality of memory representations of problems depends on previously learned problems; the more similar a problem is to a previously learned one, the more proactive interference impacts on storing in long-term-memory). This interference effect has been observed in behavioral studies, and determines a substantial part of performance beyond problem size. Unlike the problem size effect, the neural basis of the interference effect in children has not been studied. To better understand the underpinning mechanisms behind children's arithmetic fact retrieval, we aimed to investigate the neural basis of both effects in typically developing children. Twenty-four healthy 9- to 10-year-olds took part in a behavioral and fMRI scanning session, during which multiplication items had to be solved. Data were analyzed by manipulating problem size and interference level in a 2 × 2 factorial design. Concurring with previous studies, our results reveal clear behavioral effects of problem size and interference, with larger and high interfering items being solved significantly slower. On the neural level, a clear problem size effect was observed in a fronto-parietal and temporal network. The interference effect, however, was not detected; no clear neural distinctions were observed between low and high interfering items.
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Affiliation(s)
- Brecht Polspoel
- Parenting and Special Education Research Unit, KU Leuven, Leopold Vanderkelenstraat 32, Box 3765, 3000 Leuven, Belgium.
| | - Alice De Visscher
- Institut de Recherche en Sciences Psychologiques, Université catholique de Louvain, Place du Cardinal Mercier 10, Box L3.05.01, 1348 Louvain-la-Neuve, Belgium
| | - Maaike Vandermosten
- Experimental ORL, Department of Neurosciences, KU Leuven, Herestraat 49, Box 721, 3000 Leuven, Belgium
| | - Stephan E Vogel
- Educational Neuroscience, Institute of Psychology, University of Graz, Universitätsplatz 2, 8010 Graz, Austria
| | - Roland H Grabner
- Educational Neuroscience, Institute of Psychology, University of Graz, Universitätsplatz 2, 8010 Graz, Austria
| | - Bert De Smedt
- Parenting and Special Education Research Unit, KU Leuven, Leopold Vanderkelenstraat 32, Box 3765, 3000 Leuven, Belgium
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20
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Bellon E, Fias W, De Smedt B. More than number sense: The additional role of executive functions and metacognition in arithmetic. J Exp Child Psychol 2019; 182:38-60. [PMID: 30807905 DOI: 10.1016/j.jecp.2019.01.012] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2017] [Revised: 11/18/2018] [Accepted: 01/21/2019] [Indexed: 11/24/2022]
Abstract
Arithmetic is a major building block for children's development of more complex mathematical abilities. Knowing which cognitive factors underlie individual differences in arithmetic is key to gaining further insight into children's mathematical development. The current study investigated the role of executive functions and metacognition (domain-general cognitive factors) as well as symbolic numerical magnitude processing (domain-specific cognitive factor) in arithmetic, enabling the investigation of their unique contribution in addition to each other. Participants were 127 typically developing second graders (7- and 8-year-olds). Our within-participant design took into account different components of executive functions (i.e., inhibition, shifting, and updating), different aspects of metacognitive skills (i.e., task-specific and general metacognition), and different levels of experience in arithmetic, namely addition (where second graders had extensive experience) and multiplication (where second graders were still in the learning phase). This study reveals that both updating and metacognitive monitoring are important unique predictors of arithmetic in addition to each other and to symbolic numerical magnitude processing. Our results point to a strong and unique role of task-specific metacognitive monitoring skills. These individual differences in noticing one's own errors might help one to learn from his or her mistakes.
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Affiliation(s)
- Elien Bellon
- Faculty of Psychology and Educational Sciences, Parenting and Special Education Research Group, KU Leuven, 3000 Leuven, Belgium.
| | - Wim Fias
- Department of Experimental Psychology, Ghent University, 9000 Gent, Belgium
| | - Bert De Smedt
- Faculty of Psychology and Educational Sciences, Parenting and Special Education Research Group, KU Leuven, 3000 Leuven, Belgium
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21
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Tiberghien K, Sahan MI, De Smedt B, Fias W, Lyons IM. Disentangling Neural Sources of Problem Size and Interference Effects in Multiplication. J Cogn Neurosci 2018; 31:453-467. [PMID: 30457916 DOI: 10.1162/jocn_a_01359] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
Multiplication is thought to be primarily solved via direct retrieval from memory. Two of the main factors known to influence the retrieval of multiplication facts are problem size and interference. Because these factors are often intertwined, we sought to investigate the unique influences of problem size and interference on both performance and neural responses during multiplication fact retrieval in healthy adults. Behavioral results showed that both problem size and interference explained separate unique portions of RT variance, but with significantly stronger contribution from problem size, which contrasts with previous work in children. Whole-brain fMRI results relying on a paradigm that isolated multiplication fact retrieval from response selection showed highly overlapping brain areas parametrically modulated by both problem size and interference in a large network of frontal, parietal, and subcortical brain areas. Subsequent analysis within these regions revealed problem size to be the stronger and more consistent "unique" modulating factor in overlapping regions as well as those that appeared to respond only to problem size or interference at the whole-brain level, thus underscoring the need to look beyond anatomical overlap using arbitrary thresholds. Additional unique contributions of interference (beyond problem size) were identified in right angular gyrus and subcortical regions associated with procedural processing. Together, our results suggest that problem size, relative to interference, tends to be the more dominant factor in driving behavioral and neural responses during multiplication fact retrieval in adults. Nevertheless, unique contributions of both factors demonstrate the importance of considering the overlapping and unique contributions of each in explaining the cognitive and neural bases of mental multiplication.
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22
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Lee K, Lee HW. Inhibition and Mathematical Performance: Poorly Correlated, Poorly Measured, or Poorly Matched? CHILD DEVELOPMENT PERSPECTIVES 2018. [DOI: 10.1111/cdep.12304] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Kerry Lee
- The Education University of Hong Kong
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23
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Schwartz F, Epinat-Duclos J, Léone J, Poisson A, Prado J. Impaired neural processing of transitive relations in children with math learning difficulty. NEUROIMAGE-CLINICAL 2018; 20:1255-1265. [PMID: 30389345 PMCID: PMC6308383 DOI: 10.1016/j.nicl.2018.10.020] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/15/2018] [Revised: 10/05/2018] [Accepted: 10/21/2018] [Indexed: 11/24/2022]
Abstract
Math learning difficulty (i.e., MLD) is common in children and can have far-reaching consequences in personal and professional life. Converging evidence suggests that MLD is associated with impairments in the intraparietal sulcus (IPS). However, the role that these impairments play in MLD remains unclear. Although it is often assumed that IPS deficits affect core numerical abilities, the IPS is also involved in several non-numerical processes that may contribute to math skills. For instance, the IPS supports transitive reasoning (i.e., the ability to integrate relations such as A > B and B > C to infer that A > C), a skill that is central to many aspects of math learning in children. Here we measured fMRI activity of 8- to 12-year-olds with MLD and typically developing (TD) peers while they listened to stories that included transitive relations. Children also answered questions evaluating whether transitive inferences were made during story comprehension. Compared to non-transitive relations (e.g., A > B and C > D), listening to transitive relations (e.g., A > B and B > C) was associated with enhanced activity in the IPS in TD children. In children with MLD, the difference in activity between transitive and non-transitive relations in the IPS was (i) non-reliable and (ii) smaller than in TD children. Finally, children with MLD were less accurate than TD peers when making transitive inferences based on transitive relations. Thus, a deficit in the online processing of transitive relations in the IPS might contribute to math difficulties in children with MLD. Transitive reasoning is central to mathematical thinking. Transitive reasoning relies on the intra-parietal sulcus (IPS) in healthy children. Math learning difficulty (MLD) is associated with IPS impairments. Transitive reasoning is impaired in children with MLD. Transitive reasoning does not engage the IPS in children with MLD.
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Affiliation(s)
- Flora Schwartz
- Institut des Sciences Cognitives Marc Jeannerod, UMR 5304, Centre National de la Recherche Scientifique (CNRS) & Université de Lyon, 67 Boulevard Pinel, 69675 Bron cedex, France.
| | - Justine Epinat-Duclos
- Institut des Sciences Cognitives Marc Jeannerod, UMR 5304, Centre National de la Recherche Scientifique (CNRS) & Université de Lyon, 67 Boulevard Pinel, 69675 Bron cedex, France
| | - Jessica Léone
- Institut des Sciences Cognitives Marc Jeannerod, UMR 5304, Centre National de la Recherche Scientifique (CNRS) & Université de Lyon, 67 Boulevard Pinel, 69675 Bron cedex, France
| | - Alice Poisson
- GénoPsy, Reference center for rare diseases with psychiatric symptoms, Centre Hospitalier le Vinatier, 69678 Bron cedex, France
| | - Jérôme Prado
- Institut des Sciences Cognitives Marc Jeannerod, UMR 5304, Centre National de la Recherche Scientifique (CNRS) & Université de Lyon, 67 Boulevard Pinel, 69675 Bron cedex, France.
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24
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Is a fact retrieval deficit the main characteristic of children with mathematical learning disabilities? Acta Psychol (Amst) 2018; 190:95-102. [PMID: 30048856 DOI: 10.1016/j.actpsy.2018.07.007] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2017] [Revised: 07/20/2018] [Accepted: 07/20/2018] [Indexed: 11/23/2022] Open
Abstract
Although a fact retrieval deficit is widely considered to be the hallmark of children with mathematical learning disabilities (MLD), recent studies suggest that even adults use procedural strategies to solve small additions, except for ties that are unanimously considered to be solved by retrieval. Our study, based on how MLD children process ties and non-ties compared to typically developing (TD) children, sheds new light on their retrieval and procedural difficulties. Our results show that, by the end of the second grade, MLD children do not differ in their ability to solve the tie problems that are certainly solved by retrieval, but they do struggle with both small and large non-ties. These findings emphasize the extend of the difficulties that MLD children exhibit in procedural strategies relatively to retrieval ones.
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25
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Zhang X, Räsänen P, Koponen T, Aunola K, Lerkkanen MK, Nurmi JE. Early Cognitive Precursors of Children's Mathematics Learning Disability and Persistent Low Achievement: A 5-Year Longitudinal Study. Child Dev 2018; 91:7-27. [PMID: 29998603 DOI: 10.1111/cdev.13123] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Abstract
Mathematical difficulties have been distinguished as mathematics learning disability (MLD) and persistent low achievement (LA). Based on 1,880 Finnish children who were followed from kindergarten (age 6) to fourth grade, this study examined the early risk factors for MLD and LA. Distinct groups of MLD (6.0% of the sample) and LA (25.7%) children were identified on the basis of their mathematics performance between first and fourth grades with latent class growth modeling. Impairment in the same set of cognitive skills, including language, spatial, and counting skills, was found to underlie MLD and LA. The finding highlights the importance of monitoring mathematical development across the early grades and identifying early cognitive precursors of MLD and LA for screening and intervention efforts.
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26
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Marchand-Krynski MÈ, Bélanger AM, Morin-Moncet O, Beauchamp MH, Leonard G. Cognitive predictors of sequential motor impairments in children with dyslexia and/or attention deficit/hyperactivity disorder. Dev Neuropsychol 2018; 43:430-453. [PMID: 29764201 DOI: 10.1080/87565641.2018.1467421] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
This study examined cognitive predictors of sequential motor skills in 215 children with dyslexia and/or attention deficit/hyperactivity disorder (ADHD). Visual working memory and math fluency abilities contributed significantly to performance of sequential motor abilities in children with dyslexia (N = 67), ADHD (N = 66) and those with a comorbid diagnosis (N = 82), generally without differentiation between groups. In addition, primary diagnostic features of each disorder, such as reading and inattention, did not contribute to the variance in motor skill performance of these children. The results support a unifying framework of motor impairment in children with neurodevelopmental disorders such as dyslexia and ADHD.
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Affiliation(s)
- Marie-Ève Marchand-Krynski
- a Department of Psychology & Research Center in Neuropsychology and Cognition (CERNEC) , University of Montreal , Montreal , Canada
| | - Anne-Marie Bélanger
- b Department of Neurology and Neurosurgery , Montreal Neurological Institute and Hospital , Montreal , Canada
| | - Olivier Morin-Moncet
- a Department of Psychology & Research Center in Neuropsychology and Cognition (CERNEC) , University of Montreal , Montreal , Canada
| | - Miriam H Beauchamp
- c Department of Psychology , University of Montreal & Ste-Justine Hospital Research Center , Montreal , Canada
| | - Gabriel Leonard
- b Department of Neurology and Neurosurgery , Montreal Neurological Institute and Hospital , Montreal , Canada
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27
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Peake C, Jiménez JE, Rodríguez C. Data-driven heterogeneity in mathematical learning disabilities based on the triple code model. RESEARCH IN DEVELOPMENTAL DISABILITIES 2017; 71:130-142. [PMID: 29035779 DOI: 10.1016/j.ridd.2017.10.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2016] [Revised: 09/29/2017] [Accepted: 10/04/2017] [Indexed: 06/07/2023]
Abstract
Many classifications of heterogeneity in mathematical learning disabilities (MLD) have been proposed over the past four decades, however no empirical research has been conducted until recently, and none of the classifications are derived from Triple Code Model (TCM) postulates. The TCM proposes MLD as a heterogeneous disorder, with two distinguishable profiles: a representational subtype and a verbal subtype. A sample of elementary school 3rd to 6th graders was divided into two age cohorts (3rd - 4th grades, and 5th - 6th grades). Using data-driven strategies, based on the cognitive classification variables predicted by the TCM, our sample of children with MLD clustered as expected: a group with representational deficits and a group with number-fact retrieval deficits. In the younger group, a spatial subtype also emerged, while in both cohorts a non-specific cluster was produced whose profile could not be explained by this theoretical approach.
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Affiliation(s)
- Christian Peake
- Faculty of Education, Universidad Católica de la Santísima Concepción, Concepción, Chile; Centro de Investigación en Educación y Desarrollo, CIEDE-UCSC, Concepción, Chile.
| | - Juan E Jiménez
- Department of Developmental Psychology and Education, University of La Laguna, Tenerife, Spain.
| | - Cristina Rodríguez
- Faculty of Education, Universidad Católica de la Santísima Concepción, Concepción, Chile; Department of Developmental Psychology and Education, University of La Laguna, Tenerife, Spain.
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28
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Zhang J, Fan X, Cheung SK, Meng Y, Cai Z, Hu BY. The role of early language abilities on math skills among Chinese children. PLoS One 2017; 12:e0181074. [PMID: 28749950 PMCID: PMC5531550 DOI: 10.1371/journal.pone.0181074] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2017] [Accepted: 06/26/2017] [Indexed: 11/23/2022] Open
Abstract
BACKGROUND The present study investigated the role of early language abilities in the development of math skills among Chinese K-3 students. About 2000 children in China, who were on average aged 6 years, were assessed for both informal math (e.g., basic number concepts such as counting objects) and formal math (calculations including addition and subtraction) skills, language abilities and nonverbal intelligence. METHODOLOGY Correlation analysis showed that language abilities were more strongly associated with informal than formal math skills, and regression analyses revealed that children's language abilities could uniquely predict both informal and formal math skills with age, gender, and nonverbal intelligence controlled. Mediation analyses demonstrated that the relationship between children's language abilities and formal math skills was partially mediated by informal math skills. RESULTS The current findings indicate 1) Children's language abilities are of strong predictive values for both informal and formal math skills; 2) Language abilities impacts formal math skills partially through the mediation of informal math skills.
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Affiliation(s)
- Juan Zhang
- Faculty of Education, University of Macau, Macau, China
| | - Xitao Fan
- School of Humanities and Social Science, The Chinese University of Hong Kong (Shenzhen), China
| | - Sum Kwing Cheung
- School of Continuing Education, Hong Kong Baptist University, Hong Kong, China
| | - Yaxuan Meng
- Faculty of Education, University of Macau, Macau, China
| | - Zhihui Cai
- School of Psychology, Central China Normal University, Wuhan, China
| | - Bi Ying Hu
- Faculty of Education, University of Macau, Macau, China
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29
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“Compacted” procedures for adults’ simple addition: A review and critique of the evidence. Psychon Bull Rev 2017; 25:739-753. [DOI: 10.3758/s13423-017-1328-2] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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30
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De Visscher A, Noël MP, De Smedt B. The role of physical digit representation and numerical magnitude representation in children's multiplication fact retrieval. J Exp Child Psychol 2016; 152:41-53. [PMID: 27454238 DOI: 10.1016/j.jecp.2016.06.014] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2016] [Revised: 06/21/2016] [Accepted: 06/24/2016] [Indexed: 10/21/2022]
Abstract
Arithmetic facts, in particular multiplication tables, are thought to be stored in long-term memory and to be interference prone. At least two representations underpinning these arithmetic facts have been suggested: a physical representation of the digits and a numerical magnitude representation. We hypothesized that both representations are possible sources of interference that could explain individual differences in multiplication fact performance and/or in strategy use. We investigated the specificity of these interferences on arithmetic fact retrieval and explored the relation between interference and performance on the different arithmetic operations and on general mathematics achievement. Participants were 79 fourth-grade children (Mage=9.6 years) who completed a products comparison and a multiplication production task with verbal strategy reports. Performances on a speeded calculation test including the four operations and on a general mathematics achievement test were also collected. Only the interference coming from physical representations was a significant predictor of the performance across multiplications. However, both the magnitude and physical representations were unique predictors of individual differences in multiplication. The frequency of the retrieval strategy across multiplication problems and across individuals was determined only by the physical representation, which therefore is suggested as being responsible for memory storage issues. Interestingly, this impact of physical representation was not observed when predicting performance on subtraction or on general mathematical achievement. In contrast, the impact of the numerical magnitude representation was more general in that it was observed across all arithmetic operations and in general mathematics achievement.
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Affiliation(s)
- Alice De Visscher
- Institut de Recherche en Sciences Psychologiques, Université catholique de Louvain, 1348 Louvain-la-Neuve, Belgium; Parenting and Special Education Research Unit, Faculty of Psychology and Educational Sciences, KU Leuven-University of Leuven, 3000 Leuven, Belgium.
| | - Marie-Pascale Noël
- Institut de Recherche en Sciences Psychologiques, Université catholique de Louvain, 1348 Louvain-la-Neuve, Belgium
| | - Bert De Smedt
- Parenting and Special Education Research Unit, Faculty of Psychology and Educational Sciences, KU Leuven-University of Leuven, 3000 Leuven, Belgium
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31
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Bellon E, Fias W, De Smedt B. Are Individual Differences in Arithmetic Fact Retrieval in Children Related to Inhibition? Front Psychol 2016; 7:825. [PMID: 27378961 PMCID: PMC4905982 DOI: 10.3389/fpsyg.2016.00825] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2015] [Accepted: 05/17/2016] [Indexed: 12/30/2022] Open
Abstract
Although it has been proposed that inhibition is related to individual differences in mathematical achievement, it is not clear how it is related to specific aspects of mathematical skills, such as arithmetic fact retrieval. The present study therefore investigated the association between inhibition and arithmetic fact retrieval and further examined the unique role of inhibition in individual differences in arithmetic fact retrieval, in addition to numerical magnitude processing. We administered measures of cognitive inhibition (i.e., numerical and non-numerical stroop tasks) and a complementary, more ecologically valid measure of children’s inhibition in the classroom (i.e., teacher questionnaire), as well as numerical magnitude processing (i.e., symbolic and non-symbolic numerical magnitude comparison) and arithmetic fact retrieval (i.e., two verification tasks) in 86 typically developing third graders. We used a correlation, a regression and a Bayesian analysis. This study failed to observe a significant association between inhibition and arithmetic fact retrieval. Consequently, our results did not reveal a unique contribution of inhibition to arithmetic fact retrieval in addition to numerical magnitude processing. On the other hand, symbolic numerical magnitude processing turned out to be a very powerful predictor of arithmetic fact retrieval, as indicated by both frequentist and Bayesian approaches.
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Affiliation(s)
- Elien Bellon
- Psychology and Educational Sciences, Parenting and Special Education Research Group, Katholieke Universiteit Leuven Leuven, Belgium
| | - Wim Fias
- Experimental Psychology, Ghent University Ghent, Belgium
| | - Bert De Smedt
- Psychology and Educational Sciences, Parenting and Special Education Research Group, Katholieke Universiteit Leuven Leuven, Belgium
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32
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De Visscher A, Noël MP. Similarity interference in learning and retrieving arithmetic facts. PROGRESS IN BRAIN RESEARCH 2016; 227:131-58. [PMID: 27339011 DOI: 10.1016/bs.pbr.2016.04.008] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
Storing the solution of simple calculations in long-term memory is an important learning in primary school that is subsequently essential in adult daily living. While most children succeed in storing arithmetic facts to which they have been trained at school, huge individual differences are reported, particularly in children with developmental dyscalculia, who show a severe and persistent deficit in arithmetic facts learning. This chapter reports important advances in the understanding of the development of an arithmetic facts network and focuses on the detrimental effect of similarity interference. First, at the retrieval stage, connectionist models highlighted that the similarity of the neighbor problems in the arithmetic facts network creates interference. More recently, the similarity interference during the learning stage was pointed out in arithmetic facts learning. The interference parameter, that captures the proactive interference that a problem receives from previously learned problems, was shown as a substantial determinant of the performance across multiplication problems. This proactive interference was found both in children and adults and showed that when a problem is highly similar to previously learned ones, it is more difficult to remember it. Furthermore, the sensitivity to this similarity interference determined individual differences in the learning and retrieving of arithmetic facts, giving new insights for interindividual differences. Regarding the atypical development, hypersensitivity-to-interference in memory was related to arithmetic facts deficit in a single case of developmental dyscalculia and in a group of fourth-grade children with low arithmetic facts knowledge. In sum, the impact of similarity interference is shown in the learning stage of arithmetic facts and concerns the typical and atypical development.
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Affiliation(s)
- A De Visscher
- Psychological Sciences Research Institute, Université catholique de Louvain (UCL), Louvain-la-Neuve, Belgium.
| | - M-P Noël
- Psychological Sciences Research Institute, Université catholique de Louvain (UCL), Louvain-la-Neuve, Belgium
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Vanbinst K, De Smedt B. Individual differences in children's mathematics achievement: The roles of symbolic numerical magnitude processing and domain-general cognitive functions. PROGRESS IN BRAIN RESEARCH 2016; 227:105-30. [PMID: 27339010 DOI: 10.1016/bs.pbr.2016.04.001] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
This contribution reviewed the available evidence on the domain-specific and domain-general neurocognitive determinants of children's arithmetic development, other than nonsymbolic numerical magnitude processing, which might have been overemphasized as a core factor of individual differences in mathematics and dyscalculia. We focused on symbolic numerical magnitude processing, working memory, and phonological processing, as these determinants have been most researched and their roles in arithmetic can be predicted against the background of brain imaging data. Our review indicates that symbolic numerical magnitude processing is a major determinant of individual differences in arithmetic. Working memory, particularly the central executive, also plays a role in learning arithmetic, but its influence appears to be dependent on the learning stage and experience of children. The available evidence on phonological processing suggests that it plays a more subtle role in children's acquisition of arithmetic facts. Future longitudinal studies should investigate these factors in concert to understand their relative contribution as well as their mediating and moderating roles in children's arithmetic development.
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Affiliation(s)
- K Vanbinst
- Parenting and Special Education Research Unit, Faculty of Psychology and Educational Sciences, University of Leuven, Leuven, Belgium
| | - B De Smedt
- Parenting and Special Education Research Unit, Faculty of Psychology and Educational Sciences, University of Leuven, Leuven, Belgium.
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Fischer JP, Koch AM. Mirror writing in typically developing children: A first longitudinal study. COGNITIVE DEVELOPMENT 2016. [DOI: 10.1016/j.cogdev.2016.02.005] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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De Visscher A, Szmalec A, Van Der Linden L, Noël MP. Serial-order learning impairment and hypersensitivity-to-interference in dyscalculia. Cognition 2015. [DOI: 10.1016/j.cognition.2015.07.007] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Geary DC, Hoard MK, Nugent L, Rouder JN. Individual differences in algebraic cognition: Relation to the approximate number and semantic memory systems. J Exp Child Psychol 2015; 140:211-27. [PMID: 26255604 DOI: 10.1016/j.jecp.2015.07.010] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2015] [Revised: 07/14/2015] [Accepted: 07/15/2015] [Indexed: 01/29/2023]
Abstract
The relation between performance on measures of algebraic cognition and acuity of the approximate number system (ANS) and memory for addition facts was assessed for 171 ninth graders (92 girls) while controlling for parental education, sex, reading achievement, speed of numeral processing, fluency of symbolic number processing, intelligence, and the central executive component of working memory. The algebraic tasks assessed accuracy in placing x,y pairs in the coordinate plane, speed and accuracy of expression evaluation, and schema memory for algebra equations. ANS acuity was related to accuracy of placements in the coordinate plane and expression evaluation but not to schema memory. Frequency of fact retrieval errors was related to schema memory but not to coordinate plane or expression evaluation accuracy. The results suggest that the ANS may contribute to or be influenced by spatial-numerical and numerical-only quantity judgments in algebraic contexts, whereas difficulties in committing addition facts to long-term memory may presage slow formation of memories for the basic structure of algebra equations. More generally, the results suggest that different brain and cognitive systems are engaged during the learning of different components of algebraic competence while controlling for demographic and domain general abilities.
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Affiliation(s)
- David C Geary
- Department of Psychological Sciences, University of Missouri, Columbia, MO 65211, USA.
| | - Mary K Hoard
- Department of Psychological Sciences, University of Missouri, Columbia, MO 65211, USA
| | - Lara Nugent
- Department of Psychological Sciences, University of Missouri, Columbia, MO 65211, USA
| | - Jeffrey N Rouder
- Department of Psychological Sciences, University of Missouri, Columbia, MO 65211, USA
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De Visscher A, Berens SC, Keidel JL, Noël MP, Bird CM. The interference effect in arithmetic fact solving: An fMRI study. Neuroimage 2015; 116:92-101. [DOI: 10.1016/j.neuroimage.2015.04.063] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2014] [Revised: 04/22/2015] [Accepted: 04/29/2015] [Indexed: 10/23/2022] Open
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Abstract
Developmental dyscalculia (DD) is a specific learning disorder that affects the acquisition of arithmetic skills and number processing in children. A high comorbidity between DD and other neurodevelopmental disorders (e.g., dyslexia, attention-deficit/hyperactivity disorder [ADHD]) as well as substantial heterogeneity in cognitive profiles have been reported. Current studies indicate that DD is persistent, has a genetic component, and is related to functional and structural alterations of brain areas involved in magnitude representation. Recent neuronal and behavioral evidence is presented, showing that DD entails (a) impairments in two preverbal core systems of number, an approximate system for estimating larger magnitudes and an exact system for representing small magnitudes, (b) deficits in symbolic number processing, (c) aberrant and nonadaptive neuronal activation in basic magnitude processing and calculation, (d) dysfunctional arithmetic fact retrieval and persistent use of counting strategies in calculation, and (e) deficits in visuospatial working memory and the central executive. Finally, open research questions, including the role of domain-general cognitive resources in DD, causes and developmental consequences of comorbidity, as well as design and evaluation of interventions for DD, are briefly discussed.
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Abstract
When diagnosing children with learning disorders (as per ICD-10), their scholastic performance has to be significantly below the level of intelligence. Although this discrepancy criterion has received much criticism in the field of literacy, few researchers in mathematics have examined it. We used a two (mathematical performance) by two (intelligence) factorial design to analyze the arithmetic fact retrieval of low-performing children in mathematics who met the criterion (developmental dyscalculia) or did not (mathematical difficulties) and of two groups of average-achieving children matched for intelligence. The four groups (each n = 27 third-graders) were matched for their attention span and their literacy skills. Children solved addition verification tasks with numbers up to 10 and 20 under standard and under dual task conditions requiring further working memory capacity to evaluate the potential use of counting strategies. Performance in addition tasks proved to be associated with mathematical achievement especially in the higher number range, whereas dual task performance did not point to the use of counting strategies among low performers in mathematics. No interaction between mathematics and intelligence was identified, which would have confirmed the discrepancy criterion. These results illustrate that stable knowledge of arithmetic facts is essential for mathematical achievement, regardless of whether the discrepancy criterion is met.
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Affiliation(s)
- Jenny Busch
- Carl von Ossietzky University, Oldenburg, Germany
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Vanbinst K, Ceulemans E, Ghesquière P, De Smedt B. Profiles of children's arithmetic fact development: a model-based clustering approach. J Exp Child Psychol 2015; 133:29-46. [PMID: 25731679 DOI: 10.1016/j.jecp.2015.01.003] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2014] [Revised: 12/30/2014] [Accepted: 01/12/2015] [Indexed: 10/23/2022]
Abstract
The current longitudinal study tried to capture profiles of individual differences in children's arithmetic fact development. We used a model-based clustering approach to delineate profiles of arithmetic fact development based on empirically derived differences in parameters of arithmetic fact mastery repeatedly assessed at the start of three subsequent school years: third, fourth, and fifth grades. This cluster analysis revealed three profiles in a random sample-slow and variable (n = 8), average (n = 24), and efficient (n = 20)-that were marked by differences in children's development in arithmetic fact mastery from third grade to fifth grade. These profiles did not differ in terms of age, sex, socioeconomic status, or intellectual ability. In addition, we explored whether these profiles varied in cognitive skills that have been associated with individual differences in single-digit arithmetic. The three profiles differed in nonsymbolic and symbolic numerical magnitude processing as well as phonological processing, but not in digit naming or working memory. After also controlling for cluster differences in general mathematics achievement and reading ability, only differences in symbolic numerical magnitude processing remained significant. Taken together, our longitudinal data reveal that symbolic numerical magnitude processing represents an important variable that contributes to individual variability in children's acquisition of arithmetic facts.
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Affiliation(s)
- Kiran Vanbinst
- Parenting and Special Education Research Unit, Faculty of Psychology and Educational Sciences, KU Leuven, B-3000 Leuven, Belgium.
| | - Eva Ceulemans
- Parenting and Special Education Research Unit, Faculty of Psychology and Educational Sciences, KU Leuven, B-3000 Leuven, Belgium
| | - Pol Ghesquière
- Parenting and Special Education Research Unit, Faculty of Psychology and Educational Sciences, KU Leuven, B-3000 Leuven, Belgium
| | - Bert De Smedt
- Parenting and Special Education Research Unit, Faculty of Psychology and Educational Sciences, KU Leuven, B-3000 Leuven, Belgium.
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