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Wortha SM, Klein E, Lambert K, Dackermann T, Moeller K. The relevance of basic numerical skills for fraction processing: Evidence from cross-sectional data. PLoS One 2023; 18:e0281241. [PMID: 36719901 PMCID: PMC9888716 DOI: 10.1371/journal.pone.0281241] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2021] [Accepted: 01/18/2023] [Indexed: 02/01/2023] Open
Abstract
Recent research indicated that fraction understanding is an important predictor of later mathematical achievement. In the current study we investigated associations between basic numerical skills and students' fraction processing. We analyzed data of 939 German secondary school students (age range = 11.92 to 18.00 years) and evaluated the determinants of fraction processing considering basic numerical skills as predictors (i.e., number line estimation, basic arithmetic operations, non-symbolic magnitude comparison, etc.). Additionally, we controlled for general cognitive ability, grade level, and sex. We found that multiplication, subtraction, conceptual knowledge, number line estimation, and basic geometry were significantly associated with fraction processing beyond significant associations of general cognitive ability and sex. Moreover, relative weight analysis revealed that addition and approximate arithmetic should also be considered as relevant predictors for fraction processing. The current results provide food for thought that further research should focus on investigating whether recapitulating basic numerical content in secondary school mathematics education can be beneficial for acquiring more complex mathematical concepts such as fractions.
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Affiliation(s)
- Silke M. Wortha
- LEAD Graduate School & Research Network, University of Tuebingen, Tuebingen, Germany
- Department of Neurology, University Medicine Greifswald, Greifswald, Germany
- Centre for Mathematical Cognition, School of Science, Loughborough University, Loughborough, United Kingdom
- * E-mail:
| | - Elise Klein
- University of Paris, LaPsyDÉ, CNRS, Paris, France
- Leibniz-Institut für Wissensmedien, Tuebingen, Germany
| | - Katharina Lambert
- LEAD Graduate School & Research Network, University of Tuebingen, Tuebingen, Germany
- University of Education, Heidelberg, Germany
| | | | - Korbinian Moeller
- LEAD Graduate School & Research Network, University of Tuebingen, Tuebingen, Germany
- Centre for Mathematical Cognition, School of Science, Loughborough University, Loughborough, United Kingdom
- Leibniz-Institut für Wissensmedien, Tuebingen, Germany
- Individual Development and Adaptive Education Center, Frankfurt am Main, Germany
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Lazzaro G, Fucà E, Caciolo C, Battisti A, Costanzo F, Varuzza C, Vicari S, Menghini D. Understanding the Effects of Transcranial Electrical Stimulation in Numerical Cognition: A Systematic Review for Clinical Translation. J Clin Med 2022; 11:jcm11082082. [PMID: 35456176 PMCID: PMC9032363 DOI: 10.3390/jcm11082082] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2022] [Revised: 03/31/2022] [Accepted: 04/02/2022] [Indexed: 02/04/2023] Open
Abstract
Atypical development of numerical cognition (dyscalculia) may increase the onset of neuropsychiatric symptoms, especially when untreated, and it may have long-term detrimental social consequences. However, evidence-based treatments are still lacking. Despite plenty of studies investigating the effects of transcranial electrical stimulation (tES) on numerical cognition, a systematized synthesis of results is still lacking. In the present systematic review (PROSPERO ID: CRD42021271139), we found that the majority of reports (20 out of 26) showed the effectiveness of tES in improving both number (80%) and arithmetic (76%) processing. In particular, anodal tDCS (regardless of lateralization) over parietal regions, bilateral tDCS (regardless of polarity/lateralization) over frontal regions, and tRNS (regardless of brain regions) strongly enhance number processing. While bilateral tDCS and tRNS over parietal and frontal regions and left anodal tDCS over frontal regions consistently improve arithmetic skills. In addition, tACS seems to be more effective than tDCS at ameliorating arithmetic learning. Despite the variability of methods and paucity of clinical studies, tES seems to be a promising brain-based treatment to enhance numerical cognition. Recommendations for clinical translation, future directions, and limitations are outlined.
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Affiliation(s)
- Giulia Lazzaro
- Child and Adolescent Neuropsychiatry Unit, Department of Neuroscience, Bambino Gesù Children’s Hospital, IRCCS, 00146 Rome, Italy; (G.L.); (E.F.); (C.C.); (A.B.); (F.C.); (C.V.); (S.V.)
| | - Elisa Fucà
- Child and Adolescent Neuropsychiatry Unit, Department of Neuroscience, Bambino Gesù Children’s Hospital, IRCCS, 00146 Rome, Italy; (G.L.); (E.F.); (C.C.); (A.B.); (F.C.); (C.V.); (S.V.)
| | - Cristina Caciolo
- Child and Adolescent Neuropsychiatry Unit, Department of Neuroscience, Bambino Gesù Children’s Hospital, IRCCS, 00146 Rome, Italy; (G.L.); (E.F.); (C.C.); (A.B.); (F.C.); (C.V.); (S.V.)
| | - Andrea Battisti
- Child and Adolescent Neuropsychiatry Unit, Department of Neuroscience, Bambino Gesù Children’s Hospital, IRCCS, 00146 Rome, Italy; (G.L.); (E.F.); (C.C.); (A.B.); (F.C.); (C.V.); (S.V.)
- Department of Human Science, LUMSA University, 00193 Rome, Italy
| | - Floriana Costanzo
- Child and Adolescent Neuropsychiatry Unit, Department of Neuroscience, Bambino Gesù Children’s Hospital, IRCCS, 00146 Rome, Italy; (G.L.); (E.F.); (C.C.); (A.B.); (F.C.); (C.V.); (S.V.)
| | - Cristiana Varuzza
- Child and Adolescent Neuropsychiatry Unit, Department of Neuroscience, Bambino Gesù Children’s Hospital, IRCCS, 00146 Rome, Italy; (G.L.); (E.F.); (C.C.); (A.B.); (F.C.); (C.V.); (S.V.)
| | - Stefano Vicari
- Child and Adolescent Neuropsychiatry Unit, Department of Neuroscience, Bambino Gesù Children’s Hospital, IRCCS, 00146 Rome, Italy; (G.L.); (E.F.); (C.C.); (A.B.); (F.C.); (C.V.); (S.V.)
- Department of Life Science and Public Health, Università Cattolica del Sacro Cuore, 00168 Rome, Italy
- Centro di Riabilitazione Casa San Giuseppe, Opera Don Guanella, 00165 Rome, Italy
| | - Deny Menghini
- Child and Adolescent Neuropsychiatry Unit, Department of Neuroscience, Bambino Gesù Children’s Hospital, IRCCS, 00146 Rome, Italy; (G.L.); (E.F.); (C.C.); (A.B.); (F.C.); (C.V.); (S.V.)
- Correspondence: ; Tel.: +39-066-859-7091
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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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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.
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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
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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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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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De Visscher A, Vogel SE, Reishofer G, Hassler E, Koschutnig K, De Smedt B, Grabner RH. Interference and problem size effect in multiplication fact solving: Individual differences in brain activations and arithmetic performance. Neuroimage 2018; 172:718-727. [DOI: 10.1016/j.neuroimage.2018.01.060] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2017] [Revised: 12/20/2017] [Accepted: 01/23/2018] [Indexed: 11/29/2022] Open
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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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Lonnemann J, Linkersdörfer J, Hasselhorn M, Lindberg S. Differences in Arithmetic Performance between Chinese and German Children Are Accompanied by Differences in Processing of Symbolic Numerical Magnitude. Front Psychol 2016; 7:1337. [PMID: 27630606 PMCID: PMC5005975 DOI: 10.3389/fpsyg.2016.01337] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2016] [Accepted: 08/22/2016] [Indexed: 11/17/2022] Open
Abstract
Symbolic numerical magnitude processing skills are assumed to be fundamental to arithmetic learning. It is, however, still an open question whether better arithmetic skills are reflected in symbolic numerical magnitude processing skills. To address this issue, Chinese and German third graders were compared regarding their performance in arithmetic tasks and in a symbolic numerical magnitude comparison task. Chinese children performed better in the arithmetic tasks and were faster in deciding which one of two Arabic numbers was numerically larger. The group difference in symbolic numerical magnitude processing was fully mediated by the performance in arithmetic tasks. We assume that a higher degree of familiarity with arithmetic in Chinese compared to German children leads to a higher speed of retrieving symbolic numerical magnitude knowledge.
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Affiliation(s)
- Jan Lonnemann
- Department of Education and Human Development, German Institute for International Educational Research (DIPF)Frankfurt am Main, Germany; Center for Individual Development and Adaptive Education of Children at RiskFrankfurt am Main, Germany
| | - Janosch Linkersdörfer
- Department of Education and Human Development, German Institute for International Educational Research (DIPF)Frankfurt am Main, Germany; Center for Individual Development and Adaptive Education of Children at RiskFrankfurt am Main, Germany
| | - Marcus Hasselhorn
- Department of Education and Human Development, German Institute for International Educational Research (DIPF)Frankfurt am Main, Germany; Center for Individual Development and Adaptive Education of Children at RiskFrankfurt am Main, Germany; Department of Educational Psychology, Institute for Psychology, Goethe-UniversityFrankfurt am Main, Germany
| | - Sven Lindberg
- Center for Individual Development and Adaptive Education of Children at RiskFrankfurt am Main, Germany; Faculty of Arts and Humanities, Paderborn UniversityPaderborn, Germany
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