Publications by authors named "Bert De Smedt"

88 Publications

Can the interference effect in multiplication fact retrieval be modulated by an arithmetic training? An fMRI study.

Neuropsychologia 2021 Apr 12:107849. Epub 2021 Apr 12.

Educational Neuroscience, Institute of Psychology, University of Graz, Austria.

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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http://dx.doi.org/10.1016/j.neuropsychologia.2021.107849DOI Listing
April 2021

Fact retrieval or compacted counting in arithmetic-A neurophysiological investigation of two hypotheses.

J Exp Psychol Learn Mem Cogn 2021 Feb 4. Epub 2021 Feb 4.

Parenting and Special Education Research Unit.

There is broad consensus on the assumption that adults solve single-digit multiplication problems almost exclusively by fact retrieval from memory. In contrast, there has been a long-standing debate on the cognitive processes involved in solving single-digit addition problems. This debate has evolved around two theoretical accounts. Proponents of a fact-retrieval account postulate that these are also solved through fact retrieval, whereas proponents of a compacted-counting account propose that solving very small additions (with operands between 1 and 4) involves highly automatized and unconscious compacted counting. In the present electroencephalography (EEG) study, we put these two accounts to the test by comparing neurophysiological correlates of solving very small additions and multiplications. Forty adults worked on an arithmetic production task involving all (nontie) single-digit additions and multiplications. Afterward, participants completed trial-by-trial strategy self-reports. In our EEG analyses, we focused on induced activity (event-related synchronization/desynchronization, ERS/ERD) in three frequency bands (theta, lower alpha, upper alpha). Across all frequency bands, we found higher evidential strength for similar rather than different neurophysiological processes accompanying the solution of very small addition and multiplication problems. In the alpha bands, evidence for similarity was even stronger when operand-1-problems were excluded. In two additional analyses, we showed that ERS/ERD can differentiate between self-reported problem-solving strategies (retrieval vs. procedure) and between very small × 1 and + 1 problems, demonstrating its high sensitivity to cognitive processes in arithmetic. The present findings support a fact-retrieval account, suggesting that both very small additions and multiplications are solved through fact retrieval. (PsycInfo Database Record (c) 2021 APA, all rights reserved).
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http://dx.doi.org/10.1037/xlm0000982DOI Listing
February 2021

Associations Between Repeating Patterning, Growing Patterning, and Numerical Ability: A Longitudinal Panel Study in 4- to 6-Year Olds.

Child Dev 2021 Jan 4. Epub 2021 Jan 4.

Centre for Instructional Psychology and Technology.

The present study aimed to analyze the direction of the associations between repeating patterning, growing patterning, and numerical ability. Participants were 410 children who were annually assessed on their repeating patterning, growing patterning, and numerical ability, at ages 4, 5, and 6 years (i.e., spring 2017, 2018, and 2019). A cross-lagged panel model identified bidirectional associations between all three abilities from ages 4 to 5 years while taking into account spatial skills. From ages 5 to 6 years, both patterning abilities predicted later numerical ability, but the reverse was no longer true. Associations between performances on both pattern types also disappeared. Results highlight the unique associations between repeating patterning, growing patterning, and numerical ability, above spatial skills.
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http://dx.doi.org/10.1111/cdev.13490DOI Listing
January 2021

No Association Between the Home Math Environment and Numerical and Patterning Skills in a Large and Diverse Sample of 5- to 6-year-olds.

Front Psychol 2020 10;11:547626. Epub 2020 Dec 10.

Faculty of Psychology and Educational Sciences, KU Leuven, Leuven, Belgium.

Selecting a large and diverse sample of 5-6-year-old preschool children (179 boys and 174 girls; = 70.03 months, = 3.43), we aimed to extend previous findings on variability in children's home math environment (i.e., home math activities, parental expectations, and attitudes) and its association with children's mathematical skills. We operationalized mathematics in a broader way than in previous studies, by considering not only children's numerical skills but also their patterning skills as integral components of early mathematical development. We investigated the effects of children's gender and socioeconomic status (SES) on their home math environment, examined the associations between children's home math environment and their mathematical skills, and verified whether these associations were moderated by children's gender and/or SES. Parents of 353 children completed a home math environment questionnaire and all children completed measures of their numerical (e.g., object counting) and patterning skills (e.g., extending repeating patterns). Results indicated no effect of children's gender on their home math environment. There was no effect of SES on the performed home math activities, but small SES differences existed in parents' math-related expectations and their attitudes. We found no evidence for associations between children's home math environment and their mathematical skills. Furthermore, there were no moderating effects of gender or SES on these associations. One explanation for these findings might relate to the characteristics of the general preschool system in the country of the present study (Belgium). Future studies should consider the effect of the preschool learning environment because it might explain differences between studies and countries with regard to the home math environment and its association with mathematical skills.
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http://dx.doi.org/10.3389/fpsyg.2020.547626DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7758193PMC
December 2020

Cognitive correlates of dyslexia, dyscalculia and comorbid dyslexia/dyscalculia: Effects of numerical magnitude processing and phonological processing.

Res Dev Disabil 2020 Dec 3;107:103806. Epub 2020 Nov 3.

Parenting and Special Education Research Unit, University of Leuven, Belgium.

Specific learning disorders (i.e., dyscalculia and dyslexia) are common, as is their comorbidity. It has been suggested that the core cognitive deficit in dyscalculia is an impairment in numerical magnitude processing; similarly, in dyslexia, phonological processing deficits are considered to be the main cognitive deficit. Cognitive theories on comorbid dyslexia/dyscalculia have suggested a number of hypotheses about which cognitive deficits underlie the comorbidity. However, few studies have thus far directly compared the abovementioned cognitive correlates of dyscalculia and dyslexia. In this study, we assessed symbolic and non-symbolic numerical magnitude and three subcomponents of phonological processing (phonological awareness, lexical access and verbal short-term memory). In addition, we investigated children's domain-general spatial and verbal skills. The effect of these cognitive correlates on dyscalculia, dyslexia and their comorbidity was explored. We did not find differences between children with and without dyscalculia on numerical magnitude processing. On the other hand, children with dyscalculia had significantly lower spatial skills compared to children without dyscalculia. Children with dyslexia performed significantly lower on all subcomponents of phonological processing. Finally, we found an additive effect for comorbid dyslexia/dyscalculia: impairments in children with co-occurring dyslexia and dyscalculia were similar to the sum of the impairments in the isolated dyslexia and isolated dyscalculia groups. The strongest unique predictor of isolated dyscalculia and comorbid dyslexia/dyscalculia was spatial skills, the strongest unique predictor of isolated dyslexia was phonological awareness. As only a limited number of cognitive variables were assessed in this study and the sample sizes were very small, we should be cautious when interpreting these results.
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http://dx.doi.org/10.1016/j.ridd.2020.103806DOI Listing
December 2020

Probing the Relationship Between Home Numeracy and Children's Mathematical Skills: A Systematic Review.

Front Psychol 2020 18;11:2074. Epub 2020 Sep 18.

Faculty of Psychology and Educational Sciences, KU Leuven Kulak, Kortrijk, Belgium.

The concept of home numeracy has been defined as parent-child interactions with numerical content. This concept started to receive increasing attention since the last decade. Most of the studies indicated that the more parents and their children engage in numerical experiences, the better children perform in mathematical tasks. However, there are also contrasting results indicating that home numeracy does not play a role or that there is a negative association between the parent-child interactions and children's mathematics performance. To shed light on these discrepancies, a systematic review searching for available articles examining the relationship between home numeracy and mathematical skills was conducted. Thirty-seven articles were retained and a -curve analysis showed a true positive association between home numeracy and children's mathematical skills. A more qualitative investigation of the articles revealed five common findings: (1) Advanced home numeracy interactions but not basic ones are associated with children's mathematical skills. (2) Most participants in the studies were mothers, however, when both parents participated and were compared, only mothers' reports of formal home numeracy activities (i.e., explicit numeracy teaching) were linked to children's mathematical skill. (3) Formal home numeracy activities have been investigated more commonly than informal home numeracy activities (i.e., implicit numeracy teaching). (4) The number of studies that have used questionnaires to assess home numeracy is larger compared with the ones that have used observations. (5) The majority of the studies measured children's mathematical skills with comprehensive tests that index mathematical ability with one composite score rather than with specific numerical tasks. These five common findings might explain the contradictory results regarding the relationship between home numeracy and mathematical skills. Therefore, more research is necessary to draw quantitative conclusions about these five points.
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http://dx.doi.org/10.3389/fpsyg.2020.02074DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7530373PMC
September 2020

Towards Greater Collaboration in Educational Neuroscience: Perspectives From the 2018 Earli-SIG22 Conference.

Mind Brain Educ 2020 May 18;14(2):124-129. Epub 2020 Jun 18.

Department of Psychological Sciences, Centre for Brain and Cognitive Development Birkbeck, University of London UK.

The special issue resulting from the 2018 Earli-SIG22 conference reflects the current state of the field, the diversity of methods, the persevering limitations and promising directions towards solutions. About half of the empirical papers in this special issue that consist of three parts, uses behavioral, self-report or qualitative measures to understand the "mind" level of . The other half investigates the "brain" level, using neuroimaging but also genetics or eye-tracking to gain access to the wider range of biological substrates of learning and cognition. These biological studies mostly have added value by refining psychological theories, such that these inspire new hypotheses to test in the field, to ultimately better inform teaching. Importantly, the special issue presents several approaches to more intensive, bi-directional and systematic practice-research collaborations to better connect the "mind" and "brain" levels to education, and to equip researchers to realize such collaborations successfully in the future.
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http://dx.doi.org/10.1111/mbe.12250DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7384141PMC
May 2020

The neural basis of metacognitive monitoring during arithmetic in the developing brain.

Hum Brain Mapp 2020 Nov 23;41(16):4562-4573. Epub 2020 Jul 23.

Parenting and Special Education Research Unit, KU Leuven, Leuven, Belgium.

In contrast to a substantial body of research on the neural basis of cognitive performance in several academic domains, less is known about how the brain generates metacognitive (MC) awareness of such performance. The existing work on the neurobiological underpinnings of metacognition has almost exclusively been done in adults and has largely focused on lower level cognitive processing domains, such as perceptual decision-making. Extending this body of evidence, we investigated MC monitoring by asking children to solve arithmetic problems, an educationally relevant higher-order process, while providing concurrent MC reports during fMRI acquisition. Results are reported on 50 primary school children aged 9-10 years old. The current study is the first to demonstrate that brain activity during MC monitoring, relative to the control task, increased in the left inferior frontal gyrus in children. This brain activity further correlated with children's arithmetic development over a 3-year time period. These data are in line with the frequently suggested, yet never empirically tested, hypothesis that activity in the prefrontal cortex during arithmetic is related to the higher-order process of MC monitoring.
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http://dx.doi.org/10.1002/hbm.25142DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7555088PMC
November 2020

Metacognition across domains: Is the association between arithmetic and metacognitive monitoring domain-specific?

PLoS One 2020 12;15(3):e0229932. Epub 2020 Mar 12.

Parenting and Special Education Research Unit, KU Leuven, Leuven, Belgium.

Metacognitive monitoring is a critical predictor of arithmetic in primary school. One outstanding question is whether this metacognitive monitoring is domain-specific or whether it reflects a more general performance monitoring process. To answer this conundrum, we investigated metacognitive monitoring in two related, yet distinct academic domains: arithmetic and spelling. This allowed us to investigate whether monitoring in one domain correlated with monitoring in the other domain, and whether monitoring in one domain was predictive of performance in the other, and vice versa. Participants were 147 typically developing 8-9-year-old children (Study 1) and 77 typically developing 7-8-year-old children (Study 2), who were in the middle of an important developmental period for both metacognitive monitoring and academic skills. Pre-registered analyses revealed that within-domain metacognitive monitoring was an important predictor of arithmetic and spelling at both ages. In 8-9-year-olds the metacognitive monitoring measures in different academic domains were predictive of each other, even after taking into account academic performance in these domains. Monitoring in arithmetic was an important predictor of spelling performance, even when arithmetic performance was controlled for. Likewise, monitoring in spelling was an important predictor of arithmetic performance, even when spelling performance was controlled for. In 7-8-year-olds metacognitive monitoring was domain-specific, with neither correlations between the monitoring measures, nor correlations between monitoring in one domain and performance in the other. Taken together, these findings indicate that more domain-general metacognitive monitoring processes emerge over the ages from 7 to 9.
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http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0229932PLOS
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7067420PMC
June 2020

Editorial: Individual Differences in Arithmetical Development.

Front Psychol 2019 3;10:2672. Epub 2019 Dec 3.

Department of Experimental Clinical and Health Psychology, Ghent University, Ghent, Belgium.

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http://dx.doi.org/10.3389/fpsyg.2019.02672DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6902078PMC
December 2019

Are preschoolers who spontaneously create patterns better in mathematics?

Br J Educ Psychol 2020 Sep 9;90(3):753-769. Epub 2019 Dec 9.

Centre for Instructional Psychology and Technology, KU Leuven, Belgium.

Background: Early patterning competence has recently been identified as an important precursor of mathematical development. Whereas the focus of this research has been on children's ability regarding repeating patterns, children might also differ in their spontaneous attention to patterns.

Aims: The present study aimed to explore 4- to 5-year olds' Spontaneous Focusing On Patterns (SFOP) and its association with their patterning and mathematical ability.

Sample: Participants were 378 children (M  = 4 years 10 months; 191 boys) from 17 preschools.

Methods: Spontaneous Focusing On Patterns was measured with a construction task in which children had to build a tower with 15 blocks of three different colours. The constructions of the children were grouped into three categories (i.e., pattern, random, and sorting). We additionally administered tasks assessing their patterning ability, mathematical ability, spatial ability, and visuospatial working memory.

Results: When building a tower, 37% of the preschoolers spontaneously created a pattern, 49% made a random construction, and 14% sorted the blocks per colour. Preschoolers who spontaneously created a pattern had better patterning and mathematical ability than children in the random group. Group differences in patterning ability and spatial skills accounted for the difference in mathematical ability.

Conclusions: The current data suggest that children's spontaneous attention to patterns is an important component of their mathematical ability. Children's spontaneous pattern constructions may provide opportunities to discuss and practice patterns in preschool settings or at home, but more research is required to further analyse the role of SFOP in early mathematical development.
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http://dx.doi.org/10.1111/bjep.12329DOI Listing
September 2020

The association of grey matter volume and cortical complexity with individual differences in children's arithmetic fluency.

Neuropsychologia 2020 02 3;137:107293. Epub 2019 Dec 3.

Parenting and Special Education Research Unit, KU Leuven, Belgium. Electronic address:

Only a small amount of studies have looked at the structural neural correlates of children's arithmetic. Furthermore, these studies mainly implemented voxel-based morphometry, which only takes the volume of regions into account, without looking at other structural properties. The current study aimed to contribute knowledge on which brain regions are important for children's arithmetic on a structural level, by not only implementing voxel-based morphometry, but also cortical complexity analyses, based on the fractal dimension index. This complexity measure describes a characteristic of surface shape. Data of 43 typically developing 9-10 year-olds were analyzed. All children were asked to take part in two test sessions: behavioral data collection and MRI data acquisition. For data analysis, mean values for volume and cortical complexity were estimated within regions of interest (ROIs) and extracted for further analysis. The selected ROIs were based on regions found to be related to children's mathematical abilities in previous research. Results point towards associations between arithmetic fluency and the volume of the right fusiform gyrus, as well as the cortical complexity of the left postcentral gyrus, right insular sulcus, and left lateral orbital sulcus. Remarkably, no significant associations were observed between the children's arithmetic fluency and the volume or cortical complexity of typically arithmetic-associated parietal regions, such as the superior parietal lobe, intraparietal sulcus, or angular gyrus. Accordingly, the current study highlights the importance of structural characteristics of brain regions other than these typically arithmetic-associated parietal regions for children's arithmetic fluency.
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http://dx.doi.org/10.1016/j.neuropsychologia.2019.107293DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7000239PMC
February 2020

Interference during the retrieval of arithmetic and lexico-semantic knowledge modulates similar brain regions: Evidence from functional magnetic resonance imaging (fMRI).

Cortex 2019 11 19;120:375-393. Epub 2019 Jul 19.

Educational Neuroscience, Institute of Psychology, University of Graz, Austria. Electronic address:

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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http://dx.doi.org/10.1016/j.cortex.2019.06.007DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6853793PMC
November 2019

Distinguishing between cognitive explanations of the problem size effect in mental arithmetic via representational similarity analysis of fMRI data.

Neuropsychologia 2019 09 12;132:107120. Epub 2019 Jun 12.

Georgetown University, Psychology Department, United States. Electronic address:

Not all researchers interested in human behavior remain convinced that modern neuroimaging techniques have much to contribute to distinguishing between competing cognitive models for explaining human behavior, especially if one removes reverse inference from the table. Here, we took up this challenge in an attempt to distinguish between two competing accounts of the problem size effect (PSE), a robust finding in investigations of mathematical cognition. The PSE occurs when people solve arithmetic problems and indicates that numerically large problems are solved more slowly and erroneously than small problems. Neurocognitive explanations for the PSE can be categorized into representation-based and process-based views. Behavioral and traditional univariate neural measures have struggled to distinguish between these accounts. By contrast, a representational similarity analysis (RSA) approach with fMRI data provides competing hypotheses that can distinguish between accounts without recourse to reverse inference. To that end, our RSA (but not univariate) results provided clear evidence in favor of the representation-based over the process-based account of the PSE in multiplication; for addition, the results were less clear. Post-hoc similarity analysis distinguished still further between competing representation-based theoretical accounts. Namely, data favored the notion that individual multiplication problems are stored as individual memory traces sensitive to input frequency over a strictly magnitude-based account of memory encoding. Together, these results provide an example of how human neuroimaging evidence can directly inform cognitive-level explanations of a common behavioral phenomenon, the problem size effect. More broadly, these data may expand our understanding of calculation and memory systems in general.
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http://dx.doi.org/10.1016/j.neuropsychologia.2019.107120DOI Listing
September 2019

The neural substrates of the problem size and interference effect in children's multiplication: An fMRI study.

Brain Res 2019 07 2;1714:147-157. Epub 2019 Mar 2.

Parenting and Special Education Research Unit, KU Leuven, Leopold Vanderkelenstraat 32, Box 3765, 3000 Leuven, Belgium.

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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http://dx.doi.org/10.1016/j.brainres.2019.03.002DOI Listing
July 2019

More than number sense: The additional role of executive functions and metacognition in arithmetic.

J Exp Child Psychol 2019 06 23;182:38-60. Epub 2019 Feb 23.

Faculty of Psychology and Educational Sciences, Parenting and Special Education Research Group, KU Leuven, 3000 Leuven, Belgium.

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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http://dx.doi.org/10.1016/j.jecp.2019.01.012DOI Listing
June 2019

Disentangling Neural Sources of Problem Size and Interference Effects in Multiplication.

J Cogn Neurosci 2019 03 20;31(3):453-467. Epub 2018 Nov 20.

Georgetown University.

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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http://dx.doi.org/10.1162/jocn_a_01359DOI Listing
March 2019

Relating individual differences in white matter pathways to children's arithmetic fluency: a spherical deconvolution study.

Brain Struct Funct 2019 Jan 13;224(1):337-350. Epub 2018 Oct 13.

Parenting and Special Education Research Unit, KU Leuven, Leopold Vanderkelenstraat 32, box 3765, 3000, Leuven, Belgium.

Connectivity between brain regions is integral to efficient complex cognitive processing, making the study of white matter pathways in clarifying the neural mechanisms of individual differences in arithmetic abilities critical. This white matter connectivity underlying arithmetic has only been investigated through classic diffusion tensor imaging, which, due to methodological limitations, might lead to an oversimplification of the underlying anatomy. More complex non-tensor models, such as spherical deconvolution, however, allow a much more fine-grained delineation of the underlying brain anatomy. Against this background, the current study is the first to use spherical deconvolution to investigate white matter tracts and their relation to individual differences in arithmetic fluency in typically developing children. Participants were 48 typically developing 9-10-year-olds, who were all in grade 4, and who underwent structural diffusion-weighted magnetic resonance imaging scanning. Theoretically relevant white matter tracts were manually delineated with a region of interest approach, after which the hindrance modulated orientational anisotropy (HMOA) index, which provides information on the structural integrity of the tract at hand, was derived for each tract. These HMOA indices were correlated with measures of arithmetic fluency, using frequentist and Bayesian approaches. Our results point towards an association between the HMOA of the right inferior longitudinal fasciculus and individual differences in arithmetic fluency. This might reflect the efficiency with which children process Arabic numerals. Other previously found associations between white matter and individual differences in arithmetic fluency were not observed.
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http://dx.doi.org/10.1007/s00429-018-1770-6DOI Listing
January 2019

Patterning counts: Individual differences in children's calculation are uniquely predicted by sequence patterning.

J Exp Child Psychol 2019 01 8;177:152-165. Epub 2018 Sep 8.

Faculty of Psychology and Educational Sciences, KU Leuven-University of Leuven, B-3000 Leuven, Belgium. Electronic address:

Many studies have examined the cognitive determinants of children's calculation, yet the specific contribution of children's patterning abilities to calculation remains relatively unexplored. This study investigated whether children's ability to complete sequence patterns (i.e., add the missing element into 2-4-?-8) uniquely predicted individual differences in calculation and whether these associations differed depending on the type of stimuli in these sequence patterns (i.e., number, letter, time, or rotation). Participants were 65 children in first and second grade (M = 7.40 years, SD = 0.44). All children completed four tasks of sequence patterning: number, letter, time, and rotation. Calculation was measured via addition and subtraction tasks. We also measured cognitive determinants of individual differences in calculation-namely symbolic number comparison, motor processing speed, visuospatial working memory, and nonverbal IQ-to verify whether patterning predicted calculation when controlling for these additional measures. We observed significant relationships between the patterning dimensions and calculation, except for the rotation dimension. Follow-up regressions, controlling for the aforementioned cognitive determinants of calculation, revealed that the number and time dimensions were strong predictors of calculation, whereas the evidence for the letter dimension was only anecdotal and the evidence for the rotation dimension was nonexistent, suggesting some degree of specificity of different types of sequence patterning in predicting calculation. Symbolic magnitude processing remained a powerful unique correlate of calculation performance. These findings add to our understanding of individual differences in calculation ability, such that sequence patterning could begin to be considered as one of the cognitive skills underlying calculation ability in young children.
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http://dx.doi.org/10.1016/j.jecp.2018.07.016DOI Listing
January 2019

Gender equality in 4- to 5-year-old preschoolers' early numerical competencies.

Dev Sci 2019 01 2;22(1):e12718. Epub 2018 Sep 2.

Parenting and Special Education Research Unit, Faculty of Psychology and Educational Sciences, KU Leuven, Leuven, Belgium.

Numerical competencies acquired in preschool are foundational and predictive for children's later mathematical development. It remains to be determined whether there are gender differences in these early numerical competencies which could explain the often-reported gender differences in later mathematics and STEM-related abilities. Using a Bayesian approach, we quantified the evidence in favor of the alternative hypothesis of gender differences versus the null hypothesis of gender equality. Participants were 402 4- to 5-year-old children attending preschool in Flanders (Belgium). Children were selected via stratified cluster sampling to represent the full range of socioeconomic backgrounds. All children completed eight numerical tasks (verbal counting, object counting, numeral recognition, symbolic comparison, nonsymbolic comparison, nonverbal calculation, number order, dot enumeration). Results supported the gender equality hypothesis, and this evidence was substantial for seven of the eight numerical tasks. Preschoolers' early numerical competencies are characterized by gender equality. They probably do not explain later-reported gender differences.
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http://dx.doi.org/10.1111/desc.12718DOI Listing
January 2019

Multi-method brain imaging reveals impaired representations of number as well as altered connectivity in adults with dyscalculia.

Neuroimage 2019 04 7;190:289-302. Epub 2018 Jun 7.

Parenting and Special Education Research Unit, Faculty of Psychology and Educational Sciences, KU Leuven, Leuven, 3000, Belgium.

Two hypotheses have been proposed about the etiology of neurodevelopmental learning disorders, such as dyslexia and dyscalculia: representation impairments and disrupted access to representations. We implemented a multi-method brain imaging approach to directly investigate these representation and access hypotheses in dyscalculia, a highly prevalent but understudied neurodevelopmental disorder in learning to calculate. We combined several magnetic resonance imaging methods and analyses, including univariate and multivariate analyses, functional and structural connectivity. Our sample comprised 24 adults with dyscalculia and 24 carefully matched controls. Results showed a clear deficit in the non-symbolic magnitude representations in parietal, temporal and frontal regions, as well as hyper-connectivity in visual brain regions in adults with dyscalculia. Dyscalculia in adults was thereby related to both impaired number representations and altered connectivity in the brain. We conclude that dyscalculia is related to impaired number representations as well as altered access to these representations.
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http://dx.doi.org/10.1016/j.neuroimage.2018.06.012DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6494208PMC
April 2019

Dyscalculia and dyslexia: Different behavioral, yet similar brain activity profiles during arithmetic.

Neuroimage Clin 2018 4;18:663-674. Epub 2018 Mar 4.

Parenting and Special Education Research Unit, KU Leuven, Belgium. Electronic address:

Brain disorders are often investigated in isolation, but very different conclusions might be reached when studies directly contrast multiple disorders. Here, we illustrate this in the context of specific learning disorders, such as dyscalculia and dyslexia. While children with dyscalculia show deficits in arithmetic, children with dyslexia present with reading difficulties. Furthermore, the comorbidity between dyslexia and dyscalculia is surprisingly high. Different hypotheses have been proposed on the origin of these disorders (number processing deficits in dyscalculia, phonological deficits in dyslexia) but these have never been directly contrasted in one brain imaging study. Therefore, we compared the brain activity of children with dyslexia, children with dyscalculia, children with comorbid dyslexia/dyscalculia and healthy controls during arithmetic in a design that allowed us to disentangle various processes that might be associated with the specific or common neural origins of these learning disorders. Participants were 62 children aged 9 to 12, 39 of whom had been clinically diagnosed with a specific learning disorder (dyscalculia and/or dyslexia). All children underwent fMRI scanning while performing an arithmetic task in different formats (dot arrays, digits and number words). At the behavioral level, children with dyscalculia showed lower accuracy when subtracting dot arrays, and all children with learning disorders were slower in responding compared to typically developing children (especially in symbolic formats). However, at the neural level, analyses pointed towards substantial neural similarity between children with learning disorders: Control children demonstrated higher activation levels in frontal and parietal areas than the three groups of children with learning disorders, regardless of the disorder. A direct comparison between the groups of children with learning disorders revealed similar levels of neural activation throughout the brain across these groups. Multivariate subject generalization analyses were used to statistically test the degree of similarity, and confirmed that the neural activation patterns of children with dyslexia, dyscalculia and dyslexia/dyscalculia were highly similar in how they deviated from neural activation patterns in control children. Collectively, these results suggest that, despite differences at the behavioral level, the brain activity profiles of children with different learning disorders during arithmetic may be more similar than initially thought.
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http://dx.doi.org/10.1016/j.nicl.2018.03.003DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5987869PMC
January 2019

Associations of Number Line Estimation With Mathematical Competence: A Meta-analysis.

Child Dev 2018 09 10;89(5):1467-1484. Epub 2018 Apr 10.

University of Leuven.

The number line estimation task is widely used to investigate mathematical learning and development. The present meta-analysis statistically synthesized the extensive evidence on the correlation between number line estimation and broader mathematical competence. Averaged over 263 effect sizes with 10,576 participants with sample mean ages from 4 to 14 years, this correlation was r = .443. The correlation increased with age, mainly because it was higher for fractions than for whole numbers. The correlation remained stable across a wide range of task variants and mathematical competence measures (i.e., counting, arithmetic, school achievement). These findings demonstrate that the task is a robust tool for diagnosing and predicting broader mathematical competence and should be further investigated in developmental and experimental training studies.
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http://dx.doi.org/10.1111/cdev.13068DOI Listing
September 2018

Frequency of Home Numeracy Activities Is Differentially Related to Basic Number Processing and Calculation Skills in Kindergartners.

Front Psychol 2018 22;9:340. Epub 2018 Mar 22.

Brain and Cognition, Faculty of Psychology and Educational Sciences, KU Leuven, Leuven, Belgium.

Home numeracy has been shown to play an important role in children's mathematical performance. However, findings are inconsistent as to which home numeracy activities are related to which mathematical skills. The present study disentangled between various mathematical abilities that were previously masked by the use of composite scores of mathematical achievement. Our aim was to shed light on the specific associations between home numeracy and various mathematical abilities. The relationships between kindergartners' home numeracy activities, their basic number processing and calculation skills were investigated. Participants were 128 kindergartners ( = 5.43 years, = 0.29, range: 4.88-6.02 years) and their parents. The children completed non-symbolic and symbolic comparison tasks, non-symbolic and symbolic number line estimation tasks, mapping tasks (enumeration and connecting), and two calculation tasks. Their parents completed a home numeracy questionnaire. Results indicated small but significant associations between formal home numeracy activities that involved (i.e., identifying numerals, counting) and children's enumeration skills. There was no correlation between formal home numeracy activities and non-symbolic number processing. Informal home numeracy activities that involved , such as "playing games" and "using numbers in daily life," were (weakly) correlated with calculation and symbolic number line estimation, respectively. The present findings suggest that disentangling between various basic number processing and calculation skills in children might unravel specific relations with both formal and informal home numeracy activities. This might explain earlier reported contradictory findings on the association between home numeracy and mathematical abilities.
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http://dx.doi.org/10.3389/fpsyg.2018.00340DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5874519PMC
March 2018

Arithmetic skills correlate negatively with the overlap of symbolic and non-symbolic number representations in the brain.

Cortex 2018 04 31;101:306-308. Epub 2018 Jan 31.

Brain and Cognition, Faculty of Psychology and Educational Sciences, KU Leuven, Leuven, 3000, Belgium.

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http://dx.doi.org/10.1016/j.cortex.2018.01.008DOI Listing
April 2018

Interference and problem size effect in multiplication fact solving: Individual differences in brain activations and arithmetic performance.

Neuroimage 2018 05 11;172:718-727. Epub 2018 Feb 11.

Educational Neuroscience, Institute of Psychology, University of Graz, Austria.

In the development of math ability, a large variability of performance in solving simple arithmetic problems is observed and has not found a compelling explanation yet. One robust effect in simple multiplication facts is the problem size effect, indicating better performance for small problems compared to large ones. Recently, behavioral studies brought to light another effect in multiplication facts, the interference effect. That is, high interfering problems (receiving more proactive interference from previously learned problems) are more difficult to retrieve than low interfering problems (in terms of physical feature overlap, namely the digits, De Visscher and Noël, 2014). At the behavioral level, the sensitivity to the interference effect is shown to explain individual differences in the performance of solving multiplications in children as well as in adults. The aim of the present study was to investigate the individual differences in multiplication ability in relation to the neural interference effect and the neural problem size effect. To that end, we used a paradigm developed by De Visscher, Berens, et al. (2015) that contrasts the interference effect and the problem size effect in a multiplication verification task, during functional magnetic resonance imaging (fMRI) acquisition. Forty-two healthy adults, who showed high variability in an arithmetic fluency test, participated in our fMRI study. In order to control for the general reasoning level, the IQ was taken into account in the individual differences analyses. Our findings revealed a neural interference effect linked to individual differences in multiplication in the left inferior frontal gyrus, while controlling for the IQ. This interference effect in the left inferior frontal gyrus showed a negative relation with individual differences in arithmetic fluency, indicating a higher interference effect for low performers compared to high performers. This region is suggested in the literature to be involved in resolution of proactive interference. Besides, no correlation between the neural problem size effect and multiplication performance was found. This study supports the idea that the interference due to similarities/overlap of physical traits (the digits) is crucial in memorizing arithmetic facts and in determining individual differences in arithmetic.
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http://dx.doi.org/10.1016/j.neuroimage.2018.01.060DOI Listing
May 2018

Investigating the relationship between two home numeracy measures: A questionnaire and observations during Lego building and book reading.

Br J Dev Psychol 2018 06 2;36(2):354-370. Epub 2018 Feb 2.

Brain and Cognition, Faculty of Psychology and Educational Sciences, KU Leuven, Belgium.

Home numeracy has been defined as the parent-child interactions that include experiences with numerical content in daily-life settings. Previous studies have commonly operationalized home numeracy either via questionnaires or via observational methods. These studies have shown that both types of measures are positively related to variability in children's mathematical skills. This study investigated whether these distinctive data collection methods index the same aspect of home numeracy. The frequencies of home numeracy activities and parents' opinions about their children's mathematics education were assessed via a questionnaire. The amount of home numeracy talk was observed via two semi-structured videotaped parent-child activity sessions (Lego building and book reading). Children's mathematical skills were examined with two calculation subtests. We observed that parents' reports and number of observed numeracy interactions were not related to each other. Interestingly, parents' reports of numeracy activities were positively related to children's calculation abilities, whereas the observed home numeracy talk was negatively related to children's calculation abilities. These results indicate that these two methods tap on different aspects of home numeracy. Statement of contribution What is already known on this subject? Home numeracy, that is, parent-child interactions that include experiences with numerical content, is supposed to have a positive impact on calculation or mathematical ability in general. Despite many positive results, some studies have failed to find such an association. Home numeracy has been assessed with questionnaires on the frequency of numerical experiences and observations of parent-child interactions; however, those two measures of home numeracy have never been compared directly. What does this study add? This study assessed home numeracy through questionnaires and observations in the 44 parent-child dyads and showed that home numeracy measures derived from questionnaires and observations are not related. Moreover, the relation between the reported frequency of home numeracy activities and calculation on the one hand, and parent-child number talk (derived from observations) and calculation on the other hand is in opposite directions; the frequency of activities is positively related to calculation performance; and the amount of number talk is negatively related to calculation. This study shows that both measures tap into different aspects of home numeracy and can be an important factor explaining inconsistencies in literature.
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http://dx.doi.org/10.1111/bjdp.12235DOI Listing
June 2018

Verbal and action-based measures of kindergartners' SFON and their associations with number-related utterances during picture book reading.

Br J Educ Psychol 2018 Dec 20;88(4):550-565. Epub 2017 Nov 20.

Centre for Instructional Psychology and Technology, KU Leuven, Belgium.

Background: Young children's spontaneous focusing on numerosity (SFON) as measured by experimental tasks is related to their mathematics achievement. This association is hypothetically explained by children's self-initiated practice in number recognition during everyday activities. As such, experimentally measured SFON should be associated with SFON exhibited during everyday activities and play. However, prior studies investigating this assumed association provided inconsistent findings.

Aims: We aimed to address this issue by investigating the association between kindergartners' SFON as measured by two different experimental tasks and the frequency of their number-related utterances during a typical picture book reading activity.

Sample: Participants were 65 4- to 6-year-olds in kindergarten (before the start of formal education).

Methods: Kindergartners individually participated in two sessions. First, they completed an action-based SFON Imitation task and a verbal SFON Picture task, with a short visuo-motor task in between. Next, children were invited to spontaneously comment on the pictures of a picture book during a typical picture book reading activity.

Results: Results revealed a positive association between children's SFON as measured by the Picture task and the frequency of their number-related utterances during typical picture book reading, but no such association for the Imitation task.

Conclusions: Our findings indicate that children with higher SFON as measured by a verbal experimental task also tend to focus more frequently on number during verbal everyday activities, such as picture book reading. In view of the divergent associations between our SFON measures under study with everyday number activities, the current data suggest that SFON may not be a unitary construct and/or might be task-dependent.
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http://dx.doi.org/10.1111/bjep.12201DOI Listing
December 2018

Developmental trajectories of children's symbolic numerical magnitude processing skills and associated cognitive competencies.

J Exp Child Psychol 2018 Feb 22;166:232-250. Epub 2017 Sep 22.

Parenting and Special Education Research Unit, Faculty of Psychology and Educational Sciences, University of Leuven, 3000 Leuven, Belgium.

Although symbolic numerical magnitude processing skills are key for learning arithmetic, their developmental trajectories remain unknown. Therefore, we delineated during the first 3years of primary education (5-8years of age) groups with distinguishable developmental trajectories of symbolic numerical magnitude processing skills using a model-based clustering approach. Three clusters were identified and were labeled as inaccurate, accurate but slow, and accurate and fast. The clusters did not differ in age, sex, socioeconomic status, or IQ. We also tested whether these clusters differed in domain-specific (nonsymbolic magnitude processing and digit identification) and domain-general (visuospatial short-term memory, verbal working memory, and processing speed) cognitive competencies that might contribute to children's ability to (efficiently) process the numerical meaning of Arabic numerical symbols. We observed minor differences between clusters in these cognitive competencies except for verbal working memory for which no differences were observed. Follow-up analyses further revealed that the above-mentioned cognitive competencies did not merely account for the cluster differences in children's development of symbolic numerical magnitude processing skills, suggesting that other factors account for these individual differences. On the other hand, the three trajectories of symbolic numerical magnitude processing revealed remarkable and stable differences in children's arithmetic fact retrieval, which stresses the importance of symbolic numerical magnitude processing for learning arithmetic.
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http://dx.doi.org/10.1016/j.jecp.2017.08.008DOI Listing
February 2018

Strategy over operation: neural activation in subtraction and multiplication during fact retrieval and procedural strategy use in children.

Hum Brain Mapp 2017 09 19;38(9):4657-4670. Epub 2017 Jun 19.

Parenting and Special Education Research Unit, KU Leuven, Leuven, Belgium.

Arithmetic development is characterized by strategy shifts between procedural strategy use and fact retrieval. This study is the first to explicitly investigate children's neural activation associated with the use of these different strategies. Participants were 26 typically developing 4th graders (9- to 10-year-olds), who, in a behavioral session, were asked to verbally report on a trial-by-trial basis how they had solved 100 subtraction and multiplication items. These items were subsequently presented during functional magnetic resonance imaging. An event-related design allowed us to analyze the brain responses during retrieval and procedural trials, based on the children's verbal reports. During procedural strategy use, and more specifically for the decomposition of operands strategy, activation increases were observed in the inferior and superior parietal lobes (intraparietal sulci), inferior to superior frontal gyri, bilateral areas in the occipital lobe, and insular cortex. For retrieval, in comparison to procedural strategy use, we observed increased activity in the bilateral angular and supramarginal gyri, left middle to inferior temporal gyrus, right superior temporal gyrus, and superior medial frontal gyrus. No neural differences were found between the two operations under study. These results are the first in children to provide direct evidence for alternate neural activation when different arithmetic strategies are used and further unravel that previously found effects of operation on brain activity reflect differences in arithmetic strategy use. Hum Brain Mapp 38:4657-4670, 2017. © 2017 Wiley Periodicals, Inc.
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http://dx.doi.org/10.1002/hbm.23691DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6866817PMC
September 2017