Bert De Smedt

• Prof. Dr.
• Professor at KU Leuven

In this chapter I summarize research on individual differences in arithmetic fact retrieval through the lens of educational neuroscience. By generating predictions about underlying cognitive processes based on neuroimaging data, developmental behavioral studies have revealed that symbolic numerical magnitude processing plays a unique role in childr...

Many studies have demonstrated that auditory attention to natural speech can be decoded from EEG data. However, most studies focus on selective auditory attention decoding (sAAD) with competing speakers, while the dynamics of absolute auditory attention decoding (aAAD) to a single target remains underexplored. The goal of aAAD is to measure the deg...

Nous présentons l’instrument de mesure Math4Speed (M4S), un test papier-crayon combinant les quatre opérations arithmétiques avec des items de complexité variable. Le test M4S comprend 50 problèmes d’addition, 50 problèmes de soustraction, 50 problèmes de multiplication et 50 problèmes de division, limités à 2 minutes par opération. L’évaluation ps...

Children's white matter development is driven by experience, yet it remains poorly understood how it is shaped by attending formal education. A small number of studies compared children before and after the start of formal schooling to understand this, yet they do not allow to separate maturational effects from schooling‐related effects. A clever w...

This 5‐year longitudinal study examined whether high mathematics achievers in primary school had cognitive advantages before entering formal education. High mathematics achievement was defined as performing above Pc 90 in Grades 1 and 3. The predominantly White sample ( M age in preschool: 64 months) included 31 high achievers (12 girls) and 114 av...

In recent years, an increasing number of studies have examined the association between mathematical abilities and executive functions (EFs). However, it remains unknown via which mechanisms’ mathematical performance is associated with EFs. The current study examined the associations of overall task proficiency, strategy selection, and strategy exec...

This study is the first to examine the associations between the occurrence, frequency, and adaptivity of children’s subtraction by addition strategy use (SBA; e.g., 712 − 346 = ?; 346 + 54 = 400, 400 + 300 = 700, 700 + 12 = 712, and 54 + 300 + 12 = 366) and their underlying conceptual knowledge. Specifically, we focused on two rarely studied compon...

Early detection of and relevant information on children’s mathematical difficulties is important to initiate targeted teaching and intervention. This study investigated the extent to which strategy use in single-digit addition provides additional predictive information about 61 grade one children’s (6-year-old) mathematical achievement 3 years late...

Background We present a dashboard for the evaluation of the impact of school closures on children and parents during the first wave of the COVID pandemic in 2020 on the various components of wellbeing. Methods Starting from an explorative literature search by a team of experts from diverse fields (e.g., epidemiology, virology, psychology, educatio...

Diffusion-weighted imaging studies in preschoolers have almost exclusively been done in the field of reading. As a result, virtually nothing is known about white matter tracts associated with individual differences in mathematics at this age. Studying the preschoolers’ brain is crucial because it allows us to identify individual differences in brai...

Arithmetic development is quintessential for learning more advanced mathematics. A key aspect of arithmetic development is a shift from calculation-based procedural strategies to memory-based fact retrieval. For example, children start to learn 3 × 4 by adding 4 + 4 + 4, which is an example of a procedure. After enough repetitions, this becomes an...

While symbolic number processing is an important correlate for typical and low mathematics achievement, it remains to be determined whether children with high mathematics achievement also have excellent symbolic number processing abilities. We investigated this question in 64 children (aged 8 to 10), i.e., 32 children with persistent high achieveme...

In 2016, we started a 6-year-longitudinal research project on the development of 4- to 9-year-olds’ competencies in four early core mathematical domains, i.e., (1) mathematical patterns and structures, (2) computational estimation, (3) proportional reasoning, and (4) probabilistic reasoning. These four competencies are conceived of as a combination...

When solving subtraction problems such as 83–46, children use the direct subtraction (DS) strategy (e.g., 83 – 40 = 43, 43 – 6 = 37) or the subtraction by addition (SBA) strategy (e.g., 46 + 4 = 50, 50 + 30 = 80, 80 + 3 = 83, so the answer is 4 + 30 + 3 = 37). This study is the first to use the choice/no-choice method to examine DS and SBA use in t...

This study investigated age group differences in Spontaneous Focusing on Numerosity (SFON) tendency and arithmetical skills across age groups with differing starting ages of formal mathematics instruction. Children (N = 685) aged 4-7 years participated from four countries, i.e., Northern Ireland, England, Belgium and Finland, where children start f...

Young children frequently make a peculiar counting mistake. When asked to count units that are sets of multiple items, such as the number of families at a party, they often count discrete items (i.e., individual people) rather than the number of sets (i.e., families). One explanation concerns children’s incomplete understanding of what constitutes...

Children start preschool with large individual differences in their early numerical abilities. Little is known about the importance of heterogeneous patterns that exist within these individual differences. A person-centered analytic approach might be helpful to unravel these patterns and the cognitive and environmental factors that are associated w...

This study examined adults’ frequent, efficient and adaptive use of direct subtraction (DS) and subtraction by addition (SBA) in mental multi-digit subtraction with the choice/no-choice method. Participants were offered subtractions in one choice condition (choice between DS and SBA) and two no-choice conditions (mandatory use of either DS or SBA)....

A disruption of white matter connectivity is negatively associated with language (recovery) in patients with aphasia after stroke, and behavioral gains have been shown to coincide with white matter neuroplasticity. However, most brain-behavior studies have been carried out in the chronic phase after stroke, with limited generalizability to earlier...

Although several studies have aimed for accurate predictions of language recovery in post stroke aphasia, individual language outcomes remain hard to predict. Large-scale prediction models are built using data from patients mainly in the chronic phase after stroke, although it is clinically more relevant to consider data from the acute phase. Previ...

The developmental literature has revealed a wide variety of factors that correlate with individual differences in mathematical cognition. These factors have been classified along the simple distinction between domain-specific and domain-general factors. Here, I review a series of recent meta-analyses that have summarized the existing evidence for e...

Investigating how the brain may constrain academic achievement is not only relevant to understanding brain structure but also to providing insight into the origins of individual differences in these academic abilities. In this pre-registered study, we investigated whether the variability of sulcal patterns, a qualitative feature of the brain determ...

There are massive developments in children’s early number skills in the ages 4- to 6-year old during which they attend preschool education and before they transition to formal school. We investigated to which extent these developments can be explained by children’ schooling experiences during preschool or by chronological age related maturational c...

It is well established that early general language during preschool is critical for children's mathematical abilities. In an attempt to further characterize this association between language and mathematics, an increasing number of studies show that one specific type of language, namely mathematical language or the key linguistic concepts that are...

The developmental literature has revealed a wide variety of factors that correlate with individual differences in mathematical cognition. These factors have been classified along the simple distinction between domain-specific and domain-general factors. Here, I review a series of recent meta-analyses that have summarized the existing evidence for e...

Young children frequently make a peculiar counting mistake. When asked to count abstract units, such as the number of families at a party, they often count discrete items (i.e. individual people) rather than the number of abstract units (i.e. families). A proposed explanation concerns children’s incomplete understanding of what constitutes a unit,...

Arithmetic learning is characterized by a change from procedural strategies to fact retrieval. fMRI training studies in adults have revealed that this change coincides with decreased activation in the prefrontal cortex (PFC) and that within the parietal lobe, a shift occurs from the intraparietal sulcus (IPS) to the angular gyrus (AG) during this c...

We investigated elementary school children's use of direct subtraction (DS) and subtraction by addition (SBA) when mentally solving multi-digit subtractions. Fourth- to sixth-grade children of varying mathematical achievement levels were offered subtractions in one choice condition (choice between DS or SBA) and two no-choice conditions (mandatory...

Numerous studies have identified neurophysiological correlates of performing arithmetic in adults. For example, oscillatory electroencephalographic (EEG) patterns associated with retrieval and procedural strategies are well established. Whereas fact retrieval has been linked to enhanced left-hemispheric theta ERS (event-related synchronization), pr...

The development of numerical and arithmetic abilities constitutes a crucial cornerstone in our modern and educated societies. Difficulties to acquire these central skills can lead to severe consequences for an individual’s well-being and nation’s economy. In the present review, we describe our current broad understanding of the functional and struc...

Ellis et al. (2021, this issue; in the following abbreviated as EEA) conducted a conceptual replication and extension of a recent meta-analysis relating number line estimation to broader mathematical competence (Schneider et al., 2018; in the following: SEA). EEA pooled and analyzed data from seven new studies and compared the results to SEA’s find...

Knowledge on statistical learning (SL) in healthy elderly is scarce. Theoretically, it is not clear whether aging affects modality-specific and/or domain-general learning mechanisms. Practically, there is a lack of research on simplified SL tasks, which would ease the burden of testing in clinical populations. Against this background, we conducted...

Both mathematics anxiety and metacognitive monitoring have been identified as associated with or predictive of individual differences in arithmetic achievement in primary school children. Although there are various theoretical reasons for an association between mathematics anxiety and metacognitive monitoring, it is unclear at the empirical level h...

Many studies in the past decades have focused on low and typical mathematics achievers, yet little is known about children with high mathematics achievement, particularly at a young age. The current study aimed to fill this gap and started from the early work of Krutetskii (1976) as a theoretical lens to study the characteristics of high mathematic...

How do different measures of brain structure correlate with individual differences in arithmetic fluency? This paper builds on two previously published studies in which individual differences in children’s arithmetic fluency were correlated with measures of white (Polspoel et al., 2019) and grey matter (Polspoel et al., 2020) in one sample of child...

This study presents a patterning intervention for 5-year-olds, who were in their third year of preschool in Flanders (Belgium), with two key elements: A focus on the structure of patterns, and the inclusion of growing patterns (e.g., ABAABAAAB) in addition to repeating patterns (e.g., ABABAB). We evaluated the impact of this intervention on pattern...

This article synthesizes findings from an international virtual conference, funded by the United States National Science Foundation, focused on the home mathematics environment (HME). In light of inconsistencies and gaps in research investigating relations between the HME and children’s outcomes, the purpose of the conference was to discuss actiona...

Numerous studies have identified neurophysiological correlates of performing arithmeticin adults. For example, oscillatory electroencephalographic(EEG) patterns associated with retrieval and procedural strategies are well established. Whereas fact retrieval has beenlinked to enhancedleft-hemispherictheta ERS(event-related synchronization), procedur...

This longitudinal cross-lagged panel study investigated the development of the structure of young children’s spontaneous number focusing tendencies and their longitudinal associations with numerical abilities and mathematics achievement over the course of a 3-year period, that is, in the second and third year of kindergarten and in first grade of p...

The current study examined upper elementary school children’s frequent, efficient and adaptive use of direct subtraction ( DS ) and subtraction by addition ( SBA ) when mentally solving multi-digit subtractions, replicating and expanding previous research by Torbeyns et al. (2018). First, children were offered subtractions in two choice conditions...

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 ret...

Investigating how the brain may constrain academic achievement is not only relevant to understanding brain structure but also to providing insight into the origins of individual differences in these academic abilities. In this pre-registered study, we investigated whether the variability of sulcal patterns, a qualitative feature of the brain determ...

Investigating how the brain may constrain academic achievement is not only relevant to understanding brain structure but also to providing insight into the origins of individual differences in these academic abilities. In this pre-registered study, we investigated whether the variability of sulcal patterns, a qualitative feature of the brain determ...

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...

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-lagge...

This chapter reflects on the impact of education on numerical cognition. Mathematics is a symbolic activity, which must be learned via education, and this learning process will impact on how we process number. There are huge differences in the educational contexts around the globe in which this learning occurs, but these contexts are relatively und...

In this chapter, we review a long-standing and comprehensive line of research on the use of the subtraction by addition (SBA) strategy when solving subtractions, in which our own research center has played an important role. We document this phenomenon in a variety of subdomains of the elementary arithmetic curriculum, ranging from single-digit men...

Selecting a large and diverse sample of 5-6-year-old preschool children (179 boys and 174 girls; M age = 70.03 months, SD age = 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...

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 com...

Children’s spontaneous focusing on Arabic number symbols (SFONS) has been identified as a relevant component of their early mathematical development. This study investigated whether SFONS is a separate construct from spontaneous focusing on numerosity (SFON) and examined whether it is uniquely related to numerical abilities and mathematics achievem...

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 a...

Children’s spontaneous focusing on Arabic number symbols (SFONS) has been identified as a relevant component of their early mathematical development. This study investigated whether SFONS is a separate construct from spontaneous focusing on numerosity (SFON) and examined whether it is uniquely related to numerical abilities and mathematics achievem...

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 focus...

Numerous studies have investigated brain changes associated with interventions targeting a range of language problems in patients with aphasia. We strive to integrate the results of these studies to examine (1) whether the focus of the intervention (i.e. phonology, semantics, orthography, syntax or rhythmic-melodic) determines in which brain region...

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 unde...

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:...

There is broad consensus that adults solve single-digit multiplication problems almost exclusively by fact retrieval (i.e., retrieval of the solution from an arithmetic fact network). 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 t...

In this chapter we review and discuss a relatively new line of research in the domain of early mathematical development that addresses the dispositional rather than the ability aspect of children’s early mathematical competence, namely their tendencies to attend to and focus on various mathematical elements in their environment and its relation wit...

Young children show large individual differences in their tendency to focus spontaneously on numerical aspects (e.g., numerosities or Arabic number symbols) of their everyday environment. The origins of these individual differences are unclear. Given the role of the home numeracy environment (HNE) in children’s early mathematical development and th...

By analyzing longitudinal data from the start to the end of primary education, we aimed to investigate whether symbolic numerical magnitude processing at the start of primary education predicted arithmetic at the end, and whether arithmetic at the start of primary education predicted later symbolic numerical magnitude processing skills at the end....

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 ar...

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’...

In this study, we aimed to address two gaps in research on early mathematical patterning, namely the lack of attention (1) to growing patterns and (2) to the association between different aspects of patterning and numerical ability. Participants were 400 four-year olds from a wide range of socioeconomic backgrounds. Children's patterning and numeri...

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 s...

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 competi...

Activities with patterns (e.g., making a necklace with alternating blue and red pearls) are common in many preschool and kindergarten settings. These activities are assumed to play an important role in children’s mathematical development. Nevertheless, most research on early mathematical development focuses on numerical and arithmetical abilities,...

Many studies have investigated the association between children’s spontaneous attention to number and their early mathematical abilities. This work has presented number in a non-symbolic format by exclusively using numerosities as their stimuli. Therefore, little is known about children’s spontaneous attention for Arabic number symbols. We aimed to...

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 ne...

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...

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-gen...

Preliminary results of study on neurobiological basis of metacognitive monitoring in children during arithmetic performance.

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,...

In this commentary, I reflect from a neurocognitive perspective on the four chapters on natural number development included in this section. These chapters show that the development of seemingly basic number processing is much more complex than is often portrayed in neurocognitive research. The chapters collectively illustrate that children’s devel...

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 di...

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 10576 participants with sample mean ages from 4 to...

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...

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 (...

We investigated the use of the subtraction by addition strategy, an important mental calculation strategy in children with different levels of mathematics achievement. In doing so we relied on Siegler’s cognitive psychological model of strategy change (Lemaire & Siegler, 1995), which defines strategy competencies in terms of four parameters (strate...

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 prevalen...

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 mathemati...

Multivariate analyses in smaller ROIs.

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...

Children’s Spontaneous Focusing On Numerosity (SFON) predicts later mathematics performance. This association is assumed to rely on children’s self-initiated practice in number recognition during everyday activities, which would enhance their further mathematical development. Consequently, SFON in experimental tasks should be associated with SFON d...

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 chi...

Individual differences in arithmetic have been explained by differences in cognitive processes and by arithmetic strategy use and selection. In the present study, we investigated the involvement of reactive and proactive control processes. We explored how variation in proactive and reactive control was related to individual differences in strategy...

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...