Cortical representations of numbers and nonsymbolic quantities expand and segregate in children from 5 to 8 years of age.

Number symbols, such as Arabic numerals, are cultural inventions that have transformed human mathematical skills. Although their acquisition is at the core of early elementary education in children, it remains unknown how the neural representations of numerals emerge during that period. It is also unclear whether these relate to an ontogenetically earlier sense of approximate quantity. Here, we used multivariate fMRI adaptation coupled with within- and between-format machine learning to probe the cortical representations of Arabic numerals and approximate nonsymbolic quantity in 89 children either at the beginning (age 5) or four years into formal education (age 8). Although the cortical representations of both numerals and nonsymbolic quantities expanded from age 5 to age 8, these representations also segregated with learning and development. Specifically, a format-independent neural representation of quantity was found in the right parietal cortex, but only for 5-year-olds. These results are consistent with the so-called symbolic estrangement hypothesis, which argues that the relation between symbolic and nonsymbolic quantity weakens with exposure to formal mathematics in children.

Assessing Theory of Mind in Children: A Tablet-Based Adaptation of a Classic Picture Sequencing Task.

Correctly assessing children's theory of mind (TOM) is essential to clinical practice. Yet, most tasks heavily rely on language, which is an obstacle for several populations. Langdon and Coltheart's (Cognition 71(1):43-71, 1999) Picture Sequencing Task (PST), developed for research purposes, avoids this limitation through a minimally-verbal procedure. We thus developed a tablet adaptation of this task for individual application, engaging children's motivation and allowing response times collection. To assess this tablet-PST, we first tested a large sample of neurotypical children (6-11 years-old, N = 248), whose results confirmed the task's structural and content validity, and permitted the construction of three standardized clinical indices. In a second experiment, we applied those to previously diagnosed autistic children (N = 23), who were expected to show atypical TOM performance. Children's outcomes were consistent with what was hypothesized and confirmed the task's external validity and moderate clinical sensitivity. The tablet-PST thus appears as a suitable tool, providing detailed profiles to inform clinical decisions.

Task-independent neural bases of peer presence effect on cognition in children and adults.

There is ample behavioral evidence that others' mere presence can affect any behavior in human and non-human animals, generally facilitating the expression of mastered responses while impairing the acquisition of novel ones. Much less is known about i) how the brain orchestrates the modulation of such a wide array of behaviors by others' presence and ii) when these neural underpinnings mature during development. To address these issues, fMRI data were collected in children and adults alternately observed and unobserved by a familiar peer. Subjects performed a numerosity comparison task and a phonological comparison task. While the former involves number-processing brain areas, the latter involves language-processing areas. Consistent with previous behavioral findings, adults' and children's performance improved in both tasks when observed by a peer. Across all participants, task-specific brain regions showed no reliable change in activity under peer observation. Rather, we found task-independent changes in domain-general brain regions typically involved in mentalizing, reward, and attention. Bayesian analyses singled out the attention network as the exception to the close child-adult resemblance of peer observation neural substrates. These findings suggest that i) social facilitation of some human education-related skills is primarily orchestrated by domain-general brain networks, rather than by task-selective substrates, and ii) apart from attention, peer presence neural processing is largely mature in children.

Neural representations of absolute and relative magnitudes in symbolic and nonsymbolic formats.

Humans differ from other animal species in their unique ability to use symbols to represent numerical information. This ability is thought to emerge from the "neural recycling" of mechanisms supporting nonsymbolic magnitudes in the intraparietal sulcus (IPS), a hypothesis that has been applied to both absolute magnitudes (e.g., whole numbers) and relative magnitudes (e.g., fractions). Yet, evidence for the neuronal recycling hypothesis is inconsistent for absolute magnitudes and scarce for relative magnitudes. Here, we investigated to what extent the neural representations of absolute and relative magnitudes in symbolic and nonsymbolic formats overlap in the IPS. In a functional magnetic resonance imaging (fMRI) adaptation design, 48 adult participants were sequentially presented with lines, whole numbers, line ratios, and fractions that varied (vs. not varied) in magnitudes. Univariate analyses showed that the extent to which IPS mechanisms associated with whole numbers relied on mechanisms associated with lines depended upon participants' arithmetic fluency. Multivariate analyses revealed that the right IPS encoded differences in format (nonsymbolic vs. symbolic) across both absolute and relative magnitudes. Therefore, IPS activity associated with magnitude processing may depend on the presentation format (nonsymbolic vs. symbolic) more than it depends on the type of magnitude (absolute vs. relative), at least for most adult participants.

The development of simple addition problem solving in children: Reliance on automatized counting or memory retrieval depends on both expertise and problem size.

In an experiment, 98 children aged 8 to 9, 10 to 12, and 13 to 15 years solved addition problems with a sum up to 10. In another experiment, the same children solved the same calculations within a sign priming paradigm where half the additions were displayed with the "+" sign 150 ms before the addends. Therefore, size effects and priming effects could be considered conjointly within the same populations. Our analyses revealed that small problems, constructed with addends from 1 to 4, presented a linear increase of solution times as a function of problem sums (i.e., size effect) in all age groups. However, an operator priming effect (i.e., facilitation of the solving process with the anticipated presentation of the "+" sign) was observed only in the group of oldest children. These results support the idea that children use a counting procedure that becomes automatized (as revealed by the priming effect) around 13 years of age. For larger problems and whatever the age group, no size or priming effects were observed, suggesting that the answers to these problems were already retrieved from memory at 8 to 9 years of age. For this specific category of large problems, negative slopes in solution times demonstrate that retrieval starts from the largest problems during development. These results are discussed in light of a horse race model in which procedures can win over retrieval.

Nurturing the Mathematical Brain: Home Numeracy Practices Are Associated With Children's Neural Responses to Arabic Numerals.

Disparities in home numeracy environments contribute to variations in children's mathematical skills. However, the neural mechanisms underlying the relation between home numeracy experiences and mathematical learning are unknown. Here, parents of 66 eight-year-olds completed a questionnaire assessing the frequency of home numeracy practices. Neural adaptation to the repetition of Arabic numerals and words was measured in children using functional MRI (n = 50) to assess how sensitive the brain is to the presentation of numerical and nonnumerical information. Disparities in home numeracy practices were related to differences in digit (but not word) processing in a region of the left intraparietal sulcus (IPS) that was also related to children's arithmetic fluency. Furthermore, digit-related processing in the IPS influenced the relation between home numeracy practices and arithmetic fluency. Results were consistent with a model hypothesizing that home numeracy practices may affect children's mathematical skills by modulating the IPS response to symbolic numerical information.

Neurocognitive basis of deductive reasoning in children varies with parental education.

The neurocognitive basis of elementary academic skills varies with parental socioeconomic status (SES). Little is known, however, about SES-related differences underlying higher-order cognitive skills that are critical for school success, such as reasoning. Here we used fMRI to examine how the neurocognitive basis of deductive reasoning varies as a function of parental education in school-aged children. Higher parental education was associated with greater reliance on the left inferior frontal gyrus when solving set-inclusion problems, consistent with other work suggesting that these problems might more heavily rely on verbal systems in the brain. In addition, children who are at the lower end of the parental education continuum, but have higher nonverbal skills relied on right parietal areas to a greater degree than their peers for solving set-inclusion problems. Finally, lower parental education children with higher verbal or nonverbal skill engaged dorsolateral prefrontal regions to a greater degree for set-inclusion and linear-order relations than their peers. These findings suggest that children with lower parental education rely on spatial and cognitive control mechanisms to achieve parity with their peers with parents who have more education. Better understanding variability in the neurocognitive networks that children recruit as a function of their parental factors might benefit future individualized interventions that best match children's characteristics.

Effects of Montessori Education on the Academic, Cognitive, and Social Development of Disadvantaged Preschoolers: A Randomized Controlled Study in the French Public-School System.

Previous research on Montessori preschool education is inconsistent and prone to analytic flexibility. In this preregistered study, disadvantaged preschoolers in a French public school were randomly assigned to either conventional or Montessori classrooms, with the latter being adapted to French public education. Adaptations included fewer materials, shorter work periods, and relatively limited Montessori teacher training. Cross-sectional analyses in kindergarten (N = 176; Mage  = 5-6) and longitudinal analyses over the 3 years of preschool (N = 70; Mage  = 3-6) showed that the adapted Montessori curriculum was associated with outcomes comparable to the conventional curriculum on math, executive functions, and social skills. However, disadvantaged kindergarteners from Montessori classrooms outperformed their peers on reading (d = 0.68). This performance was comparable to that of advantaged children from an accredited Montessori preschool.

What's Behind a "+" Sign? Perceiving an Arithmetic Operator Recruits Brain Circuits for Spatial Orienting.

Do mathematical symbols evoke spatial representations? Although behavioral studies have long demonstrated interactions between space and the processing of Arabic digits, how to interpret these results remains controversial. Here, we tested whether activity in regions supporting spatial processing contributes to the processing of symbols conveying fundamental arithmetic concepts-such as operation signs-even in the absence of associated digits. Using functional magnetic resonance imaging, we show that merely perceiving a "+" sign triggers activity in brain regions that support the orienting of spatial attention in adults. Activity in these regions was greater for "+" than for "×" signs, indicating that it is modulated by whether an operator reflects an operation that evokes numerical manipulation (rather than rote memorization). Finally, the degree to which subjects activated a spatial region in response to a "+" sign was correlated with the degree to which subjects benefited from being briefly presented with that sign before having to calculate a single-digit addition problem, an effect termed operator-priming. Therefore, not only are some arithmetic operators linked to spatial intuitions, but such intuitions might also have an important role during arithmetic calculation. More generally, our findings support the view that mathematical symbols inherently evoke spatial representations.

Lack of improvement in multiplication is associated with reverting from verbal retrieval to numerical operations.

Models of the neural basis of arithmetic argue that left inferior frontal cortex is involved in cognitive control of verbal representations of math facts in left lateral temporal cortex, whereas bilateral intra-parietal cortex is involved in numerical calculation. Lower levels of math competence for multiplications is associated with greater effortful retrieval because of less robust verbal representations and the engagement of numerical operations as a back-up strategy. Previous studies on multiplication have focused on brain activation in isolated nodes of the network, so we do not know how functional connectivity between these nodes is related to competence. Moreover, previous studies have not employed longitudinal designs, so we do not know how changes in multiplication performance over time is related to changes in its neural basis. The objective of this study was to investigate how changes in multiplication task performance is associated with changes in functional connectivity of temporal cortex with frontal and parietal cortices. Longitudinal data was collected from 45 children, with an average 2.2-year interval between the two sessions, when they were about 11 years old at time 1 (T1) and 13 years old at time 2 (T2). A Psychophysiological Interaction (PPI) analysis was carried out by defining the seed in the temporal cortex (i.e. posterior superior and middle temporal gyri) and examining changes in connectivity with frontal cortex (i.e. left inferior frontal gyrus) as well as parietal cortex (i.e. left and right inferior and superior parietal lobules). We found that children who did not improve in a multiplication task showed greater levels of functional connectivity of left temporal cortex with left inferior frontal gyrus (IFG) and left intraparietal sulcus (IPS) at T2, as compared to their peers who improved. The cluster showing greater levels of connectivity in the left IFG at T2 for the Non-improvers overlapped a cluster independently identified by a verbal localizer task and the cluster showing greater levels of connectivity in the left IPS Non-improvers overlapped a cluster independently identified by a numerosity localizer task. These results suggest that lack of improvement in multiplications are associated with greater cognitive control of verbal representations and greater engagement of numerical operations.

The neural development of pragmatic inference-making in natural discourse.

Older interlocutors are more likely than younger ones to make pragmatic inferences, that is, inferences that go beyond the linguistically encoded meaning of a sentence. Here we ask whether pragmatic development is associated with increased activity in brain structures associated with inference-making or in those associated with Theory of Mind. We employed a reading task that presents vignettes in one of two versions, one of which is expected to prompt more pragmatic processing. Both versions present a major premise containing three possibilities (e.g., Xavier is considering Thursday, Friday or Saturday for inviting his girlfriend out). In the Fully-Deductive (control) condition, the major premise is followed by two disjunction-elimination premises through two separate lines (one indicating that Saturday is not convenient and another saying that Thursday is not convenient); this is followed by a valid conclusion (e.g., "I'll reserve Friday"). In the Implicated-Premise condition, the first disjunction-elimination premise is followed by a second similar one that eliminates the same disjunction (e.g., both lines explain why Saturday is not convenient). In this condition, readers may pragmatically enrich the conclusion (i.e., "I'll reserve Friday" pragmatically implicates that Xavier is also eliminating Thursday from consideration). Reading times in Experiment 1 showed that processing the speaker's conclusion in the Implicated-Premise condition becomes increasingly more effort-demanding as readers reach adolescence. Experiment 2 showed that this developmental pattern is related to age-related increases in fMRI activity in fronto-parietal regions typically involved in inference-making processes. We found no evidence indicating age effects related to Theory of Mind areas.

The neural development of conditional reasoning in children: Different mechanisms for assessing the logical validity and likelihood of conclusions.

Scientific and mathematical thinking relies on the ability to evaluate whether conclusions drawn from conditional (if-then) arguments are logically valid. Yet, the neural development of this ability -- termed deductive reasoning -- is largely unknown. Here we aimed to identify the neural mechanisms that underlie the emergence of deductive reasoning with conditional rules in children. We further tested whether these mechanisms have their roots in the neural mechanisms involved in judging the likelihood of conclusions. In a functional Magnetic Resonance Imaging (fMRI) scanner, 8- to 13-year-olds were presented with causal conditional problems such as "If a baby is hungry then he will start crying; The baby is crying; Is the baby hungry?". In Validity trials, children were asked to indicate whether the conclusion followed out of necessity from the premises. In Likelihood trials, they indicated the degree of likelihood of the conclusion. We found that children who made accurate judgments of logical validity (as compared to those who did not) exhibited enhanced activity in left and medial frontal regions. In contrast, differences in likelihood ratings between children were related to differences of activity in right frontal and bilateral parietal regions. There was no overlap between the brain regions underlying validity and likelihood judgments. Therefore, our results suggest that the ability to evaluate the logical validity of conditional arguments emerges from brain mechanisms that qualitatively differ from those involved in evaluating the likelihood of these arguments in children.

Neural interaction between logical reasoning and pragmatic processing in narrative discourse.

Logical connectives (e.g., or, if, and not) are central to everyday conversation, and the inferences they generate are made with little effort in pragmatically sound situations. In contrast, the neural substrates of logical inference-making have been studied exclusively in abstract tasks where pragmatic concerns are minimal. Here, we used fMRI in an innovative design that employed narratives to investigate the interaction between logical reasoning and pragmatic processing in natural discourse. Each narrative contained three premises followed by a statement. In Fully-deductive stories, the statement confirmed a conclusion that followed from two steps of disjunction-elimination (e.g., Xavier considers Thursday, Friday, or Saturday for inviting his girlfriend out; he removes Thursday before he rejects Saturday and declares "I will invite her out for Friday"). In Implicated-premise stories, an otherwise identical narrative included three premises that twice removed a single option from consideration (i.e., Xavier rejects Thursday for two different reasons). The conclusion therefore necessarily prompts an implication (i.e., Xavier must have removed Saturday from consideration as well). We report two main findings. First, conclusions of Implicated-premise stories are associated with more activity than conclusions of Fully-deductive stories in a bilateral frontoparietal system, suggesting that these regions play a role in inferring an implicated premise. Second, brain connectivity between these regions increases with pragmatic abilities when reading conclusions in Implicated-premise stories. These findings suggest that pragmatic processing interacts with logical inference-making when understanding arguments in narrative discourse.

Distributed neural representations of logical arguments in school-age children.

Children's understanding of linear-order (e.g., Dan is taller than Lisa, Lisa is taller than Jess) and set-inclusion (i.e., All tulips are flowers, All flowers are plants) relationships is critical for the acquisition of deductive reasoning, that is, the ability to reach logically valid conclusions from given premises. Behavioral and neuroimaging studies in adults suggest processing differences between these relations: While arguments that involve linear-orders may be preferentially associated with spatial processing, arguments that involve set-inclusions may be preferentially associated with verbal processing. In this study, we used functional magnetic resonance imaging to investigate whether these processing differences appear during the period of elementary school in development. Consistent with previous studies in adults, we found that arguments that involve linear-order and set-inclusion relationships preferentially involve spatial and verbal brain mechanisms (respectively) in school-age children (9-14 year olds). Because this neural sensitivity was not related to age, it likely emerges before the period of elementary education. However, the period of elementary education might play an important role in shaping the neural processing of logical reasoning, as indicated by developmental changes in frontal and parietal regions that were dependent on the type of relation.

Parental socioeconomic status and the neural basis of arithmetic: differential relations to verbal and visuo-spatial representations.

We examined the relation of parental socioeconomic status (SES) to the neural bases of subtraction in school-age children (9- to 12-year-olds). We independently localized brain regions subserving verbal versus visuo-spatial representations to determine whether the parental SES-related differences in children's reliance on these neural representations vary as a function of math skill. At higher SES levels, higher skill was associated with greater recruitment of the left temporal cortex, identified by the verbal localizer. At lower SES levels, higher skill was associated with greater recruitment of right parietal cortex, identified by the visuo-spatial localizer. This suggests that depending on parental SES, children engage different neural systems to solve subtraction problems. Furthermore, SES was related to the activation in the left temporal and frontal cortex during the independent verbal localizer task, but it was not related to activation during the independent visuo-spatial localizer task. Differences in activation during the verbal localizer task in turn were related to differences in activation during the subtraction task in right parietal cortex. The relation was stronger at lower SES levels. This result suggests that SES-related differences in the visuo-spatial regions during subtraction might be based in SES-related verbal differences.

Developmental dissociation in the neural responses to simple multiplication and subtraction problems.

Mastering single-digit arithmetic during school years is commonly thought to depend upon an increasing reliance on verbally memorized facts. An alternative model, however, posits that fluency in single-digit arithmetic might also be achieved via the increasing use of efficient calculation procedures. To test between these hypotheses, we used a cross-sectional design to measure the neural activity associated with single-digit subtraction and multiplication in 34 children from 2nd to 7th grade. The neural correlates of language and numerical processing were also identified in each child via localizer scans. Although multiplication and subtraction were undistinguishable in terms of behavior, we found a striking developmental dissociation in their neural correlates. First, we observed grade-related increases of activity for multiplication, but not for subtraction, in a language-related region of the left temporal cortex. Second, we found grade-related increases of activity for subtraction, but not for multiplication, in a region of the right parietal cortex involved in the procedural manipulation of numerical quantities. The present results suggest that fluency in simple arithmetic in children may be achieved by both increasing reliance on verbal retrieval and by greater use of efficient quantity-based procedures, depending on the operation.

Fractionating the neural substrates of transitive reasoning: task-dependent contributions of spatial and verbal representations.

It has long been suggested that transitive reasoning relies on spatial representations in the posterior parietal cortex (PPC). Previous neuroimaging studies, however, have always focused on linear arguments, such as "John is taller than Tom, Tom is taller than Chris, therefore John is taller than Chris." Using functional magnetic resonance imaging (fMRI), we demonstrate here that verbal representations contribute to transitive reasoning when it involves set-inclusion relations (e.g., "All Tulips are Flowers, All Flowers are Plants, therefore All Tulips are Plants"). In the present study, such arguments were found to engage verbal processing regions of the left inferior frontal gyrus (IFG) and left PPC that were identified in an independent localizer task. Specifically, activity in these verbal regions increased as the number of relations increased in set-inclusion arguments. Importantly, this effect was specific to set-inclusion arguments because left IFG and left PPC were not differentially engaged when the number of relations increased in linear arguments. Instead, such an increase was linked to decreased activity in a spatial processing region of the right PPC that was identified in an independent localizer task. Therefore, both verbal and spatial representations can underlie transitive reasoning, but their engagement depends upon the structure of the argument.

Spatial attention in mental arithmetic: A literature review and meta-analysis.

We review the evidence for the conceptual association between arithmetic and space and quantify the effect size in meta-analyses. We focus on three effects: (a) the operational momentum effect (OME), which has been defined as participants' tendency to overestimate results of addition problems and underestimate results of subtraction problems; (b) the arithmetic cueing effect, in which arithmetic problems serve as spatial cues in target detection or temporal order judgment tasks; and (c) the associations between arithmetic and space observed with eye- and hand-tracking studies. The OME was consistently found in paradigms that provided the participants with numerical response alternatives. The OME shows a large effect size, driven by an underestimation during subtraction while addition was unbiased. In contrast, paradigms in which participants indicated their estimate by transcoding their final estimate to a spatial reference frame revealed no consistent OME. Arithmetic cueing studies show a reliable small to medium effect size, driven by a rightward bias for addition. Finally, eye- and hand-tracking studies point to replicable associations between arithmetic and eye or hand movements. To account for the complexity of the observed pattern, we introduce the Adaptive Pathways in Mental Arithmetic (APiMA) framework. The model accommodates central notions of numerical and arithmetic processing and helps identifying which pathway a given paradigm operates on. It proposes that the divergence between OME and arithmetic cueing studies comes from the predominant use of non-symbolic versus symbolic stimuli, respectively. Overall, our review and findings clearly support an association between arithmetic and spatial processing.

Intergenerational transmission of brain structure and function in humans: a narrative review of designs, methods, and findings.

Children often show cognitive and affective traits that are similar to their parents. Although this indicates a transmission of phenotypes from parents to children, little is known about the neural underpinnings of that transmission. Here, we provide a general overview of neuroimaging studies that explore the similarity between parents and children in terms of brain structure and function. We notably discuss the aims, designs, and methods of these so-called intergenerational neuroimaging studies, focusing on two main designs: the parent-child design and the multigenerational design. For each design, we also summarize the major findings, identify the sources of variability between studies, and highlight some limitations and future directions. We argue that the lack of consensus in defining the parent-child transmission of brain structure and function leads to measurement heterogeneity, which is a challenge for future studies. Additionally, multigenerational studies often use measures of family resemblance to estimate the proportion of variance attributed to genetic versus environmental factors, though this estimate is likely inflated given the frequent lack of control for shared environment. Nonetheless, intergenerational neuroimaging studies may still have both clinical and theoretical relevance, not because they currently inform about the etiology of neuromarkers, but rather because they may help identify neuromarkers and test hypotheses about neuromarkers coming from more standard neuroimaging designs.

Arithmetic skills are associated with left fronto-temporal gray matter volume in 536 children and adolescents.

There are large individual differences in arithmetic skills. Although a number of brain-wide association studies have attempted to identify the neural correlates of these individual differences, studies have focused on relatively small sample sizes and have yielded inconsistent results. In the current voxel-based morphometry study, we merged six structural imaging datasets of children and adolescents (from 7.5 to 15 years) whose levels of arithmetic skills were assessed, leading to a combined sample of n = 536. Controlling for individual differences in age, gender, as well as language, and intelligence, we found a unique positive relation between arithmetic skill and gray matter volume in the left inferior frontal gyrus (IFG) and middle temporal gyrus (MTG). Our results suggest that individual differences in arithmetic skills are associated with structural differences in left fronto-temporal areas, rather than in regions of the parietal cortex and hippocampus that are often associated with arithmetic processing.