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Understanding the constraints, including biological ones, that may influence mathematical development is of great importance because math ability is a key predictor of career success, income and even psychological well-being. While research in developmental cognitive neuroscience of mathematics has extensively studied the key functional regions for processing numbers, particularly the horizontal segment of intraparietal sulcus (HIPS), few studies have investigated the effects of early cerebral constraints on later mathematical abilities. In this pre-registered study, we investigated whether variability of the sulcal pattern of the HIPS, a qualitative feature of the brain determined in-utero and not affected by brain maturation and learning, accounts for individual difference in symbolic and non-symbolic number abilities. Seventy-seven typically developing school-aged children and 21 young adults participated in our study. We found that the HIPS sulcal pattern, (a) explains part of the variance in participant's symbolic number comparison and math fluency abilities, and (b) that this association between HIPS sulcal pattern and symbolic number abilities was found to be stable from childhood to young adulthood. However, (c) we did not find an association between participant's non-symbolic number abilities and HIPS sulcal morphology. Our findings suggest that early cerebral constraints may influence individual difference in math abilities, in addition to the well-established neuroplastic factors., (Copyright © 2021. Published by Elsevier Ltd.)

Jean Piaget's theory is a central reference point in the study of normal development in children. He proposed in the 20th century that distinct stages occur in the development of intellectual abilities from the preoperational period (intuitive stage: 4-7 years old) to the second stage of conceptual intelligence. One of the most famous Piagetian tasks is number conservation. Failures and successes in this task reveal two fundamental stages in children's thinking and judgment, shifting at approximately 7 years of age from visuospatial intuition to logico-mathematical operation (i.e., number conservation). New emerging techniques in the 21st century, such as functional magnetic resonance imaging, can support this preeminent theory with an understanding of the cerebral basis of the various stages. Since these new technologies are considered to be invasive in children, such techniques are subject to ethical views and concerns due to pediatric participants. The chapter discusses a brain imaging study on Piaget's conservation-of-number task, showing what can be accomplished through careful ethical considerations in the context of healthy children with normal cognitive development., (Copyright © 2020 Elsevier B.V. All rights reserved.)

In Piaget's theory of number development, children do not possess a true concept of number until they are able to reason on numerical quantity regardless of changes in other nonnumerical magnitudes, such as length. Recent studies have echoed this result by arguing that abstracting number from nonnumerical dimensions of magnitude is a developmental milestone and a strong predictor of mathematics achievement. However, the mechanisms supporting such abstraction remain largely underspecified. We aimed to study how identification of the numerical equivalence in a Piaget-like estimation task by 6-year-old children is affected by (a) the degree of interference between number and nonnumerical magnitudes and (b) children's spontaneous orientation to numerosity. Six-year-old children first performed a card sorting task assessing their spontaneous orientation towards numerosity, spacing, or item size in a set of dots. Then, they completed a Piaget-like same/different numerical estimation task using two rows of dots in which the length ratio between the two rows varied systematically. Children were less likely to accept the numerical equivalence in the Piaget-like estimation task (a) as the difference in spacing between the dots increased and (b) as the children were more spontaneously oriented towards spacing over number in the card sorting task. Our results suggest that abstracting number depends on its saliency, which varies both as a function of the context (i.e., length ratio between the two rows) and of individual differences in children's sensitivity to the numerical aspects of their environment. These factors could be at the root of the observed development of performance in the seminal number-conservation task, which appears as a progressive abstraction of number rather than a conceptual shift, as Piaget hypothesized., (Copyright © 2019 Elsevier B.V. All rights reserved.)

Since reasoning is often biased by intuitive heuristics, the development of sound reasoning has long been postulated to depend on successful bias monitoring and inhibition. The present fMRI study aimed to identify neural correlates of developmental changes in these processes. A group of adults and young adolescents were presented with ratio-bias problems in which an intuitively cued heuristic response could be incongruent (conflict item) or congruent (no-conflict item) with the correct response. Results showed that successfully avoiding biased responding on conflict items across both age groups was associated with increased activation in Anterior Cingulate Cortex (ACC) and the right Lateral Prefrontal Cortex (LPFC) regions of interest. Critically, the right LPFC activation decreased with age. Biased responding did not result in right LPFC or ACC modulation and failed to show any developmental activation changes. We discuss implications for ongoing debates on the nature of heuristic bias and its development., (Copyright © 2019 Elsevier Ltd. All rights reserved.)

Visual environments are composed of global shapes and local details that compete for attentional resources. In adults, the global level is processed more rapidly than the local level, and global information must be inhibited in order to process local information when the local information and global information are in conflict. Compared with adults, children present less of a bias toward global visual information and appear to be more sensitive to the density of local elements that constitute the global level. The current study aimed, for the first time, to investigate the key role of inhibition during global/local processing in children. By including two different conditions of global saliency during a negative priming procedure, the results showed that when the global level was salient (dense hierarchical figures), 7-year-old children and adults needed to inhibit the global level to process the local information. However, when the global level was less salient (sparse hierarchical figures), only children needed to inhibit the local level to process the global information. These results confirm a weaker global bias and the greater impact of saliency in children than in adults. Moreover, the results indicate that, regardless of age, inhibition of the most salient hierarchical level is systematically required to select the less salient but more relevant level. These findings have important implications for future research in this area., (Copyright © 2018 Elsevier Inc. All rights reserved.)

Reasoners make systematic logical errors by giving heuristic responses that reflect deviations from the logical norm. Influential studies have suggested first that our reasoning is often biased because we minimize cognitive effort to surpass a cognitive conflict between heuristic response from system 1 and analytic response from system 2 thinking. Additionally, cognitive control processes might be necessary to inhibit system 1 responses to activate a system 2 response. Previous studies have shown a significant effect of executive learning (EL) on adults who have transferred knowledge acquired on the Wason selection task (WST) to another isomorphic task, the rule falsification task (RFT). The original paradigm consisted of teaching participants to inhibit a classical matching heuristic that sufficed the first problem and led to significant EL transfer on the second problem. Interestingly, the reasoning tasks differed in inhibiting-heuristic metacognitive cost. Success on the WST requires half-suppression of the matching elements. In contrast, the RFT necessitates a global rejection of the matching elements for a correct answer. Therefore, metacognitive learning difficulty most likely differs depending on whether one uses the first or second task during the learning phase. We aimed to investigate this difficulty and various matching-bias inhibition effects in a new (reversed) paradigm. In this case, the transfer effect from the RFT to the WST could be more difficult because the reasoner learns to reject all matching elements in the first task. We observed that the EL leads to a significant reduction in matching selections on the WST without increasing logical performances. Interestingly, the acquired metacognitive knowledge was too "strictly" transferred and discouraged matching rather than encouraging logic. This finding underlines the complexity of learning transfer and adds new evidence to the pedagogy of reasoning.

Cognitive development is generally conceived as incremental with knowledge of increasing complexity acquired throughout childhood and adolescence. However, several studies have now demonstrated not only that infants possess complex cognitive abilities but also that older children, adolescents, and adults tend to make systematic errors even in simple logical reasoning tasks. Therefore, one of the main issues for any theory of typical cognitive development is to provide an explanation of why at some age and in some contexts children, adolescents, and adults do not express a knowledge or cognitive principle that they already acquired when they were younger. In this review, we present convergent behavioural and neurocognitive evidence that cognitive development is more similar to a non-linear dynamic system than to a linear, stage-like system. In this theoretical framework, errors can emerge in problems similar to the ones infants or young children were succeeding when older children, adolescents, and adults rely on a misleading heuristic rather than on the correct logical algorithm to solve such problems. And the core mechanism for overcoming these errors is inhibitory control (i.e. the ability to inhibit the misleading heuristics). Therefore, typical cognitive development relies not only on the ability to acquire knowledge of incremental complexity but also to inhibit previously acquired knowledge., (© 2015 The Authors. Developmental Medicine & Child Neurology © 2015 Mac Keith Press.)

Cognitive success at school and later in life is supported by executive functions including cognitive control (CC). The pFC plays a major role in CC, particularly the dorsal part of ACC or midcingulate cortex. Genes, environment (including school curricula), and neuroplasticity affect CC. However, no study to date has investigated whether ACC sulcal pattern, a stable brain feature primarily determined in utero, influences CC efficiency in the early stages of cognitive and neural development. Using anatomical MRI and three-dimensional reconstruction of cortical folds, we investigated the effect that ACC sulcal pattern may have on the Stroop score, a classical behavioral index of CC efficiency, in 5-year-old preschoolers. We found higher CC efficiency, that is, lower Stroop interference scores for both RTs and error rates, in children with asymmetrical ACC sulcal pattern (i.e., different pattern in each hemisphere) compared with children with symmetrical pattern (i.e., same pattern in both hemispheres). Critically, ACC sulcal pattern had no effect on performance in the forward and backward digit span tasks suggesting that ACC sulcal pattern contributes to the executive ability to resolve conflicts but not to the ability to maintain and manipulate information in working memory. This finding provides the first evidence that preschoolers' CC efficiency is likely associated with ACC sulcal pattern, thereby suggesting that the brain shape could result in early constraints on human executive ability.

Most children under 7 years of age presented with 10 daisies and 2 roses fail to indicate that there are more flowers than daisies. Instead of the appropriate comparison of the relative numerosities of the superordinate class (flowers) to its subordinate class (daisies), they perform a direct perceptual comparison of the extensions of the 2 subordinate classes (daisies vs. roses). In our experiment, we investigated whether increasing efficiency in solving the Piagetian class-inclusion task is related to increasing efficiency in the ability to resist (inhibit) this direct comparison of the subordinate classes' extensions. Ten-year-old and young adult participants performed a computerized priming version of a Piaget-like class-inclusion task. The experimental design was such that the misleading perceptual strategy to inhibit on the prime (in which a superordinate class had to be compared with a subordinate class) became a congruent strategy to activate on the probe (in which the two subordinate classes' extensions were directly compared). We found a negative priming effect of 291 ms in children and 129 ms in adults. These results provide evidence for the first time (a) that adults still need to inhibit the comparison of the subordinate classes' extensions in class-inclusion tasks and (b) that the ability to inhibit this heuristic increases with age (resulting in a lower executive cost). Taken together, these findings provide additional support for the neo-Piagetian approach of cognitive development that suggests that the acquisition of increasingly complex knowledge is based on the ability to resist (inhibit) heuristics and previously acquired knowledge.

Jean Piaget's theory is a central reference point in the study of logico-mathematical development in children. One of the most famous Piagetian tasks is number conservation. Failures and successes in this task reveal two fundamental stages in children's thinking and judgment, shifting at approximately 7 years of age from visuospatial intuition to number conservation. In the current study, preschool children (nonconservers, 5-6 years of age) and school-age children (conservers, 9-10 years of age) were presented with Piaget's conservation-of-number task and monitored by functional magnetic resonance imaging (fMRI). The cognitive change allowing children to access conservation was shown to be related to the neural contribution of a bilateral parietofrontal network involved in numerical and executive functions. These fMRI results highlight how the behavioral and cognitive stages Piaget formulated during the 20th century manifest in the brain with age., (Copyright © 2011 Elsevier Inc. All rights reserved.)

Objective: We combined event-related potential (ERP) and magnetoencephalography (MEG) acquisition and analysis to investigate the electrophysiological markers of the inhibitory processes involved in the number/length interference in a Piaget-like numerical task., Methods: Eleven healthy subjects performed four gradually interfering conditions with the heuristic "length equals number" to be inhibited. Low resolution tomography reconstruction was performed on the combined grand averaged electromagnetic data at the early (N1, P1) and late (P2, N2, P3(early) and P3(late)) latencies. Every condition was analyzed at both scalp and regional brain levels., Results: The inhibitory processes were visible on the late components of the electromagnetic brain activity. A right P2-related frontal orbital activation reflected the change of strategy in the inhibitory processes. N2-related SMA/cingulate activation revealed the first occurrence of the stimuli processing to be inhibited. Both P3 components revealed the working memory processes operating in a medial temporal complex and the mental imagery processes subtended by the precuneus., Conclusions: Simultaneous ERP and MEG signal acquisition and analysis allowed to describe the spatiotemporal patterns of neural networks involved in the inhibition of the "length equals number" interference., Significance: Combining ERP and MEG ensured a sensitivity which could be reached previously only through invasive intracortical recordings.

Our previous studies provide some evidence of between-language effects on arithmetic performance in 2-year-olds. French-speaking children were especially biased by the use of the word un as a cardinal value and as an article in the singular/plural opposition (1 vs. the set 2, 3, ...). Here we evaluated the ability of a new action-based assessment method to avoid this bias. A total of 80 French-speaking 2- and 3-year-olds were confronted with impossible (1+1=1 or 1+1=3) and possible (1+1=2) addition problems that triggered the bias. The problems were either presented to the children by the experimenter (onlooker mode) or realized by themselves (actor mode). The 2-year-olds performed better in the actor mode than in the onlooker mode. A subtraction control with no language ambiguity (2-1=2 or 1) was conducted with 80 other children; both modes elicited comparable performances regardless of age. These data indicate that the actor mode is effective for assessing arithmetic ability in French-speaking 2-year-olds.

A current issue in developmental science is that greater continuity in cognition between children and adults may exist than is usually appreciated in Piaget-like (stages or 'staircase') models. This phenomenon has been demonstrated at the behavioural level, but never at the brain level. Here we show with functional magnetic resonance imaging (fMRI), for the first time, that adult brains do not fully overcome the biases of childhood. More specifically, the aim of this fMRI study was to evaluate whether the perceptual bias that leads to incorrect performance during cognitive development in a Piaget-like task is still a bias in the adult brain and hence requires an executive network to overcome it. Here, we compared two numerical-judgment tasks, one being a Piaget-like task with number-length interference (called 'INT') and the other being a control task with number-length covariation ('COV'). We also used a colour-detection task to control for stimuli numerosity, spatial distribution, and frequency. Our behavioural results confirmed that INT remains a difficult task for young adults. Indeed, response times were significantly higher in INT than in COV. Moreover, we observed that only in INT did response times increase linearly as a function of the number of items. The fMRI results indicate that the brain network common to INT and COV shows a large rightward functional asymmetry, emphasizing the visuospatial nature of these two tasks. When INT was compared with COV, activations were found within a right frontal network, including the pre-supplementary motor area, the anterior cingulate cortex, and the middle frontal gyrus, which probably reflect detection of the number/length conflict and inhibition of the 'length-equals-number' response strategy. Finally, activations related to visuospatial and quantitative processing, enhanced or specifically recruited in the Piaget-like task, were found in bilateral posterior areas.

This study investigated how global and local perceptual processes evolve during childhood according to the meaningfulness of the stimuli. Children had to decide whether visually presented pairs of items were identical or not. Items consisted of global forms made up of local forms. Both global and local forms could represent either objects or nonobjects. In dissimilar pairs, items differed at one level (target level), while the other level included similar forms on both sides (irrelevant level). The results indicate an evolution from local preference at 4 years of age to adult-like global preference at 9 years of age. Moreover, as previously reported in adults, regardless of age, identification impaired performance when the irrelevant level was made of objects and the target level was made of nonobjects (interference). However, in younger children, this interference existed even when objects were present at all levels, suggesting that the strategy used to perform the comparison task also varied according to age., (Copyright (c) 2008 APA.)

We sought to determine whether the neural traces of a previous cognitive developmental stage could be evidenced in young adults. In order to do so, 12 young adults underwent two functional imaging acquisitions (EEG then fMRI). During each session, two experimental conditions were applied: a Piaget-like task with number/length interference (INT), and a reference task with number/length covariation (COV). To succeed at Piaget's numerical task, which children under the age of 7 years usually fail, the subjects had to inhibit a misleading strategy, namely, the visuospatial length-equals-number bias, a quantification heuristic that is often relevant and that continues to be used through adulthood. Behavioral data confirmed that although there was an automation in the young adult subjects as assessed by the very high number of accurate responses (>97%), the inhibition of the "length equals number strategy" had a cognitive cost, as the reaction times were significantly higher in INT than in COV (with a difference of 230 ms). The event-related potential results acquired during the first session showed electrophysiological markers of the cognitive inhibition of the number/length interference. Indeed, the frontal N2 was greater during INT than during COV, and a P3(late)/P6 was detected only during INT. During the fMRI session, a greater activation of unimodal areas (the right middle and superior occipital cortex) and in the ventral route (the left inferior temporal cortex) was observed in INT than in COV. These results seem to indicate that when fully automated in adults, inhibition processes might take place in unimodal areas., (Copyright 2005 Wiley-Liss, Inc.)

Research on deductive reasoning in adolescents and adults has shown that errors in deductive logic are not necessarily due to a lack of logical ability but can stem from an executive failure to inhibit biases. Few studies have examined this dissociation in children. Here, we used a negative priming paradigm with 64 children (8-10 years old) to test the role of cognitive inhibition in syllogisms with belief-bias effects. On trials where negative priming was predicted, results were as follows: For the first syllogism (A), the strategy 'unbelievable-equals-invalid' had to be inhibited. The logic of the syllogism led to affirming a conclusion inconsistent with one's knowledge of the world, such as 'All elephants are light.' For the second syllogism (B), one's real-world knowledge and the syllogism's logic were congruent but the latter required affirming exactly what had been inhibited for A (i.e. that elephants are heavy). A negative priming effect on the A-B sequence was reflected in a significant drop in reasoning performance on B. This supports the idea that during cognitive development, inhibitory control is required for success on syllogisms where beliefs and logic interfere.