Do children with mathematical learning disabilities use the inversion principle to solve three-term arithmetic problems?: The impact of presentation mode.

Numerical inversion is the ability to understand that addition is the opposite of subtraction and vice versa. Three-term arithmetic problems can be solved without calculation using this conceptual shortcut. To verify that this principle is used, inverse problems (a + b - b) can be compared with standard problems (a + b - c). If this principle is used, performance on inverse problems will be higher than performance on standard problems because no calculation is required. To our knowledge, this principle has not been previously studied in children with mathematical learning disabilities (MLD). Our objectives were (a) to study whether 10-year-olds with MLD are able to use this conceptual principle in three-term arithmetic problems and (b) to evaluate the impact of the presentation mode. A total of 64 children with or without MLD solved three-term arithmetic problems (inverse and standard) in two presentation modes (symbolic and picture). The results showed that even though children with MLD have difficulties in performing arithmetic problems, they can do so when the inverse problem is presented with pictures. The picture presentation mode allowed children with MLD to efficiently identify and use the conceptual inversion shortcut and thus to achieve a similar performance to that of typically developing children. These results provide interesting perspectives for the care of children with MLD.

Anterior cingulate cortex and intuitive bias detection during number conservation.

Children's number conservation is often biased by misleading intuitions but the precise nature of these conservation errors is not clear. A key question is whether children detect that their erroneous conservation judgment is unwarranted. The present study reanalyzed available fMRI data to test the implication of the anterior cingulate cortex (ACC) in this detection process. We extracted mean BOLD (Blood Oxygen Level Dependent) signal values in an independently defined ACC region of interest (ROI) during presentation of classic and control number conservation problems. In classic trials, an intuitively cued visuospatial response conflicted with the correct conservation response, whereas this conflict was not present in the control trials. Results showed that ACC activation increased when solving the classic conservation problems. Critically, this increase did not differ between participants who solved the classic problems correctly (i.e., so-called conservers) and incorrectly (i.e., so-called non-conservers). Additional control analyses of inferior and lateral prefrontal ROIs showed that the group of conservers did show stronger activation in the right inferior frontal gyrus and right lateral middle frontal gyrus. In line with recent behavioral findings, these data lend credence to the hypothesis that even non-conserving children detect the biased nature of their judgment. The key difference between conservers and non-conservers seems to lie in a differential recruitment of inferior and lateral prefrontal regions associated with inhibitory control.

Dynamics of the anatomical changes that occur in the brains of schoolchildren as they learn to read.

Although the functional brain network involved in reading for adults and children is now well documented, a critical lack of knowledge still exists about the structural development of these brain areas. To provide a better overview of the structural dynamics of the brain that sustain reading acquisition, we acquired anatomical MRI brain images from 55 children that were divided into two groups: one prior to the formal learning of reading (n = 33, 5-6 years old) and the second a few years after formal learning (n = 22, 9-10 years old). Reading performances were collected based on the "Alouette-R" test, a standardized test for reading text in French. Voxel-based morphometry analysis of gray matter showed that only the right insula volume was different between the two groups. Moreover, the reading group showed that the volumes of the left fusiform gyrus (corresponding to the well-known visual word form area, VWFA), the anterior part of the left inferior occipital gyrus and the left thalamus were significantly modulated by reading performance. This study reinforces the crucial role of the Visual Word Form Area in reading and correlation analyses performed between ROIs volumes suggesting that the VWFA is fully connected with the traditional left-hemispheric language brain network.

Numerical Transcoding Proficiency in 10-Year-Old Schoolchildren is Associated with Gray Matter Inter-Individual Differences: A Voxel-Based Morphometry Study.

Are individual differences in numerical performance sustained by variations in gray matter volume in schoolchildren? To our knowledge, this challenging question for neuroeducation has not yet been investigated in typical development. We used the Voxel-Based Morphometry method to search for possible structural brain differences between two groups of 10-year-old schoolchildren (N = 22) whose performance differed only in numerical transcoding between analog and symbolic systems. The results indicated that children with low numerical proficiency have less gray matter volume in the parietal (particularly in the left intraparietal sulcus and the bilateral angular gyri) and occipito-temporal areas. All the identified regions have previously been shown to be functionally involved in transcoding between analog and symbolic numerical systems. Our data contribute to a better understanding of the intertwined relationships between mathematics learning and brain structure in healthy schoolchildren.

Structural brain correlates of executive engagement in working memory: children's inter-individual differences are reflected in the anterior insular cortex.

Although the development of executive functions has been extensively investigated at a neurofunctional level, studies of the structural relationships between executive functions and brain anatomy are still scarce. Based on our previous meta-analysis of functional neuroimaging studies examining executive functions in children (Houdé, Rossi, Lubin, and Joliot, (2010). Developmental Science, 13, 876-885), we investigated six a priori regions of interest: the left anterior insular cortex (AIC), the left and the right supplementary motor areas, the right middle and superior frontal gyri, and the left precentral gyrus. Structural magnetic resonance imaging scans were acquired from 22 to 10-year-old children. Local gray matter volumes, assessed automatically using a standard voxel-based morphometry approach, were correlated with executive and storage working memory capacities evaluated using backward and forward digit span tasks, respectively. We found an association between smaller gray matter volume--i.e., an index of neural maturation--in the left AIC and high backward memory span while gray matter volumes in the a priori selected regions of interest were not linked with forward memory span. These results were corroborated by a whole-brain a priori free analysis that revealed a significant negative correlation in the frontal and prefrontal regions, including the left AIC, with the backward memory span, and in the right inferior parietal lobe, with the forward memory span. Taken together, these results suggest a distinct and specific association between regional gray matter volume and the executive component vs. the storage component of working memory. Moreover, they support a key role for the AIC in the executive network of children.

Is human decision making under ambiguity guided by loss frequency regardless of the costs? A developmental study using the Soochow Gambling Task.

Converging developmental decision-making studies have demonstrated that until late adolescence, individuals prefer options for which the risk of a loss is low regardless of the final outcome. Recent works have shown a similar inability to consider both loss frequency and final outcome among adults. The current study aimed to identify developmental changes in feedback-monitoring ability to consider both loss frequency and final outcome in decision making under ambiguity. Children, adolescents, and adults performed an adapted version of the Soochow Gambling Task. Our results showed that children and adolescents presented an exclusive preference for options associated with infrequent punishment. In contrast, only adults seemed to consider both loss frequency and the final outcome by favoring the advantageous options when the frequency of losses was low. These findings suggest that the ability to integrate both loss frequency and final outcome develops with age. Moreover, the analysis of strategic adjustments following gains and losses reveals that adults switch less often after losses compared with children and adolescents. This finding suggests that psychological tolerance to loss may facilitate learning the characteristics of each option and improve the ability to choose advantageously.

The shift from local to global visual processing in 6-year-old children is associated with grey matter loss.

BACKGROUND: A real-world visual scene consists of local elements (e.g. trees) that are arranged coherently into a global configuration (e.g. a forest). Children show psychological evolution from a preference for local visual information to an adult-like preference for global visual information, with the transition in visual preference occurring around 6 years of age. The brain regions involved in this shift in visual preference have not been described. METHODS AND RESULTS: We used voxel-based morphometry (VBM) to study children during this developmental window to investigate changes in gray matter that underlie the shift from a bias for local to global visual information. Six-year-old children were assigned to groups according to their judgment on a global/local task. The first group included children who still presented with local visual processing biases, and the second group included children who showed global visual processing biases. VBM results indicated that compared to children with local visual processing biases, children with global visual processing biases had a loss of gray matter in the right occipital and parietal visuospatial areas. CONCLUSIONS: These anatomical findings are in agreement with previous findings in children with neurodevelopmental disorders and represent the first structural identification of brain regions that allow healthy children to develop a global perception of the visual world.

Functional magnetic resonance imaging study of Piaget's conservation-of-number task in preschool and school-age children: a neo-Piagetian approach.

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.

Evidence of different developmental trajectories for length estimation according to egocentric and allocentric viewpoints in children and adults.

This study investigated the influence of egocentric and allocentric viewpoints on a comparison task of length estimation in children and adults. A total of 100 participants ranging in age from 5 years to adulthood were presented with virtual scenes representing a park landscape with two paths, one straight and one serpentine. Scenes were presented either from an egocentric or allocentric viewpoint. Results showed that when the two paths had the same length, participants always overestimated the length of the straight line for allocentric trials, whereas a development from a systematic overestimation in children to an underestimation of the straight line length in adults was found for egocentric trials. We discuss these findings in terms of the influences of both bias-inhibition processes and school acquisitions.

Mapping numerical processing, reading, and executive functions in the developing brain: an fMRI meta-analysis of 52 studies including 842 children.

Tracing the connections from brain functions to children's cognitive development and education is a major goal of modern neuroscience. We performed the first meta-analysis of functional magnetic resonance imaging (fMRI) data obtained over the past decade (1999-2008) on more than 800 children and adolescents in three core systems of cognitive development and school learning: numerical abilities, reading, and executive functions (i.e. cognitive control). We ran Activation Likelihood Estimation (ALE) meta-analyses to obtain regions of reliable activity across all the studies. The results indicate that, unlike results usually reported for adults, children primarily engage the frontal cortex when solving numerical tasks. With age, there may be a shift from reliance on the frontal cortex to reliance on the parietal cortex. In contrast, the frontal, temporo-parietal and occipito-temporal regions at work during reading in children are very similar to those reported in adults. The executive frontal regions are also consistent with the imaging literature on cognitive control in adults, but the developmental comparison between children and adolescents demonstrates a key role of the anterior insular cortex (AIC) with an additional right AIC involvement in adolescents.

Pedagogical effect of action on arithmetic performances in Wynn-like tasks solved by 2-year-olds.

Previous studies have provided evidence of interference due to a language-default mode (i.e., the singular/plural opposition) in 2-year-old children when solving arithmetic problems using a traditional onlooker method. However, an action-based method could help to bypass this language bias. In particular, when an arithmetic problem is presented to the children by the experimenter (onlooker mode) or realized by the children themselves (actor mode), performances are better with the latter. Thus, an experimental procedure based on "math in action" allows a brain-and-mind shift from a global language-bias (singular/plural) strategy to an exact numerical strategy. In this framework, we examined whether the exact numerical strategy induced by the actor method remains operational when children had to subsequently solve the same arithmetic problem using the traditional onlooker method. Results from 112 children suggest that this pedagogical effect of action bypasses the interference from language in onlooker mode after an initial confrontation of the problem in actor mode. This enduring embodiment effect has important implications for cognitive and preschool assessment in toddlers.

Math in actions: actor mode reveals the true arithmetic abilities of French-speaking 2-year-olds in a magic task.

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.

Adult brains don't fully overcome biases that lead to incorrect performance during cognitive development: an fMRI study in young adults completing a Piaget-like task.

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.