Commonalities for Numerical and Continuous Quantity Skills at Temporo-parietal Junction

Auditory time perception impairment in children with developmental dyscalculia

Developmental dyscalculia (DD) is a specific learning disability which prevents children from acquiring adequate numerical and arithmetical competences. We investigated whether difficulties in children with DD spread beyond the numerical domain and impact also their ability to perceive time. A group of 37 children/adolescent with and without DD were tested with an auditory categorization task measuring time perception thresholds in the sub-second (0.25-1 s) and supra-second (0.75-3 s) ranges. Results showed that auditory time perception was strongly impaired in children with DD at both time scales. The impairment remained even when age, non-verbal reasoning, and gender were regressed out. Overall, our results show that the difficulties of DD can affect magnitudes other than numerical and contribute to the increasing evidence that frames dyscalculia as a disorder affecting multiple neurocognitive and perceptual systems.

Children dynamically update and extend the interface between number words and perceptual magnitudes

As adults, we represent and think about number, space, and time in at least two ways: our intuitive-but imprecise-perceptual representations, and the slowly learned-but precise-number words. With development, these representational formats interface, allowing us to use precise number words to estimate imprecise perceptual experiences. We test two accounts of this developmental milestone. Either slowly learned associations are required for the interface to form, predicting that deviations from typical experiences (e.g., presentation of a novel unit or unpracticed dimension) will disrupt children's ability to map number words to their perceptual experiences or children's understanding of the logical similarity between number words and perceptual representations allows them to flexibly extend this interface to novel experiences (e.g., units and dimensions they have not yet learned how to formally measure). 5-11-year-olds completed verbal estimation and perceptual sensitivity tasks across three dimensions: Number, Length, and Area. For verbal estimation, they were given novel units (i.e., a three-dot unit called one "toma" for Number, a 44 px long line called one "blicket" for Length, a 111 px2 blob called one "modi" for Area) and asked to estimate how many tomas/blickets/modies they saw when shown a larger set of dots, lines, and blobs. Children could flexibly link number words to novel units across dimensions, demonstrating positive estimation slopes, even for Length and Area, which younger children had limited experience with. This suggests that the logic of structure mapping can be dynamically utilized across perceptual dimensions, even without extensive experience.

A Bird's eye view from below: Activity in the temporo-parietal junction predicts from-above Necker Cube percepts

The temporo-parietal junction (TPJ) consistently emerges in other-regarding behavior, including tasks probing affective phenomena such as morality and empathy. Yet the TPJ is also recruited in processes with no affective or social component, such as visuo-spatial processing and mathematical cognition. We present serendipitous findings from a perceptual decision-making task on a bistable stimulus, the Necker Cube, performed in an MRI scanner. The stimulus in question is a transparent, wire-frame cube that evokes spontaneous switches in perception. Individuals can view the cube from below or from above, though a consistent bias is shown towards seeing the cube from above. We replicate this bias, finding participants spend more time in the from-above percept. However, in testing for BOLD differences between percept orientations, we found robust responses in bilateral TPJ for the from-above > from-below perceptual state. We speculate that this neural response comes from the sensory incongruence of viewing an object from above while lying supine in the scanner. We further speculate that the TPJ resolves this incongruence by facilitating an egocentric projection. Such a function would explain the TPJ's ubiquitous response to other-regarding, visuo-spatial and mathematical cognition, as all these phenomena demand an ability to ambulate through the coordinate space. Our findings suggest the TPJ may not play a specific role in social or moral components of other-regarding behavior, such as altruism, and further indirectly suggest that "pure", allocentric altruism may not correlate with the TPJ. Results further have implications on how the TPJ may be modulated by activities such as flight or drone operation. Finally, this study highlights the possible need for congruence between stimuli and body position in neuroimaging studies.

Learning disabilities: Developmental dyscalculia

Developmental dyscalculia (DD) is a developmental learning disability that manifests as a persistent difficulty in comprehending even the most basic numeric and arithmetic concepts, despite normal intelligence and schooling opportunities. Given the predominant use of numbers in modern society, this condition can pose major challenges in the sufferer's everyday life, both in personal and professional development. Since, to date, we still lack a universally recognized and psychometrically driven definition of DD, its diagnosis has been applied to a wide variety of cognitive profiles. In this chapter, we review the behavioral and neural characterization of DD as well as the different neurocognitive and etiologic accounts of this neurodevelopmental disorder. We underline the multicomponential nature of this heterogeneous disability: different aspects of mathematical competence can be affected by both the suboptimal recruitment of general cognitive functions supporting mathematical cognition (such as attention, memory, and cognitive control) and specific deficits in mastering numeric concepts and operations. Accordingly, both intervention paradigms focused on core numeric abilities and more comprehensive protocols targeting multiple neurocognitive systems have provided evidence for effective positive outcomes.

The interplay between non-symbolic number and its continuous visual properties revisited: Effects of mixing trials of different types

In the last few years, the existence of a pure number sense has been challenged. Recent studies suggest that numerosity processing is influenced not only by the number of elements in a display but also by continuous magnitudes, such as the size of the elements. The aim of our study was to replicate and extend the findings by Gebuis and Reynvoet, who systematically manipulated different continuous magnitudes either congruently or incongruently with discrete numerosity. We were particularly interested in finding the same pattern of congruency effects and assess its stability and robustness as this pattern indicates a complex influence of continuous magnitudes on numerosity judgements. We did so by showing stimuli of different conditions either in separate blocks or mixed together while participants solved a dot comparison task. Our results are in line with the notion that discrete number and continuous magnitudes are integrated in numerosity judgements by means of a weighing process. Moreover, our findings suggest that this integration is modified by the mode of presentation (blocked vs. mixed).

A causal role for right temporo-parietal junction in signaling moral conflict

The right temporo-parietal junction (rTPJ) has been proposed to play a key role in guiding human altruistic behavior, but its precise functional contribution to altruism remains unclear. We aimed to disentangle three possible functions of the rTPJ for human altruism, namely: implementing the motivation to help, signaling conflicts between moral and material values, or representing social reputation concerns. Our novel donation-decision task consisted of decisions requiring trade-offs of either positive moral values and monetary cost when donating to a good cause, or negative moral values and monetary benefits when sending money to a bad cause. Disrupting the rTPJ using transcranial magnetic stimulation did not change the general motivation to give or to react to social reputation cues, but specifically reduced the behavioral impact of moral-material conflicts. These findings reveal that signaling moral-material conflict is a core rTPJ mechanism that may contribute to a variety of human moral behaviors.

Asymmetrical interference between number and item size perception provides evidence for a domain specific impairment in dyscalculia

Dyscalculia, a specific learning disability that impacts arithmetical skills, has previously been associated to a deficit in the precision of the system that estimates the approximate number of objects in visual scenes (the so called 'number sense' system). However, because in tasks involving numerosity comparisons dyscalculics' judgements appears disproportionally affected by continuous quantitative dimensions (such as the size of the items), an alternative view linked dyscalculia to a domain-general difficulty in inhibiting task-irrelevant responses. To arbitrate between these views, we evaluated the degree of reciprocal interference between numerical and non-numerical quantitative dimensions in adult dyscalculics and matched controls. We used a novel stimulus set orthogonally varying in mean item size and numerosity, putting particular attention into matching both features' perceptual discriminability. Participants compared those stimuli based on each of the two dimensions. While control subjects showed no significant size interference when judging numerosity, dyscalculics' numerosity judgments were strongly biased by the unattended size dimension. Importantly however, both groups showed the same degree of interference from the unattended dimension when judging mean size. Moreover, only the ability to discard the irrelevant size information when comparing numerosity (but not the reverse) significantly predicted calculation ability across subjects. Overall, our results show that numerosity discrimination is less prone to interference than discrimination of another quantitative feature (mean item size) when the perceptual discriminability of these features is matched, as here in control subjects. By quantifying, for the first time, dyscalculic subjects' degree of interference on another orthogonal dimension of the same stimuli, we are able to exclude a domain-general inhibition deficit as explanation for their poor / biased numerical judgement. We suggest that enhanced reliance on non-numerical cues during numerosity discrimination can represent a strategy to cope with a less precise number sense.

Development of a Possible General Magnitude System for Number and Space

There is strong evidence for a link between numerical and spatial processing. However, whether this association is based on a common general magnitude system is far from conclusive and the impact of development is not yet known. Hence, the present study aimed to investigate the association between discrete non-symbolic number processing (comparison of dot arrays) and continuous spatial processing (comparison of angle sizes) in children between the third and sixth grade (N = 367). Present findings suggest that the processing of comparisons of number of dots or angle are related to each other, but with angle processing developing earlier and being more easily comparable than discrete number representations for children of this age range. Accordingly, results favor the existence of a more complex underlying magnitude system consisting of dissociated but closely interacting representations for continuous and discrete magnitudes.

Developmental Dyscalculia in Adults: Beyond Numerical Magnitude Impairment

Numerous studies have tried to identify the core deficit of developmental dyscalculia (DD), mainly by assessing a possible deficit of the mental representation of numerical magnitude. Research in healthy adults has shown that numerosity, duration, and space share a partly common system of magnitude processing and representation. However, in DD, numerosity processing has until now received much more attention than the processing of other non-numerical magnitudes. To assess whether or not the processing of non-numerical magnitudes is impaired in DD, the performance of 15 adults with DD and 15 control participants was compared in four categorization tasks using numerosities, lengths, durations, and faces (as non-magnitude-based control stimuli). Results showed that adults with DD were impaired in processing numerosity and duration, while their performance in length and face categorization did not differ from controls' performance. Our findings support the idea of a nonsymbolic magnitude deficit in DD, affecting numerosity and duration processing but not length processing.

Adolescents with Developmental Dyscalculia Do Not Have a Generalized Magnitude Deficit - Processing of Discrete and Continuous Magnitudes

The link between number and space has been discussed in the literature for some time, resulting in the theory that number, space and time might be part of a generalized magnitude system. To date, several behavioral and neuroimaging findings support the notion of a generalized magnitude system, although contradictory results showing a partial overlap or separate magnitude systems are also found. The possible existence of a generalized magnitude processing area leads to the question how individuals with developmental dyscalculia (DD), known for deficits in numerical-arithmetical abilities, process magnitudes. By means of neuropsychological tests and functional magnetic resonance imaging (fMRI) we aimed to examine the relationship between number and space in typical and atypical development. Participants were 16 adolescents with DD (14.1 years) and 14 typically developing (TD) peers (13.8 years). In the fMRI paradigm participants had to perform discrete (arrays of dots) and continuous magnitude (angles) comparisons as well as a mental rotation task. In the neuropsychological tests, adolescents with dyscalculia performed significantly worse in numerical and complex visuo-spatial tasks. However, they showed similar results to TD peers when making discrete and continuous magnitude decisions during the neuropsychological tests and the fMRI paradigm. A conjunction analysis of the fMRI data revealed commonly activated higher order visual (inferior and middle occipital gyrus) and parietal (inferior and superior parietal lobe) magnitude areas for the discrete and continuous magnitude tasks. Moreover, no differences were found when contrasting both magnitude processing conditions, favoring the possibility of a generalized magnitude system. Group comparisons further revealed that dyscalculic subjects showed increased activation in domain general regions, whilst TD peers activate domain specific areas to a greater extent. In conclusion, our results point to the existence of a generalized magnitude system in the occipito-parietal stream in typical development. The detailed investigation of spatial and numerical magnitude abilities in DD reveals that the deficits in number processing and arithmetic cannot be explained with a general magnitude deficiency. Our results further indicate that multiple neuro-cognitive components might contribute to the explanation of DD.

The implications for education of an innate numerosity-processing mechanism

One specific cause of low numeracy is a deficit in a mechanism for representing and processing numerosities that humans inherited and which is putatively shared with many other species. This deficit is evident at each of the four levels of explanation in the 'causal modelling' framework of Morton and Frith (Morton and Frith 1995 In Manual of developmental psychopathology, vol. 1 (eds D Cichetti, D Cohen), pp. 357-390). Very low numeracy can occur in cognitively able individuals with normal access to good education: it is linked to an easily measured deficit in basic numerosity processing; it has a distinctive neural signature; and twin studies suggest specific heritability, though the relevant genes have not yet been identified. Unfortunately, educators and policymakers seem largely unaware of this cause, but appropriate interventions could alleviate the suffering and handicap of those with low numeracy, and would be a major benefit to society.This article is part of a discussion meeting issue 'The origins of numerical abilities'.

Time processing impairments in preschoolers at risk of developing difficulties in mathematics

The occurrence of time processing problems in individuals with Development Dyscalculia (DD) has favored the view of a general magnitude system devoted to both numerical and temporal information. Yet, this scenario has been partially challenged by studies indicating that time difficulties can be attributed to poor calculation or counting skills, which can support reasoning on time in school-aged children and adults. Here, we tackle this debate by exploring the performance of young children before they fully develop the symbolic number system. Preschoolers at risk of developing DD were compared with typically developing children in a series of tasks investigating time processing and in their 'sense of time', evaluated by parents and teachers. Results yielded a poorer performance in time reproduction of 5-second intervals and in time discrimination, as well as a weaker 'sense of time', in children at risk of DD. These findings provide evidence of a common magnitude system that would be responsible for deficits in both numerical and temporal domains, already at early stages of life.

Dyscalculia and the Calculating Brain

Dyscalculia, like dyslexia, affects some 5% of school-age children but has received much less investigative attention. In two thirds of affected children, dyscalculia is associated with another developmental disorder like dyslexia, attention-deficit disorder, anxiety disorder, visual and spatial disorder, or cultural deprivation. Infants, primates, some birds, and other animals are born with the innate ability, called subitizing, to tell at a glance whether small sets of scattered dots or other items differ by one or more item. This nonverbal approximate number system extends mostly to single digit sets as visual discrimination drops logarithmically to "many" with increasing numerosity (size effect) and crowding (distance effect). Preschoolers need several years and specific teaching to learn verbal names and visual symbols for numbers and school agers to understand their cardinality and ordinality and the invariance of their sequence (arithmetic number line) that enables calculation. This arithmetic linear line differs drastically from the nonlinear approximate number system mental number line that parallels the individual number-tuned neurons in the intraparietal sulcus in monkeys and overlying scalp distribution of discrete functional magnetic resonance imaging activations by number tasks in man. Calculation is a complex skill that activates both visual and spatial and visual and verbal networks. It is less strongly left lateralized than language, with approximate number system activation somewhat more right sided and exact number and arithmetic activation more left sided. Maturation and increasing number skill decrease associated widespread non-numerical brain activations that persist in some individuals with dyscalculia, which has no single, universal neurological cause or underlying mechanism in all affected individuals.

Neural foundations and functional specificity of number representations

Number is a complex category, as with the word "number" we may refer to different entities. First, it is a perceptual property that characterizes any set of individual items, namely its cardinality. The ability to extract the (approximate) cardinality of sets is almost universal in the animal domain and present in humans since birth. In primates, posterior parietal cortex seems to be a crucial site for this ability, even if the degree of selectivity of numerical representations in parietal cortex reported to date appears much lower compared to that of other semantic categories in the ventral stream. Number can also be intended as a mathematical object, which we humans use to count, measure, and order: a (verbal or visual) symbol that stands for the cardinality of a set, the intensity of a continuous quantity or the position of an item on a list. Evidence points to a convergence towards parietal cortex for the semantic coding of numerical symbols and to the bilateral occipitotemporal cortex for the shape coding of Arabic digits and other number symbols.

Time Adaptation Shows Duration Selectivity in the Human Parietal Cortex

Although psychological and computational models of time estimation have postulated the existence of neural representations tuned for specific durations, empirical evidence of this notion has been lacking. Here, using a functional magnetic resonance imaging (fMRI) adaptation paradigm, we show that the inferior parietal lobule (IPL) (corresponding to the supramarginal gyrus) exhibited reduction in neural activity due to adaptation when a visual stimulus of the same duration was repeatedly presented. Adaptation was strongest when stimuli of identical durations were repeated, and it gradually decreased as the difference between the reference and test durations increased. This tuning property generalized across a broad range of durations, indicating the presence of general time-representation mechanisms in the IPL. Furthermore, adaptation was observed irrespective of the subject’s attention to time. Repetition of a nontemporal aspect of the stimulus (i.e., shape) did not produce neural adaptation in the IPL. These results provide neural evidence for duration-tuned representations in the human brain.

A series of functional magnetic resonance imaging (fMRI) adaptation experiments provide empirical evidence for the existence of neural populations in the human inferior parietal lobule that are tuned to specific durations of time.

The human brain has the ability to estimate the passage of time, which allows us to perform complex cognitive tasks such as playing music, dancing, and understanding speech. Scientists have just begun to understand which brain areas become active when we estimate time. However, it still remains a mystery how exactly the information about time is represented in the brain. In this study, we hypothesized that time might be represented by neurons that are specifically tuned to a specific duration, as has been known for simple visual features such as the orientation and the motion direction in the visual cortex. To test this idea, we performed multiple functional magnetic resonance imaging (fMRI) adaptation experiments in which we sought evidence of neuronal adaptation, that is, a reduction in the responsiveness of neurons to repeated presentations of similar durations. Our experiments revealed that the level of brain activity in the right inferior parietal lobule (IPL) was strongly reduced when a stimulus of the same duration was repeatedly presented. This finding was reproduced for a range of subsecond durations. Our results indicate that neurons in the human IPL are tuned to specific preferred durations.

What contributes to individual differences in brain structure?

Individual differences in adult human brain structure have been found to reveal a great deal of information about variability in behaviors, cognitive abilities and mental and physical health. Driven by such evidence, what contributes to individual variation in brain structure has gained accelerated attention as a research question. Findings thus far appear to support the notion that an individual’s brain architecture is determined largely by genetic and environmental influences. This review aims to evaluate the empirical literature on whether and how genes and the environment contribute to individual differences in brain structure. It first considers how genetic and environmental effects may separately contribute to brain morphology, by examining evidence from twin, genome-wide association, cross-sectional and longitudinal studies. Next, evidence for the influence of the complex interplay between genetic and environmental factors, characterized as gene-environment interactions and correlations, is reviewed. In evaluating the extant literature, this review will conclude that both genetic and environmental factors play critical roles in contributing to individual variability in brain structure.

Residual number processing in dyscalculia

Developmental dyscalculia – a congenital learning disability in understanding numerical concepts – is typically associated with parietal lobe abnormality. However, people with dyscalculia often retain some residual numerical abilities, reported in studies that otherwise focused on abnormalities in the dyscalculic brain. Here we took a different perspective by focusing on brain regions that support residual number processing in dyscalculia. All participants accurately performed semantic and categorical colour-decision tasks with numerical and non-numerical stimuli, with adults with dyscalculia performing slower than controls in the number semantic tasks only. Structural imaging showed less grey-matter volume in the right parietal cortex in people with dyscalculia relative to controls. Functional MRI showed that accurate number semantic judgements were maintained by parietal and inferior frontal activations that were common to adults with dyscalculia and controls, with higher activation for participants with dyscalculia than controls in the right superior frontal cortex and the left inferior frontal sulcus. Enhanced activation in these frontal areas was driven by people with dyscalculia who made faster rather than slower numerical decisions; however, activation could not be accounted for by response times per se, because it was greater for fast relative to slow dyscalculics but not greater for fast controls relative to slow dyscalculics. In conclusion, our results reveal two frontal brain regions that support efficient number processing in dyscalculia.

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Dyscalculics (DD) show congenital number impairment due to parietal abnormalities.

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However DD often show residual number skills which have not been studied before.

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We studied the brain networks supporting residual skills and individual differences

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DD: reduced parietal grey-matter, accurate but slower than controls in number tasks

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Faster DD responses over-activated two frontal areas