Relationships between number and space processing in adults with and without dyscalculia

Dyscalculia in Early Adulthood: Implications for Numerical Activities of Daily Living

Numerical abilities are fundamental in our society. As a consequence, poor numerical skills might have a great impact on daily living. This study analyzes the extent to which the numerical deficit observed in young adults with Developmental Dyscalculia (DD) impacts their activities of everyday life. For this purpose, 26 adults with DD and 26 healthy controls completed the NADL, a standardized battery that assesses numerical skills in both formal and informal contexts. The results showed that adults with DD had poorer arithmetical skills in both formal and informal settings. In particular, adults with DD presented difficulties in time and measure estimation as well as money usage in real-world numerical tasks. In contrast, everyday tasks regarding distance estimation were preserved. In addition, the assessment revealed that adults with DD were aware of their numerical difficulties, which were often related to emotional problems and negatively impacted their academic and occupational decisions. Our study highlights the need to design innovative interventions and age-appropriate training for adults with DD to support their numerical skills as well as their social and emotional well-being.

The Cognitive Profile of Math Difficulties: A Meta-Analysis Based on Clinical Criteria

Math difficulties (MD) manifest across various domain-specific and domain-general abilities. However, the existing cognitive profile of MD is incomplete and thus not applicable in typical settings such as schools or clinics. So far, no review has applied inclusion criteria according to DSM or ICD, summarized domain-specific abilities or examined the validity of response time scores for MD identification. Based upon stringent clinical criteria, the current meta-analysis included 34 studies which compared cognitive performances of a group with MD (n = 680) and a group without MD (n = 1565). Criteria according to DSM and ICD were applied to identify MD (percentile rank ≤ 16, age range 8-12 years, no comorbidities/low IQ). Effect sizes for 22 abilities were estimated and separated by their level and type of scoring (AC = accuracy, RT = response time). A cognitive profile of MD was identified, characterized by distinct weaknesses in: (a) computation (calculation [AC], fact retrieval [AC]), (b) number sense (quantity processing [AC], quantity-number linking [RT], numerical relations [AC]), and (c) visual-spatial short-term storage [AC]. No particular strength was found. Severity of MD, group differences in reading performance and IQ did not significantly moderate the results. Further analyses revealed that (a) effects are larger when dealing with numbers or number words than with quantities, (b) MD is not accompanied by any weakness in abilities typically assigned to reading, and (c) weaknesses in visual-spatial short-term storage emphasize the notion that number and space are interlinked. The need for high-quality studies investigating domain-general abilities is discussed.

Multi-method brain imaging reveals impaired representations of number as well as altered connectivity in adults with dyscalculia

Two hypotheses have been proposed about the etiology of neurodevelopmental learning disorders, such as dyslexia and dyscalculia: representation impairments and disrupted access to representations. We implemented a multi-method brain imaging approach to directly investigate these representation and access hypotheses in dyscalculia, a highly prevalent but understudied neurodevelopmental disorder in learning to calculate. We combined several magnetic resonance imaging methods and analyses, including univariate and multivariate analyses, functional and structural connectivity. Our sample comprised 24 adults with dyscalculia and 24 carefully matched controls. Results showed a clear deficit in the non-symbolic magnitude representations in parietal, temporal and frontal regions, as well as hyper-connectivity in visual brain regions in adults with dyscalculia. Dyscalculia in adults was thereby related to both impaired number representations and altered connectivity in the brain. We conclude that dyscalculia is related to impaired number representations as well as altered access to these representations.

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.

Examining the Triple Code Model in numerical cognition: An fMRI study

The Triple Code Model (TCM) of numerical cognition argues for the existence of three representational codes for number: Arabic digits, verbal number words, and analog nonsymbolic magnitude representations, each subserved by functionally dissociated neural substrates. Despite the popularity of the TCM, no study to date has explored all three numerical codes within one fMRI paradigm. We administered three tasks, associated with each of the aforementioned numerical codes, in order to explore the neural correlates of numerosity processing in a sample of adults (N = 46). Independent task-control contrast analyses revealed task-dependent activity in partial support of the model, but also highlight the inherent complexity of a distributed and overlapping fronto-parietal network involved in all numerical codes. The results indicate that the TCM correctly predicts the existence of some functionally dissociated neural substrates, but requires an update that accounts for interactions with attentional processes. Parametric contrasts corresponding to differences in task difficulty revealed specific neural correlates of the distance effect, where closely spaced numbers become more difficult to discriminate than numbers spaced further apart. A conjunction analysis illustrated overlapping neural correlates across all tasks, in line with recent proposals for a fronto-parietal network of number processing. We additionally provide tentative results suggesting the involvement of format-independent numerosity-sensitive retinotopic maps in the early visual stream, extending previous findings of nonsymbolic stimulus selectivity. We discuss the functional roles of the components associated with the model, as well as the purported fronto-parietal network, and offer arguments in favor of revising the TCM.

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.

Representations of numerical and non-numerical magnitude both contribute to mathematical competence in children

A growing body of evidence suggests that non-symbolic representations of number, which humans share with nonhuman animals, are functionally related to uniquely human mathematical thought. Other research suggesting that numerical and non-numerical magnitudes not only share analog format but also form part of a general magnitude system raises questions about whether the non-symbolic basis of mathematical thinking is unique to numerical magnitude. Here we examined this issue in 5- and 6-year-old children using comparison tasks of non-symbolic number arrays and cumulative area as well as standardized tests of math competence. One set of findings revealed that scores on both magnitude comparison tasks were modulated by ratio, consistent with shared analog format. Moreover, scores on these tasks were moderately correlated, suggesting overlap in the precision of numerical and non-numerical magnitudes, as expected under a general magnitude system. Another set of findings revealed that the precision of both types of magnitude contributed shared and unique variance to the same math measures (e.g. calculation and geometry), after accounting for age and verbal competence. These findings argue against an exclusive role for non-symbolic number in supporting early mathematical understanding. Moreover, they suggest that mathematical understanding may be rooted in a general system of magnitude representation that is not specific to numerical magnitude but that also encompasses non-numerical magnitude.

A general number-to-space mapping deficit in developmental dyscalculia

Previous research on developmental dyscalculia (DD) suggested that deficits in the number line estimation task are related to a failure to represent number magnitude linearly. This conclusion was derived from the observation of logarithmically shaped estimation patterns. However, recent research questioned this idea of an isomorphic relationship between estimation patterns and number magnitude representation. In the present study, we evaluated an alternative hypothesis: impairments in the number line estimation task are due to a general deficit in mapping numbers onto space. Adults with DD and a matched control group had to learn linear and non-linear layouts of the number line via feedback. Afterwards, we assessed their performance how well they learnt the new number-space mappings. We found irrespective of the layouts worse performance of adults with DD. Additionally, in case of the linear layout, we observed that their performance did not differ from controls near reference points, but that differences between groups increased as the distance to reference point increased. We conclude that worse performance of adults with DD in the number line task might be due a deficit in mapping numbers onto space which can be partly overcome relying on reference points.

Development of magnitude processing in children with developmental dyscalculia: space, time, and number

Developmental dyscalculia (DD) is a learning disorder associated with impairments in a preverbal non-symbolic approximate number system (ANS) pertaining to areas in and around the intraparietal sulcus (IPS). The current study sought to enhance our understanding of the developmental trajectory of the ANS and symbolic number processing skills, thereby getting insight into whether a deficit in the ANS precedes or is preceded by impaired symbolic and exact number processing. Recent work has also suggested that humans are endowed with a shared magnitude system (beyond the number domain) in the brain. We therefore investigated whether children with DD demonstrated a general magnitude deficit, stemming from the proposed magnitude system, rather than a specific one limited to numerical quantity. Fourth graders with DD were compared to age-matched controls and a group of ability-matched second graders, on a range of magnitude processing tasks pertaining to space, time, and number. Children with DD displayed difficulties across all magnitude dimensions compared to age-matched peers and showed impaired ANS acuity compared to the younger, ability-matched control group, while exhibiting intact symbolic number processing. We conclude that (1) children with DD suffer from a general magnitude-processing deficit, (2) a shared magnitude system likely exists, and (3) a symbolic number-processing deficit in DD tends to be preceded by an ANS deficit.

The impact of mathematical proficiency on the number-space association

A specific instance of the association between numerical and spatial representations is the SNARC (Spatial Numerical Association of Response Codes) effect. The SNARC effect describes the finding that during binary classification of numbers participants are faster to respond to small/large numbers with the left/right hand respectively. Even though it has been frequently replicated, important inter-individual variability has also been reported. Mathematical proficiency is an obvious candidate source for inter-individual variability in numerical judgments, but studies investigating its influence on the SNARC effect remain scarce. The present experiment included a total of 95 University students, divided into three groups differing significantly in their mathematical proficiency levels. Using group analyses, it appeared that the three groups differed significantly in the strength of their number-space associations in a parity judgment task. This result was further confirmed on an individual level, with higher levels in arithmetic leading to relatively weaker SNARC effects. To explain this negative relationship we propose accounts based on differences in access to qualitatively different numerical representations and also consider more domain general factors, with a focus on inhibition capacities.

Symbolic and non symbolic numerical representation in adults with and without developmental dyscalculia

Background

The question whether Developmental Dyscalculia (DD; a deficit in the ability to process numerical information) is the result of deficiencies in the non symbolic numerical representation system (e.g., a group of dots) or in the symbolic numerical representation system (e.g., Arabic numerals) has been debated in scientific literature. It is accepted that the non symbolic system is divided into two different ranges, the subitizing range (i.e., quantities from 1-4) which is processed automatically and quickly, and the counting range (i.e., quantities larger than 4) which is an attention demanding procedure and is therefore processed serially and slowly. However, so far no study has tested the automaticity of symbolic and non symbolic representation in DD participants separately for the subitizing and the counting ranges.

Methods

DD and control participants undergo a novel version of the Stroop task, i.e., the Enumeration Stroop. They were presented with a random series of between one and nine written digits, and were asked to name either the relevant written digit (in the symbolic task) or the relevant quantity of digits (in the non symbolic task) while ignoring the irrelevant aspect.

Result

DD participants, unlike the control group, didn't show any congruency effect in the subitizing range of the non symbolic task.

Conclusion

These findings suggest that DD may be impaired in the ability to process symbolic numerical information or in the ability to automatically associate the two systems (i.e., the symbolic vs. the non symbolic). Additionally DD have deficiencies in the non symbolic counting range.