Financial and numerical abilities: patterns of dissociation in neurological and psychiatric diseases.

The present work investigates whether financial abilities can be associated with numerical abilities and with general cognitive abilities. We compared performance on numerical and financial tests, and on tests routinely used to measure general cognitive performance, in healthy controls and in a group of people with heterogeneous pathological conditions including mild cognitive impairment, amyotrophic lateral sclerosis, traumatic brain injury, and schizophrenia. Patients showed lower performances in both numerical and financial abilities compared to controls. Numerical and financial skills were positively correlated in both groups, but they correlated poorly with measures of general cognitive functioning. Crucially, only basic financial tasks -such as counting currencies- but not advanced ones -like financial judgments- were associated with numerical or general cognitive functioning in logistic regression analyses. Conversely, advanced financial abilities, but not basic ones, were associated with abstract reasoning. At a qualitative analysis, we found that deficits in numerical and financial abilities might double dissociate. Similarly, we observed double dissociations between difficulties in financial abilities and cognitive deficits. In conclusion, financial abilities may be independent of numerical skills, and financial deficits are not always related to the presence of cognitive difficulties. These findings are important for both clinical and legal practice.

Changes in the superior longitudinal fasciculus and anterior thalamic radiation in the left brain are associated with developmental dyscalculia.

Developmental dyscalculia is a neurodevelopmental disorder specific to arithmetic learning even with normal intelligence and age-appropriate education. Difficulties often persist from childhood through adulthood lowering the individual's quality of life. However, the neural correlates of developmental dyscalculia are poorly understood. This study aimed to identify brain structural connectivity alterations in developmental dyscalculia. All participants were recruited from a large scale, non-referred population sample in a longitudinal design. We studied 10 children with developmental dyscalculia (11.3 ± 0.7 years) and 16 typically developing peers (11.2 ± 0.6 years) using diffusion-weighted magnetic resonance imaging. We assessed white matter microstructure with tract-based spatial statistics in regions-of-interest tracts that had previously been related to math ability in children. Then we used global probabilistic tractography for the first time to measure and compare tract length between developmental dyscalculia and typically developing groups. The high angular resolution diffusion-weighted magnetic resonance imaging and crossing-fiber probabilistic tractography allowed us to evaluate the length of the pathways compared to previous studies. The major findings of our study were reduced white matter coherence and shorter tract length of the left superior longitudinal/arcuate fasciculus and left anterior thalamic radiation in the developmental dyscalculia group. Furthermore, the lower white matter coherence and shorter pathways tended to be associated with the lower math performance. These results from the regional analyses indicate that learning, memory and language-related pathways in the left hemisphere might be related to developmental dyscalculia in children.

Quantity discrimination by kittens of the domestic cat (Felis silvestris catus).

Quantitative abilities are well described in many species and in diverse life situations, including in the adult domestic cat. However, such abilities have been much less studied during ontogeny. In the present study we examined spontaneous quantity discrimination by pre-weaning age kittens in two-way food choice experiments. In Experiment 1, 26 kittens performed 12 trials with different ratios between the number of same-size food items. In Experiment 2, 24 other kittens performed eight trials with different ratios between the size of two food items. We found, in general, that the kittens discriminated between the different amounts of food and spontaneously chose the larger one, but that their choice was influenced by the ratio of difference. The kittens in Experiment 1 chose the larger number of same-size food items if the ratio was smaller than 0.4 and in Experiment 2 they chose the larger pieces of food if the ratio between the items was smaller than 0.5. Because the kittens' choice was not influenced by the absolute number of food items or the numerical difference between them in Experiment 1, it suggests that their cognitive performance relied on an analog magnitude system rather than on an object file system during the quantity discrimination tasks. We discuss our results considering the ecological and social background of cats and compare it with the performance of previously studied species.

The influence of visual illusion perception on numerosity estimation could be evolutionarily conserved: exploring the numerical Delboeuf illusion in humans (Homo sapiens) and fish (Poecilia reticulata).

Discriminating between different quantities is an essential ability in daily life that has been demonstrated in a variety of non-human vertebrates. Nonetheless, what drives the estimation of numerosity is not fully understood, as numerosity intrinsically covaries with several other physical characteristics. There is wide debate as to whether the numerical and spatial abilities of vertebrates are processed by a single magnitude system or two different cognitive systems. Adopting a novel approach, we aimed to investigate this issue by assessing the interaction between area size and numerosity, which has never been conceptualized with consideration for subjective experience in non-human animals. We examined whether the same perceptual biases underlying one of the best-known size illusions, the Delboeuf illusion, can be also identified in numerical estimation tasks. We instructed or trained human participants and guppies, small teleost fish, to select a target numerosity (larger or smaller) of squares between two sets that actually differed in their numerosity. Subjects were also presented with illusory trials in which the same numerosity was presented in two different contexts, against a large and a small background, resembling the Delboeuf illusion. In these trials, both humans and fish demonstrated numerical biases in agreement with the perception of the classical version of the Delboeuf illusion, with the array perceived as larger appearing more numerous. Thus, our results support the hypothesis of a single magnitude system, as perceptual biases that influence spatial decisions seem to affect numerosity judgements in the same way.

Neurocognitive correlates of numerical abilities in Parkinson's disease.

People with Parkinson's disease (PD) experience functional limitations early in the progression of the disease, showing, among other cognitive deficits, difficulties in mathematical abilities. The neural correlates of such abilities have been scarcely investigated in PD, and it is not known whether patients may exhibit difficulties only in formal numerical tasks (e.g., mental multiplications), or also in everyday activities involving numbers (i.e., informal numerical abilities such as time estimates). The present study investigated formal and informal numerical abilities in PD patients and explored their relationship with cortical and subcortical brain volume. We examined patients with PD and mild cognitive impairment (PD-MCI) and age-matched healthy controls (HCs) using the numerical activities of daily living (NADL) battery, assessing both scholastic numerical abilities (formal test), and the ability to use numbers in everyday life (informal test). We compared NADL performances in both groups. Within the PD group, we investigated the association between NADL and cortical and subcortical volumes using multiple linear regressions. The correlation with other cognitive tests was also explored. PD-MCI performed worse than HC in the formal NADL test. In PD-MCI patients, brain-behavior correlations showed two distinct patterns: cortical volumes correlated positively, while striatal volumes correlated negatively with NADL formal tasks. Both formal and informal tests correlated with measures of cognitive functioning. Our results suggest specific impairments in formal numerical abilities in PD-MCI, but not in everyday activities. While cortical atrophy is associated with worse performance, the negative correlations with subcortical regions suggest that their activation may reflect potential compensatory mechanisms.

Towards a standardization of non-symbolic numerical experiments: GeNEsIS, a flexible and user-friendly tool to generate controlled stimuli.

Several studies have suggested that vertebrate and invertebrate species may possess a number sense, i.e. an ability to process in a non-symbolic and non-verbal way the numerousness of a set of items. However, this hypothesis has been challenged by the presence of other non-numerical continuous physical variables, which vary along with numerosity (i.e., any change in the number of visual physical elements in a set naturally involves a related change in visual features such as area, density, contour length and convex hull of the stimulus). It is therefore necessary to control and manipulate the continuous physical information when investigating the ability of humans and other animals to perceive numerousness. During decades of research, different methods have been implemented in order to address this issue, which has implications for experiment replicability and inter-species comparisons, since no general standardized procedure is currently being used. Here we present the 'Generation of Numerical Elements Images Software' (GeNEsIS) for the creation of non-symbolic numerical arrays in a standardized and user-friendly environment. The main aim of this tool is to provide researchers in the field of numerical cognition a manageable and precise instrument to produce visual numerical arrays controlled for all the continuous variables. Additionally, we implemented the ability to actively guide stimuli presentation during habituation/dishabituation and dual-choice comparison tasks used in human and comparative research.

The association of basic numerical abilities and math achievement: The mediating role of visuospatial and arithmetical abilities.

Basic numerical abilities such as number line estimation have been observed repeatedly to be associated with mathematical achievement. Recently, it was argued that the association between basic numerical abilities and mathematical achievement is fully mediated by visuospatial abilities. However, arithmetical abilities have not yet been considered as influencing this association, even though solution strategies in number line estimation as well as mathematical achievement often involve arithmetical procedures. Therefore, we investigated the mediating role of arithmetical and visuospatial abilities on the association between number line estimation and mathematical achievement in a sample of n = 599 German elementary school students. The results indicated that arithmetical abilities as well as visuospatial abilities mediated the association between number line estimation and mathematical achievement. However, neither visuospatial nor arithmetical abilities fully mediated the association between number line estimation and mathematical achievement when considered in isolation. This substantiates the relevance of the intertwined development of visuospatial and arithmetical abilities as well as basic numerical abilities such as number line estimation (i.e., the combination of domain-specific numerical and domain-general abilities) driving mathematical achievement.

Examining the relevance of basic numerical skills for mathematical achievement in secondary school using a within-task assessment approach.

Previous research repeatedly found basic numerical abilities (e.g., magnitude understanding, arithmetic fact knowledge, etc.) to predict young students' current and later arithmetic achievement as assessed by achievement tests - even when controlling for the influence of domain-general abilities (e.g., intelligence, working memory). However, to the best of our knowledge, previous studies hardly addressed this issue in secondary school students. Additionally, they primarily assessed basic numerical abilities in a between-task approach (i.e., using different tasks for different abilities). Finally, their relevance for real-life academic outcomes such as mathematics grades has only rarely been investigated. The present study therefore pursued an approach using one and the same task (i.e., a within-task approach) to reduce confounding effects driven by between-task differences. In particular, we evaluated the relevance of i) number magnitude understanding, ii) arithmetic fact knowledge, and iii) conceptual and procedural knowledge for the mathematics grades of 81 students aged between ten and thirteen (i.e., in Grades 5 and 6) employing the number bisection task. Results indicated that number magnitude understanding, arithmetic fact knowledge, and conceptual and procedural knowledge contributed to explaining mathematics grades even when controlling for domain-general cognitive abilities. Methodological and practical implications of the results are discussed.

Aphasia and Math: Deficits with Basic Number Comprehension and in Numerical Activities of Daily Living.

OBJECTIVE: In the present study, we explored numerical problems in individuals with aphasia. We investigate whether numerical deficits, usually accompanying aphasia, can be observed on number comprehension tasks that do not necessarily require an oral response. METHOD: Individuals with aphasia were classified into anterior, posterior, and global subgroups according to the lesion type. To investigate numerical cognition, we used a relatively recent tool, the Numerical Activities of Daily Living (NADL). RESULTS: The results showed that individuals with aphasia have problems with tasks of basic number comprehension as well as in most NADL. In the formal part of the NADL, anterior aphasic patients made comparatively more errors than the posterior aphasic patients. Global aphasic patients presented an invariably poor performance on almost all tasks. CONCLUSION: The results provide insight into how numerical deficits may impair an individual with aphasia in activities of daily living. This study is a preliminary attempt to start the validation process of the NADL for the Greek population.

A sense of number in invertebrates.

Non-symbolic numerical abilities are widespread among vertebrates due to their important adaptive value. Moreover, these abilities were considered peculiar of vertebrate species as numerical competence is regarded as cognitively sophisticated. However, recent evidence convincingly showed that this is not the case: invertebrates, with their limited number of neurons, proved able to successfully discriminate different quantities (e.g., of prey), to use the ordinal property of numbers, to solve arithmetic operations as addition and subtraction and even to master the concept of zero numerosity. To date, though, the debate is still open on the presence and the nature of a «sense of number¼ in invertebrates. Whether this is peculiar for discrete countable quantities (numerosities) or whether this is part of a more general magnitude system dealing with both discrete and continuous quantities, as hypothesized for humans and other vertebrates. Here we reviewed the main studies on numerical abilities of invertebrates, discussing in particular the recent findings supporting the hypothesis of a general mechanism that allows for processing of both discrete (i.e., number) and continuous dimensions (e.g., space).

Mastery of structured quantities like finger or dice patterns predict arithmetic performance.

In the present study, we investigated whether structured quantities like finger or dice patterns are enumerated better than unstructured quantities because they may not require counting. Moreover, we hypothesized children's mastery of structured quantities to predict their later arithmetic performance longitudinally. In particular, we expected that children more proficient in enumerating structured quantities early in their numerical development, should develop more effective calculation strategies later because they may rely on counting less. Therefore, we conducted a longitudinal study (including 116 children, 58 girls) over the course of about 7 months from preschool (at about 6 years of age) to the middle of first grade. Results showed that structured quantities were indeed enumerated more accurately and faster than unstructured quantities in preschool. Additionally, we observed significant associations of enumeration of structured and unstructured with children's addition performance in first grade. However, regression analysis indicated only enumeration of structured but not unstructured quantities to significantly predict later addition performance. In sum, this longitudinal study clearly indicates that mastery of structured quantities seems to be beneficial for children's development of basic arithmetic abilities.

Giraffes go for more: a quantity discrimination study in giraffes (Giraffa camelopardalis).

Many species, including humans, rely on an ability to differentiate between quantities to make decisions about social relationships, territories, and food. This study is the first to investigate whether giraffes (Giraffa camelopardalis) are able to select the larger of two sets of quantities in different conditions, and how size and density affect these decisions. In Task 1, we presented five captive giraffes with two sets containing a different quantity of identical foods items. In Tasks 2 and 3, we also modified the size and density of the food reward distribution. The results showed that giraffes (i) can successfully make quantity judgments following Weber's law, (ii) can reliably rely on size to maximize their food income, and (iii) are more successful when comparing sparser than denser distributions. More studies on different taxa are needed to understand whether specific selective pressures have favored the evolution of these skills in certain taxa.

Corrigendum: Searching for the Critical p of Macphail's Null Hypothesis: The Contribution of Numerical Abilities of Fish.

[This corrects the article on p. 55 in vol. 11, PMID: 32116895.].

Time Reading in Middle and Secondary School Students: The Influence of Basic-Numerical Abilities.

Time reading skills are central for the management of personal and professional life. However, little is known about the differential influence of basic numerical abilities on analog and digital time reading in general and in middle and secondary school students in particular. The present study investigated the influence of basic numerical skills separately for analog and digital time reading in N = 709 students from 5th to 8th grade. The present findings suggest that the development of time reading skills is not completed by the end of primary school. Results indicated that aspects of magnitude manipulation and arithmetic fact knowledge predicted analog time reading significantly over and above the influence of age. Furthermore, results showed that spatial representations of number magnitude, magnitude manipulation, arithmetic fact knowledge, and conceptual knowledge were significant predictors of digital time reading beyond general cognitive ability and sex. To the best of our knowledge, the present study is the first to show differential effects of basic numerical abilities on analog and digital time reading skills in middle and secondary school students. As time readings skills are crucial for everyday life, these results are highly relevant to better understand basic numerical processes underlying time reading.

Magnitude processing in populations with spina-bifida: The role of visuospatial and working memory processes.

People with Spina Bifida usually experience difficulties with mathematics. In a series of other developmental disorders, a magnitude processing deficit was considered to be the main source of subsequent difficulties in mathematics. The processing of magnitude could be numerical (which is the larger number) or non-numerical such as spatial (e.g., which is the longer?) or temporal (which one last longer?) for instance. However, no study yet has examined directly magnitude processes in a population with Spina Bifida. On the other hand, recent studies in people with genetic syndromes have suggested that visuospatial and working memory processes play an important role in magnitude processing, including number magnitude. Therefore, in this study we explored for the first time magnitude representation using several tasks with different visuospatial and working memory processing requirements, cognitive skills frequently impaired in Spina Bifida. Results showed children with SB presented a global magnitude processing deficit for non-numerical and numerical comparison tasks, but not in symbolic number magnitude tasks compared to controls. Importantly, visuospatial skills and working memory abilities could partially explain the differences between groups in comparison and estimation tasks. This study proposes that magnitude processing difficulties in children with SB could be due to higher cognitive factors such as visuospatial and working memory processes.

Searching for the Critical p of Macphail's Null Hypothesis: The Contribution of Numerical Abilities of Fish.

In 1985, Macphail argued that there are no differences among the intellects of non-human vertebrates and that humans display unique cognitive skills because of language. Mathematical abilities represent one of the most sophisticated cognitive skills. While it is unquestionable that humans exhibit impressive mathematical skills associated with language, a large body of experimental evidence suggests that Macphail hypothesis must be refined in this field. In particular, the evidence that also small-brained organisms, such as fish, are capable of processing numerical information challenges the idea that humans display unique cognitive skills. Like humans, fish may take advantage of using continuous quantities (such as the area occupied by the objects) as proxy of number to select the larger/smaller group. Fish and humans also showed interesting similarities in the strategy adopted to learn a numerical rule. Collective intelligence in numerical estimation has been also observed in humans and guppies. However, numerical acuity in humans is considerably higher than that reported in any fish species investigated, suggesting that quantitative but not qualitative differences do exist between humans and fish. Lastly, while it is clear that contextual factors play an important role in the performance of numerical tasks, inter-species variability can be found also when different fish species were tested in comparable conditions, a fact that does not align with the null hypothesis of vertebrate intelligence. Taken together, we believe that the recent evidence of numerical abilities in fish call for a deeper reflection of Macphail's hypothesis.

Anisotropy of perceived numerosity: Evidence for a horizontal-vertical numerosity illusion.

Many studies have investigated whether numerical and spatial abilities share similar cognitive systems. A novel approach to this issue consists of investigating whether the same perceptual biases underlying size illusions can be identified in numerical estimation tasks. In this study, we required adult participants to estimate the number of white dots in arrays made of white and black dots displayed in such a way as to generate horizontal-vertical illusions with inverted T and L configurations. In agreement with previous literature, we found that participants tended to underestimate the target numbers. However, in the presence of the illusory patterns, participants were less inclined to underestimate the number of vertically aligned white dots. This reflects the perceptual biases underlying horizontal-vertical illusions. In addition, we identified an enhanced illusory effect when participants observed vertically aligned white dots in the T shape compared to the L shape, a result that resembles the length bisection bias reported in the spatial domain. Overall, we found the first evidence that numerical estimation differs as a function of the vertical or horizontal displacement of the stimuli. In addition, the involvement of the same perceptual biases observed in spatial tasks supports the idea that spatial and numerical abilities share similar cognitive processes.

The experience-based format of probability improves probability estimates: The moderating role of individual differences in numeracy.

People with low statistical numeracy have difficulties understanding numerical information. For instance, they often misunderstand the probability of experiencing side effects, which could reduce adherence to medical treatments. We investigated whether presenting information about probability using a method based on the direct experience of events influences the accuracy of probability estimates compared to viewing a static numerical description of the same information. Participants completed a numeracy test and were randomly assigned to one of two conditions. In the description-based probability condition, participants were presented with 24 binomial distributions consisting of a target stimulus "X" and a distractor stimulus "·" in the form of odds (the distribution "7 × 13 ·" is an example of a 35% probability: here the target [distractor] stimulus was present 7[13] times in a 20-stimulus distribution). In the experience-based probability condition, participants observed the same information but the stimuli were randomly arranged and displayed sequentially. Participants in both conditions estimated the probability of the target stimulus in each trial. In the experience-based format participants with low numeracy made more accurate probability estimates in comparison to the description-based format. In contrast, accuracy in participants with high numeracy was similar in the two formats.

Arabic number writing in children with developmental dyslexia / A escrita de numerais arábicos em crianças com dislexia do desenvolvimento

Number transcoding is a basic numerical processing task that demands verbal skills during its execution. The goal of this study was to investigate number transcoding ability in children with developmental dyslexia. Twenty-three children with typical development and twenty-six children with developmental dyslexia participated in this study. Results showed that children with dyslexia show a deficit in phonological processing as well as in number transcoding. Repeated-measures analysis of covariance indicated that the dyslexia group presented performance below the average in the number transcoding. Regression analyses indicated that short-term verbal memory, phoneme deletion, rhyme judgment task and automatized naming was a strong predictor of number transcoding difficulties. Children with dyslexia present number transcoding deficits regardless of age and educational level.

A transcodificação numérica é uma tarefa do processamento numérico básico que demanda habilidades verbais durante a sua execução. O objetivo deste estudo foi investigar a habilidade de transcodificação numérica em crianças com dislexia do desenvolvimento. Participaram deste estudo 23 crianças com desenvolvimento escolar típico e 26 crianças com dislexia do desenvolvimento. Os resultados indicaram que crianças com dislexia apresentam um déficit no processamento fonológico e na transcodificação numérica ao longo de todas as séries escolares investigadas aqui. Uma análise de variância de medidas repetidas indicou que o grupo com dislexia apresentou desempenho abaixo da média na transcodificação numérica. Análises de regressão indicaram que a memória de curto prazo verbal, a supressão de fonemas, o julgamento de rimas e a tarefa de nomeação seriada rápida foram fortes preditores das dificuldades encontradas na transcodificação numérica. Crianças com dislexia apresentam déficits de transcodificação numérica independentemente da idade e nível de escolaridade.