Number skills are maintained in healthy ageing

Factors influencing the role of inhibitory control in non-symbolic numerical processing

Previous studies have found that inhibitory control plays an important role in non-symbolic numerical processing. However, this role may be influenced by the visual cue control method or the stimulus' presentation time. We investigated these questions by conducting three experiments using a priming paradigm to compare the level of inhibitory control in a sequential dot comparison task with single-dimensional and multi-dimensional control of visual cues under two presentation time conditions (300 ms and 1500 ms). We found that neither the method of visual cue control nor the presentation time of dot arrays affected the level of inhibitory control in the dot comparison task. These results reveal a stable role of inhibitory control in non-symbolic numerical processing, providing further evidence for integrating numerical and visual information during non-symbolic numerical processing.

Weaker number sense accounts for impaired numerosity perception in dyscalculia: Behavioral and computational evidence

Impaired numerosity perception in developmental dyscalculia (low "number acuity") has been interpreted as evidence of reduced representational precision in the neurocognitive system supporting non-symbolic number sense. However, recent studies suggest that poor numerosity judgments might stem from stronger interference from non-numerical visual information, in line with alternative accounts that highlight impairments in executive functions and visuospatial abilities in the etiology of dyscalculia. To resolve this debate, we used a psychophysical method designed to disentangle the contribution of numerical and non-numerical features to explicit numerosity judgments in a dot comparison task and we assessed the relative saliency of numerosity in a spontaneous categorization task. Children with dyscalculia were compared to control children with average mathematical skills matched for age, IQ, and visuospatial memory. In the comparison task, the lower accuracy of dyscalculics compared to controls was linked to weaker encoding of numerosity, but not to the strength of non-numerical biases. Similarly, in the spontaneous categorization task, children with dyscalculia showed a weaker number-based categorization compared to the control group, with no evidence of a stronger influence of non-numerical information on category choice. Simulations with a neurocomputational model of numerosity perception showed that the reduction of representational resources affected the progressive refinement of number acuity, with little effect on non-numerical bias in numerosity judgments. Together, these results suggest that impaired numerosity perception in dyscalculia cannot be explained by increased interference from non-numerical visual cues, thereby supporting the hypothesis of a core number sense deficit. RESEARCH HIGHLIGHTS: A strongly debated issue is whether impaired numerosity perception in dyscalculia stems from a deficit in number sense or from poor executive and visuospatial functions. Dyscalculic children show reduced precision in visual numerosity judgments and weaker number-based spontaneous categorization, but no increasing reliance on continuous visual properties. Simulations with deep neural networks demonstrate that reduced neural/computational resources affect the developmental trajectory of number acuity and account for impaired numerosity judgments. Our findings show that weaker number acuity in developmental dyscalculia is not necessarily related to increased interference from non-numerical visual cues.

Age-related effects in magnitude and place-value processing

While general cognitive skills decline during aging, numerical skills seem to be mainly preserved. Such skills are essential for an independent life up to old age, e.g., when dealing with money or time. Operating with numbers usually requires number magnitude and place-value processing. The question is whether these processes are negatively affected by aging due to the general cognitive decline or positively affected due to lifelong experience with numbers. Therefore, we investigated age-related changes in the distance and compatibility effects in single-digit, two-digit, and four-digit number comparison. On the one hand, older adults took longer for number processing and showed a smaller distance effect, indicating altered number magnitude representations. On the other hand, older adults were better in place-value processing as indicated by a smaller compatibility effect than in younger adults. We conclude that aging differentially affects basic numerical skills.

Duration, numerosity and length processing in healthy ageing and Parkinson's disease

People constantly process temporal, numerical, and length information in everyday activities and interactions with the environment. However, it is unclear whether quantity perception changes during ageing. Previous studies have provided heterogeneous results, sometimes showing an age-related effect on a particular quantity, and other times reporting no differences between young and elderly samples. However, three dimensions were never compared within the same study. Here, we conducted two experiments with the aim of investigating the processing of duration, numerosity and length in both healthy and pathological ageing. The experimental paradigm consisted of three bisection tasks in which participants were asked to judge whether the presented stimulus (i.e. a time interval, a group of dots, or a line) was more similar to the short/few or long/many standards. The first study recruited healthy young and elderly participants, while the second recruited healthy elderly participants and patients with Parkinson's disease, a clinical condition commonly associated with temporal impairments. The results of both experiments showed that discrimination precision differed between domains in all groups, with higher precision in the numerosity task and lower sensitivity in judging duration. Furthermore, while discrimination abilities were affected in healthy elderly and, even more so, in Parkinson's disease group, no domain-specific impairments emerged. According to our research, reduced discrimination precision might be explained by an alteration of a single system for all quantities or by an age-related general cognitive decline.

Numerosity comparison, cognitive strategies, and general cognitive functioning in older people

Introduction

Studies have shown age-related differences in numerical cognition, for example, in the level of numerosity comparison ability. Moreover, some studies point out individual differences in the cognitive strategies employed during the performance of numerosity comparison tasks and reveal that they are related to the aging process. One probable cause of these differences is the level of cognitive functioning. The aim of our study was to determine the relationships among numerosity comparison ability, the cognitive strategies utilized in the performance of numerosity comparison tasks and the general cognitive functioning in older people.

Methods

Forty-seven elderly people participated in the study. The participants were examined using overall cognitive functioning scales and computerized numerosity comparison task.

Results

The results showed many correlations between the participants' level of cognitive functioning and the percent of correct responses (PCR) and response time (RT) during numerosity comparison, as well as with the cognitive strategies applied by the participants. Task correctness was positively related to the level of performance in the attention and executive function tasks. In contrast, the long-term memory resources index and visuospatial skills level were negatively correlated with RT regarding numerosity comparison task performance. The level of long-term memory resources was also positively associated with the frequency of use of more complex cognitive strategies. Series of regression analyses showed that both the level of general cognitive functioning and the cognitive strategies employed by participants in numerosity comparison can explain 9-21 percent of the variance in the obtained results.

Discussion

In summary, these results showed significant relationships between the level of cognitive functioning and proficiency in numerosity comparison measured in older people. Moreover, it has been shown that cognitive resources level is related to the strategies utilized by older people, which indicates the potential application for cognitive strategy examinations in the development of new diagnostic tools.

How learning influences non-symbolic numerical processing: effects of feedback in the dot comparison task

It has long been debated how humans estimate the numerosity of sets of elements and what role continuous visual properties play in this process. The dot comparison task, in which the more numerous of two dot arrays must be selected, is a dominant method to investigate this phenomenon. It has been shown that the visual properties of the two dot patterns strongly influence the comparison. This influence can be systematically investigated by manipulating visual properties congruently and incongruently with numerosity. However, it remains unclear how learning and prior experience affect the influence of the visual properties. To address this question, we introduced feedback into the classical dot comparison task: during the learning phase, participants in the experimental group received feedback after each trial indicating whether their answer was correct whereas participants in the control group did not. After the learning phase, neither group received feedback. The convex hull of the dot patterns and the average dot diameter were manipulated congruently and incongruently with numerosity. Our results show that feedback had no effect on overall performance. However, when manipulated separately, dot diameter no longer affected performance in the experimental group after the learning phase, but it did in the control group. Moreover, this effect remained visible even when diameter and convex hull were manipulated simultaneously. This pattern of results is consistent with the notion of sensory integration which proposes that weights are assigned to different visual cues and that numerical judgments depend on an additive combination of these weights. We also found a correlation between performance on an arithmetic task and performance on trials in which dot size was manipulated incongruently with numerosity. However, there were no correlations between an inhibition task and performance in the dot comparison task. Taken together, the current results suggest that learning with feedback may affect some visual properties but not others. Future studies should further investigate a wider range of visual properties to examine which of them can be influenced by learning and under what conditions learning occurs.

To what extent is dot comparison an appropriate measure of approximate number system?

Introduction

Number sense has been systematically measured using dot comparison tasks. However, recent studies have reported that performance on dot comparison might be influenced inhibitory control and visual properties of dot arrays. In the present study, we analysed the influence of continuous magnitude, inhibitory control, and numerical ratio on the dot comparison performance of preschool children.

Methods

Participants were 517 preschool children from 13 different schools in Chile. Children completed a dot comparison and two inhibitory control tasks. Gebuis and Reynvoet method was used to create well-controlled dot arrays for use in the dot comparison task. A logistic mixed effects model was conducted to predict participants' dot comparison accuracy. Continuous magnitude and ratio were entered as level-1 predictors and inhibitory control as level-2 predictors.

Results

The results showed that all predictors made a significant contribution to dot comparison accuracy. Furthermore, a significant double interaction (inhibitory control x continuous magnitude) and a triple interaction (inhibitory control x continuous magnitude x ratio) showed that the contribution of inhibitory control skills in dot comparison accuracy depends on the continuous properties of dot arrays and ratio.

Discussion

These findings suggest that preschool children rely more on continuous magnitudes than numerosity in dot comparison tasks. They also indicate that the greater children's inhibitory control, the more able they are to respond based on numerosity in fully incongruent trials, particularly when ratio is low (easiest items). Taken together, the above findings support the competing processes account provided that both ANS and inhibitory control skills influence performance on dot comparison tasks.

Role of Lateral Inhibition on Visual Number Sense

Newborn animals, such as 4-month-old infants, 4-day-old chicks, and 1-day-old guppies, exhibit sensitivity to an approximate number of items in the visual array. These findings are often interpreted as evidence for an innate "number sense." However, number sense is typically investigated using explicit behavioral tasks, which require a form of calibration (e.g., habituation or reward-based training) in experimental studies. Therefore, the generation of number sense may be the result of calibration. We built a number-sense neural network model on the basis of lateral inhibition to explore whether animals demonstrate an innate "number sense" and determine important factors affecting this competence. The proposed model can reproduce size and distance effects of output responses of number-selective neurons when network connection weights are set randomly without an adjustment. Results showed that number sense can be produced under the influence of lateral inhibition, which is one of the fundamental mechanisms of the nervous system, and independent of learning.

EXPRESS: How negative emotions affect young and older adults' numerosity estimation performance

In this study, we investigated the influence of negative emotions on numerosity estimation and whether this influence changes with aging during adulthood. Young and older adults were asked to estimate and compare the numerosity of collections of elements (cars or dots) with a two-digit number. Collections of elements were preceded by emotionally neutral (e.g., mushrooms) or emotionally negative (e.g., a corpse) pictures. Stimuli were easier (i.e., small-ratio) or harder (i.e., large-ratio) items. Young and older participants obtained similar numerosity estimation performance. Interestingly, participants were less accurate under negative emotions than under neutral emotions when they estimated numerosity of collections of abstract elements (i.e., dots). In contrast, participants improved their performance under negative emotions while estimating collections of non-abstract, daily-life elements (i.e., cars). These findings have important implications for furthering our understanding of the role of negative emotions in numerosity estimation and age-related differences therein.

The ironic effect of older adults' increased task motivation: Implications for neurocognitive aging

Recent work suggests that most older adults who volunteer to take part in cognitive experiments are more motivated to do well than are undergraduate students. This empirical evidence is echoed by the impressions of cognitive aging researchers. We surveyed a large group (N = 88) of researchers asking about their perceptions of younger and older adults' motivation to take part in lab-based research. Not only were older adults seen as more motivated than younger adults, but researchers thought that the two groups participate for different reasons: younger adults to obtain course credit or monetary compensation, older adults to get a sense of their cognitive health, to further science, and out of curiosity. However, older adults' greater motivation to do well on cognitive tasks may leave them vulnerable to stereotype threat, the phenomenon by which individuals underperform when they are put in a position to either confirm or deny a negative stereotype about their group. In this opinion piece, we argue that most cognitive experiments, not just those designed to measure stereotype threat, likely induce some form of performance-related anxiety in older adults. This anxiety likely leads to greater task-related interference, or thoughts about how one is doing on the task, resulting in poorer performance. We discuss some of the potential implications for our understanding of neurocognitive aging.

Brain training using cognitive apps can improve cognitive performance and processing speed in older adults

Managing age-related decrease of cognitive function is an important public health challenge, especially in the context of the global aging of the population. Over the last years several Cognitive Mobile Games (CMG) have been developed to train and challenge the brain. However, currently the level of evidence supporting the benefits of using CMG in real-life use is limited in older adults, especially at a late age. In this study we analyzed game scores and the processing speed obtained over the course of 100 sessions in 12,000 subjects aged 60 to over 80 years. Users who trained with the games improved regardless of age in terms of scores and processing speed throughout the 100 sessions, suggesting that old and very old adults can improve their cognitive performance using CMG in real-life use.

The role of cognitive reserve as mediator for addition and multiplication skills in late adulthood

BACKGROUND

The role played by cognitive reserve for the maintenance of numeracy skills in late adulthood is still not sufficiently explored.

AIMS

This study mainly investigated whether cognitive reserve (i.e., vocabulary) mediates on the relationship between non-verbal reasoning and addition and multiplication skills of older individuals. Moreover, the impact of schooling and gender on written calculation was examined, controlling for the effect of cognitive decline.

METHODS

One hundred and six 68-94-year-old participants completed a battery of tests assessing numeracy, executive functions, and cognitive reserve skills.

RESULTS

Significant correlations were found between age, cognitive reserve, numeracy, and executive functions measures. Besides, mediation analyses indicated that cognitive reserve and non-verbal reasoning explain 23% and 29% of the variance in written addition and multiplication conditions, respectively. Finally, more educated individuals performed better numeracy tasks, whereas the solution of additions and multiplications was not impact by gender.

CONCLUSIONS

Cognitive reserve impacts numeracy in late adulthood.

Paradigm Shift Toward Digital Neuropsychology and High-Dimensional Neuropsychological Assessments: Review

Neuropsychologists in the digital age have increasing access to emerging technologies. The National Institutes of Health (NIH) initiatives for behavioral and social sciences have emphasized these developing scientific and technological potentials (eg, novel sensors) for augmented characterization of neurocognitive, behavioral, affective, and social processes. Perhaps these innovative technologies will lead to a paradigm shift from disintegrated and data-poor behavioral science to cohesive and data-rich science that permits improved translation from bench to bedside. The 4 main advances influencing the scientific priorities of a recent NIH Office of Behavioral and Social Sciences Research strategic plan include the following: integration of neuroscience into behavioral and social sciences, transformational advances in measurement science, digital intervention platforms, and large-scale population cohorts and data integration. This paper reviews these opportunities for novel brain-behavior characterizations. Emphasis is placed on the increasing concern of neuropsychology with these topics and the need for development in these areas to maintain relevance as a scientific discipline and advance scientific developments. Furthermore, the effects of such advancements necessitate discussion and modification of training as well as ethical and legal mandates for neuropsychological research and praxes.

Explaining vocabulary knowledge in adulthood through comparison with knowledge of math concepts

Previous research has assumed that all types of semantic knowledge are similarly affected by aging. We investigate whether knowledge of vocabulary and math concepts show comparable lifetime change. A sample of 252 participants aged 17-91 completed two multiple-choice tasks that examined knowledge of infrequent word meanings and knowledge of basic math concepts. Up to age 64, vocabulary scores improved, whereas math scores remained stable. After that age, vocabulary scores remained stable, while math scores declined. We suggest that the fact that the learning and use of infrequent vocabulary are incidental, incremental, and contextual contributes to maintenance of word knowledge into old age. In contrast, learning of basic math concepts occurs relatively early in life in an intentional manner, and both learning and use of these concepts involve constrained contexts. Thus, the nature of the acquisition and use of semantic knowledge across the lifespan affects its fate in old age.

Examining aging and numerosity using an integrated diffusion model

Two experiments are presented that use tasks common in research in numerical cognition with young adults and older adults as subjects. In these tasks, one or two arrays of dots are displayed, and subjects decide whether there are more or fewer dots of one kind than another. Results show that older adults, relative to young adults, tend to rely more on the perceptual feature, area, in making numerosity judgments when area is correlated with numerosity. Also, convex hull unexpectedly shows different effects depending on the task (being either correlated with numerosity or anticorrelated). Accuracy and response time (RT) data are interpreted with the integration of the diffusion decision model with models for the representation of numerosity. One model assumes that the representation of the difference depends on the difference between the numerosities and that standard deviations (SDs) increase linearly with numerosity, and the other model assumes a log representation with constant SDs. The representational models have coefficients that are applied to differences between two numerosities to produce drift rates and SDs in drift rates in the decision process. The two tasks produce qualitatively different patterns of RTs: One model fits results from one task, but the results are mixed for the other task. The effects of age on model parameters show a modest decrease in evidence driving the decision process, an increase in the duration of processes outside the decision process (nondecision time), and an increase in the amount of evidence needed to make a decision (boundary separation). (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Poor numerical performance of guppies tested in a Skinner box

We tested the hypothesis that part of the gap in numerical competence between fish and warm-blooded vertebrates might be related to the more efficient procedures (e.g. automated conditioning chambers) used to investigate the former and could be filled by adopting an adapted version of the Skinner box in fish. We trained guppies in a visual numerosity discrimination task, featuring two difficulty levels (3 vs. 5 and 3 vs. 4) and three conditions of congruency between numerical and non-numerical cues. Unexpectedly, guppies trained with the automated device showed a much worse performance compared to previous investigations employing more “ecological” procedures. Statistical analysis indicated that the guppies overall chose the correct stimulus more often than chance; however, their average accuracy did not exceed 60% correct responses. Learning measured as performance improvement over training was significant only for the stimuli with larger numerical difference. Additionally, the target numerosity was selected more often than chance level only for the set of stimuli in which area and number were fully congruent. Re-analysis of prior studies indicate that the gap between training with the Skinner box and with a naturalistic setting was present only for numerical discriminations, but not for colour and shape discriminations. We suggest that applying automated conditioning chambers to fish might increase cognitive load and therefore interfere with achievement of numerosity discriminations.

Alzheimer's disease disrupts domain-specific and domain-general processes in numerosity estimation

INTRODUCTION

This study investigated how Alzheimer's Disease (AD) affects numerosity estimation abilities (e.g., finding the approximate number of items in a collection).

METHOD

Across two experiments, performance from HOA (i.e., Healthy Older Adults; N = 48) and AD patients (N = 50) was compared on dot comparison tasks. Participants were presented with two dot arrays and had to select the more numerous dot array in comparison tasks. They also took a Simon task and a number-line tasks (i.e., number-line tasks in which they had to indicate the position of a number on a line 0 to 100 or on a line 0 to 1,000 in the number-line task).

RESULTS

In Experiment 1, (a) AD patients obtained significantly poorer performance while comparing collections of dots, especially harder (small-ratio) collections, (b) these deficits correlated with poorer performance on the number-line task for larger numerosities (i.e., 0 to 1,000), and (c) AD patients showed poorer performance on incongruent (where numerosity and area occupied by dots mismatched) than on congruent items (where both features matched), while HOA showed no congruency effects. Experiment 2 showed (a) congruency effects in both groups when convex hull was tested as an incongruent feature, and (b) comparable sequential modulations of congruency effects in both groups.

CONCLUSIONS

Our findings showed that numerosity abilities decline in AD patients, and that this decline results from impaired domain-specific processes (i.e., numerosity processing) and domain-general processes (i.e., inhibition). These findings have important implications to further our understanding of how specific and general cognitive processes contribute to numerosity estimation/comparison performance, and how such contributions change during Alzheimer's disease.

Parietal alpha-based inhibitory abilities are causally linked to numerosity discrimination

Processing numerosities relies on the innate capacity to understand and manipulate the number of items in a set, and to additional abilities such as inhibitory skills -which are known to be linked to brain oscillations in the alpha range. Whether these inhibitory skills are causally linked to numerosity processing and critical for it is unclear. To address this question, we used alpha-based brain stimulation (transcranial alternate current stimulation, tACS) to target inhibitory abilities in the context of numerosity discrimination. Twenty-nine young adults received bilateral tACS to the parietal lobe, a brain region critical for numerical processes. tACS at target (alpha, 10 Hz), control oscillation frequencies (theta, 4 Hz; beta, 22 Hz; sham, no stimulation), and control areas (bilateral frontal regions) was paired to an established numerosity paradigm that allows distinguishing between congruent and incongruent numerosity trials, the latter requiring to inhibit task-irrelevant information. Performance significantly and specifically worsened in incongruent numerosity trials following bilateral parietal alpha-tACS relative to sham and to the other stimulations used, possibly due to the desynchronization of parietal neuronal oscillations in the alpha range. No significant changes in performance were observed in parietal beta and theta-tACS, relative to sham, nor in frontal alpha-tACS. Likewise, there were no changes in performing congruent numerosity trials. We therefore concluded that parietal alpha oscillations are causally linked to inhibitory abilities, and reinforced the view that these abilities are intrinsic to numerosity discrimination.

Numerosity discrimination in deep neural networks: Initial competence, developmental refinement and experience statistics

Both humans and non-human animals exhibit sensitivity to the approximate number of items in a visual array, as indexed by their performance in numerosity discrimination tasks, and even neonates can detect changes in numerosity. These findings are often interpreted as evidence for an innate 'number sense'. However, recent simulation work has challenged this view by showing that human-like sensitivity to numerosity can emerge in deep neural networks that build an internal model of the sensory data. This emergentist perspective posits a central role for experience in shaping our number sense and might explain why numerical acuity progressively increases over the course of development. Here we substantiate this hypothesis by introducing a progressive unsupervised deep learning algorithm, which allows us to model the development of numerical acuity through experience. We also investigate how the statistical distribution of numerical and non-numerical features in natural environments affects the emergence of numerosity representations in the computational model. Our simulations show that deep networks can exhibit numerosity sensitivity prior to any training, as well as a progressive developmental refinement that is modulated by the statistical structure of the learning environment. To validate our simulations, we offer a refinement to the quantitative characterization of the developmental patterns observed in human children. Overall, our findings suggest that it may not be necessary to assume that animals are endowed with a dedicated system for processing numerosity, since domain-general learning mechanisms can capture key characteristics others have attributed to an evolutionarily specialized number system.

"Older Adults with ASD: The Consequences of Aging." Insights from a series of special interest group meetings held at the International Society for Autism Research 2016-2017

A special interest group (SIG) entitled "Older Adults with ASD: The Consequences of Aging" was held at the International Society for Autism Research (INSAR) annual meetings in 2016 and 2017. The SIG and subsequent meetings brought together, for the first time, international delegates who were members of the autistic community, researchers, practitioners and service providers. Based on aging autism research that is already underway in UK, Europe, Australia and North America, discussions focussed on conceptualising the parameters of aging when referring to autism, and the measures that are appropriate to use with older adults when considering diagnostic assessment, cognitive factors and quality of life in older age. Thus, the aim of this SIG was to progress the research agenda on current and future directions for autism research in the context of aging. A global issue on how to define 'aging' when referring to ASD was at the forefront of discussions. The 'aging' concept can in principle refer to all developmental transitions. However, in this paper we focus on the cognitive and physical changes that take place from mid-life onwards. Accordingly, it was agreed that aging and ASD research should focus on adults over the age of 50 years, given the high rates of co-occurring physical and mental health concerns and increased risk of premature death in some individuals. Moreover, very little is known about the cognitive change, care needs and outcomes of autistic adults beyond this age. Discussions on the topics of diagnostic and cognitive assessments, and of quality of life and well-being were explored through shared knowledge about which measures are currently being used and which background questions should be asked to obtain comprehensive and informative developmental and medical histories. Accordingly, a survey was completed by SIG delegates who were representatives of international research groups across four continents, and who are currently conducting studies with older autistic adults. Considerable overlap was identified across different research groups in measures of both autism and quality of life, which pointed to combining data and shared learnings as the logical next step. Regarding the background questions that were asked, the different research groups covered similar topics but the groups differed in the way these questions were formulated when working with autistic adults across a range of cognitive abilities. It became clear that continued input from individuals on the autism spectrum is important to ensure that questionnaires used in ongoing and future are accessible and understandable for people across the whole autistic spectrum, including those with limited verbal abilities.

Visuo-spatial (but not verbal) executive working memory capacity modulates susceptibility to non-numerical visual magnitudes during numerosity comparison

The present study tested whether visuo-spatial vs. verbal executive working memory capacity (hereafter EWM) modulates the degree to which non-numerical visual magnitudes influence numerosity comparison using pairs of dot arrays. We hypothesized that visuo-spatial (rather than verbal) EWM capacity would influence one’s ability to selectively focus on numerical as opposed to non-numerical visual properties (such as dot size, cumulative area, density) of the dot arrays during numerosity comparison. Participants’ performance was better on trials in which non-numerical visual magnitudes were negatively (vs. positively) correlated with numerosity (i.e., reverse congruency effect). The Low visuo-spatial EWM group manifested greater reverse congruency effect compared to the High visuo-spatial EWM group. A trial-based hierarchical regression on the accuracy of each trial using the ratio of (numerical and non-numerical) visual magnitudes as predictors revealed that the ratio of numerical vs. non-numerical visual magnitudes explained the greatest variance in the performance of the High vs. Low visuo-spatial EWM groups, respectively. In contrast, there was no difference between the High vs. Low verbal EWM groups from the same analysis. These results reveal differential susceptibility to numerical vs. non-numerical visual information depending on the capacity of visuo-spatial (but not verbal) EWM. Taken together, numerosity comparison performance measured with the dot comparison paradigm seems to reflect not only one’s acuity for numerosity discrimination but also visuo-spatial EWM capacity likely required during integration of visual magnitudes during numerosity comparison.

National Institutes of Health initiatives for advancing scientific developments in clinical neuropsychology

OBJECTIVE

The current review briefly addresses the history of neuropsychology as a context for discussion of developmental milestones that have advanced the profession, as well as areas where the progression has lagged. More recently in the digital/information age, utilization and incorporation of emerging technologies has been minimal, which has stagnated ongoing evolution of the practice of neuropsychology despite technology changing many aspects of daily living. These authors advocate for embracing National Institutes of Health (NIH) initiatives, or interchangeably referred to as transformative opportunities, for the behavioral and social sciences. These initiatives address the need for neuropsychologists to transition from fragmented and data-poor approaches to integrated and data-rich scientific approaches that ultimately improve translational applications. Specific to neuropsychology is the need for the adoption of novel means of brain-behavior characterizations.

METHOD

Narrative review Conclusions: Clinical neuropsychology has reached a developmental plateau where it is ready to embrace the measurement science and technological advances which have been readily adopted by the human neurosciences. While there are ways in which neuropsychology is making inroads into these areas, a great deal of growth is needed to maintain relevance as a scientific discipline (see Figures 1, 2, and 3) consistent with NIH initiatives to advance scientific developments. Moreover, implications of such progress require discussion and modification of training, ethical, and legal mandates of the practice of neuropsychology.

Cross-magnitude interactions across development: Longitudinal evidence for a general magnitude system

There is general agreement that humans represent numerical, spatial, and temporal magnitudes from early in development. However, there is disagreement about whether different magnitudes converge within a general magnitude system and whether this system supports behavioral demonstrations of cross-magnitude interactions at different developmental time points. Using a longitudinal design, we found a relation between children's cross-magnitude interactions assessed at two developmental time points with different behavioral measures. More specifically, stronger cross-magnitude interactions in infancy (M = 9.3 months) predicted a stronger cross-magnitude congruity effect at preschool age (M = 44.2 months), even when controlling for performance on measures of inhibitory control, analogical reasoning, and verbal competence at preschool age. The results suggest a common mechanism for cross-magnitude interactions at different points in development as well as stability of the underlying individual differences. We argue that this mechanism reflects a nonverbal general magnitude system that is operational early in life and that displays continuity from infancy to preschool age.

Strategy variability in numerosity comparison task: a study in young and older adults

We investigated strategies used by young and older adults in dot comparison tasks to further our understanding of mechanisms underlying numerosity discrimination and age-related differences therein. The participants were shown a series of two dot collections and asked to select the largest collection. Analyses of verbal protocols collected on each trial, solution times, and percentages of errors documented the strategy repertoire and strategy distribution in young and older adults. Based on visual features of dot collections, both young and older adults used a set of 9 strategies and selected strategies on a trial-by-trial basis. The findings also documented age-related differences (i.e., strategy preferences) and similarities (e.g., number of strategies used by individuals) in strategies and performance. Strategy variability found here has important implications for understanding numerosity comparison and contrasts with previous findings suggesting that participants use a single strategy when they compare dot collections.

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.

Comparing Numerical Comparison Tasks: A Meta-Analysis of the Variability of the Weber Fraction Relative to the Generation Algorithm

Since more than 15 years, researchers have been expressing their interest in evaluating the Approximate Number System (ANS) and its potential influence on cognitive skills involving number processing, such as arithmetic. Although many studies reported significant and predictive relations between ANS and arithmetic abilities, there has recently been an increasing amount of published data that failed to replicate such relationship. Inconsistencies lead many researchers to question the validity of the assessment of the ANS itself. In the current meta-analysis of over 68 experimental studies published between 2004 and 2017, we show that the mean value of the Weber fraction (w), the minimal amount of change in magnitude to detect a difference, is very heterogeneous across the literature. Within young adults, w might range from < 10 to more than 60, which is critical for its validity for research and diagnostic purposes. We illustrate here the concern that different methods controlling for non-numerical dimensions lead to substantially variable performance. Nevertheless, studies that referred to the exact same method (e.g., Panamath) showed high consistency among them, which is reassuring. We are thus encouraging researchers only to compare what is comparable and to avoid considering the Weber fraction as an abstract parameter independent from the context. Eventually, we observed that all reported correlation coefficients between the value of w and general accuracy were very high. Such result calls into question the relevance of computing and reporting at all the Weber fraction. We are thus in disfavor of the systematic use of the Weber fraction, to discourage any temptation to compare given data to some values of w reported from different tasks and generation algorithms.

The measurement of approximate number system acuity across the lifespan is compromised by congruency effects

Recent studies have highlighted the influence of visual cues such as dot size and cumulative surface area on the measurement of the approximate number system (ANS). Previous studies assessing ANS acuity in ageing have all applied stimuli generated by the Panamath protocol, which does not control nor measure the influence of convex hull. Crucially, convex hull has recently been identified as an influential visual cue present in dot arrays, with its impact on older adults’ ANS acuity yet to be investigated. The current study therefore investigated the manipulation of convex hull by the Panamath protocol, and its effect on the measurement of ANS acuity in younger and older participants. First, analyses of the stimuli generated by Panamath revealed a confound between numerosity ratio and convex hull ratio. Second, although older adults were somewhat less accurate than younger adults on convex hull incongruent trials, ANS acuity was broadly similar between the groups. These findings have implications for the valid measurement of ANS acuity across all ages, and suggest that the Panamath protocol produces stimuli that do not adequately control for the influence of convex hull on numerosity discrimination.

Effects of Healthy Aging and Mild Cognitive Impairment on a Real-Life Decision-Making Task

In this study, we investigated the effects of age and of mild cognitive impairment (MCI) on decision making under risk by adopting a task representing real-life health-related situations and involving complex numerical information. Moreover, we assessed the relationship of real-life decision making to other cognitive functions such as number processing, executive functions, language, memory, and attention. For this reason, we compared the performance of 19 healthy, relatively younger adults with that of 18 healthy older adults and the performance of the 18 healthy older adults with that of 17 patients with MCI. Results indicated difficulties in real-life decision making for the healthy older adults compared with the healthy, relatively younger adults. Difficulties of patients with MCI relative to the healthy older adults arose in particular in difficult items requiring processing of frequencies and fractions. Significant effects of age and of MCI in processing frequencies were also evident in a ratio number comparison task. Decision-making performance of healthy participants and of the patient group correlated significantly with number processing. There was a further significant correlation with executive functions for the healthy participants and with reading comprehension for the patients. Our results suggest that healthy older individuals and patients with MCI make less advantageous decisions when the information is complex and high demands are put on executive functions and numerical abilities. Moreover, we show that executive functions and numerical abilities are not only essential in laboratory gambling tasks but also in more realistic and ecological decision situations within the health context.

Arithmetic learning in advanced age

Acquisition of numerical knowledge and understanding of numerical information are crucial for coping with the changing demands of our digital society. In this study, we assessed arithmetic learning in older and younger individuals in a training experiment including brain imaging. In particular, we assessed age-related effects of training intensity, prior arithmetic competence, and neuropsychological variables on the acquisition of new arithmetic knowledge and on the transfer to new, unknown problems. Effects were assessed immediately after training and after 3 months. Behavioural results showed higher training effects for younger individuals than for older individuals and significantly better performance after 90 problem repetitions than after 30 repetitions in both age groups. A correlation analysis indicated that older adults with lower memory and executive functions at baseline could profit more from intensive training. Similarly, training effects in the younger group were higher for those individuals who had lower arithmetic competence and executive functions prior to intervention. In younger adults, successful transfer was associated with higher executive functions. Memory and set-shifting emerged as significant predictors of training effects in the older group. For the younger group, prior arithmetic competence was a significant predictor of training effects, while cognitive flexibility was a predictor of transfer effects. After training, a subgroup of participants underwent an MRI assessment. A voxel-based morphometry analysis showed a significant interaction between training effects and grey matter volume of the right middle temporal gyrus extending to the angular gyrus for the younger group relative to the older group. The reverse contrast (older group vs. younger group) did not yield any significant results. These results suggest that improvements in arithmetic competence are supported by temporo-parietal areas in the right hemisphere in younger participants, while learning in older people might be more widespread. Overall, our study indicates that arithmetic learning depends on the training intensity as well as on person-related factors including individual age, arithmetic competence before training, memory, and executive functions. In conclusion, we suggest that major progress can be also achieved by older participants, but that interventions have to take into account individual variables in order to provide maximal benefit.

Developmental differences in approaches to nonsymbolic comparison tasks

Nonsymbolic comparison tasks are widely used to measure children's and adults' approximate number system (ANS) acuity. Recent evidence has demonstrated that task performance can be influenced by changes to the visual characteristics of the stimuli, leading some researchers to suggest it is unlikely that an ANS exists that can extract number information independently of the visual characteristics of the arrays. Here, we analysed 124 children's and 120 adults' dot comparison accuracy scores from three separate studies to investigate individual and developmental differences in how numerical and visual information contribute to nonsymbolic numerosity judgements. We found that, in contrast to adults, the majority of children did not use numerical information over and above visual cue information to compare quantities. This finding was consistent across different studies. The results have implications for research on the relationship between dot comparison performance and formal mathematics achievement. Specifically, if most children's performance on dot comparison tasks can be accounted for without the involvement of numerical information, it seems unlikely that observed correlations with mathematics achievement stem from ANS acuity alone.

Risk approximation in decision making: approximative numeric abilities predict advantageous decisions under objective risk

Many decision situations in everyday life involve mathematical considerations. In decisions under objective risk, i.e., when explicit numeric information is available, executive functions and abilities to handle exact numbers and ratios are predictors of objectively advantageous choices. Although still debated, exact numeric abilities, e.g., normative calculation skills, are assumed to be related to approximate number processing skills. The current study investigates the effects of approximative numeric abilities on decision making under objective risk. Participants (N = 153) performed a paradigm measuring number-comparison, quantity-estimation, risk-estimation, and decision-making skills on the basis of rapid dot comparisons. Additionally, a risky decision-making task with exact numeric information was administered, as well as tasks measuring executive functions and exact numeric abilities, e.g., mental calculation and ratio processing skills, were conducted. Approximative numeric abilities significantly predicted advantageous decision making, even beyond the effects of executive functions and exact numeric skills. Especially being able to make accurate risk estimations seemed to contribute to superior choices. We recommend approximation skills and approximate number processing to be subject of future investigations on decision making under risk.

Individual differences influence two-digit number processing, but not their analog magnitude processing: a large-scale online study

Symbolic magnitude comparison is one of the most well-studied cognitive processes in research on numerical cognition. However, while the cognitive mechanisms of symbolic magnitude processing have been intensively studied, previous studies have paid less attention to individual differences influencing symbolic magnitude comparison. Employing a two-digit number comparison task in an online setting, we replicated previous effects, including the distance effect, the unit-decade compatibility effect, and the effect of cognitive control on the adaptation to filler items, in a large-scale study in 452 adults. Additionally, we observed that the most influential individual differences were participants' first language, time spent playing computer games and gender, followed by reported alcohol consumption, age and mathematical ability. Participants who used a first language with a left-to-right reading/writing direction were faster than those who read and wrote in the right-to-left direction. Reported playing time for computer games was correlated with faster reaction times. Female participants showed slower reaction times and a larger unit-decade compatibility effect than male participants. Participants who reported never consuming alcohol showed overall slower response times than others. Older participants were slower, but more accurate. Finally, higher grades in mathematics were associated with faster reaction times. We conclude that typical experiments on numerical cognition that employ a keyboard as an input device can also be run in an online setting. Moreover, while individual differences have no influence on domain-specific magnitude processing-apart from age, which increases the decade distance effect-they generally influence performance on a two-digit number comparison task.

The Relationship between Cognitive Reserve and Math Abilities

Cognitive Reserve is the capital of knowledge and experiences that an individual acquires over their life-span. Cognitive Reserve is strictly related to Brain Reserve, which is the ability of the brain to cope with damage. These two concepts could explain many phenomena such as the modality of onset in dementia or the different degree of impairment in cognitive abilities in aging. The aim of this study is to verify the effect of Cognitive Reserve, as measured by a questionnaire, on a variety of numerical abilities (number comprehension, reading and writing numbers, rules and principles, mental calculations and written calculations), in a group of healthy older people (aged 65–98 years). Sixty older individuals were interviewed with the Cognitive Reserve Index questionnaire (CRIq), and assessed with the Numerical Activities of Daily Living battery (NADL), which included formal tasks on math abilities, an informal test on math, one interview with the participant, and one interview with a relative on the perceived math abilities. We also took into account the years of education, as another proxy for Cognitive Reserve. In the multiple regression analyses on all formal tests, CRIq scores did not significantly predict math performance. Other variables, i.e., years of education and Mini-Mental State Examination score, accounted better for math performance on NADL. Only a subsection of CRIq, CRIq-Working-activity, was found to predict performance on a NADL subtest assessing informal use of math in daily life. These results show that education might better explain abstract math functions in late life than other aspects related to Cognitive Reserve, such as lifestyle or occupational attainment.

Computational foundations of the visual number sense

We provide an emergentist perspective on the computational mechanism underlying numerosity perception, its development, and the role of inhibition, based on our deep neural network model. We argue that the influence of continuous visual properties does not challenge the notion of number sense, but reveals limit conditions for the computation that yields invariance in numerosity perception. Alternative accounts should be formalized in a computational model.

An emergentist perspective on the origin of number sense

The finding that human infants and many other animal species are sensitive to numerical quantity has been widely interpreted as evidence for evolved, biologically determined numerical capacities across unrelated species, thereby supporting a 'nativist' stance on the origin of number sense. Here, we tackle this issue within the 'emergentist' perspective provided by artificial neural network models, and we build on computer simulations to discuss two different approaches to think about the innateness of number sense. The first, illustrated by artificial life simulations, shows that numerical abilities can be supported by domain-specific representations emerging from evolutionary pressure. The second assumes that numerical representations need not be genetically pre-determined but can emerge from the interplay between innate architectural constraints and domain-general learning mechanisms, instantiated in deep learning simulations. We show that deep neural networks endowed with basic visuospatial processing exhibit a remarkable performance in numerosity discrimination before any experience-dependent learning, whereas unsupervised sensory experience with visual sets leads to subsequent improvement of number acuity and reduces the influence of continuous visual cues. The emergent neuronal code for numbers in the model includes both numerosity-sensitive (summation coding) and numerosity-selective response profiles, closely mirroring those found in monkey intraparietal neurons. We conclude that a form of innatism based on architectural and learning biases is a fruitful approach to understanding the origin and development of number sense.This article is part of a discussion meeting issue 'The origins of numerical abilities'.

Probabilistic Models and Generative Neural Networks: Towards an Unified Framework for Modeling Normal and Impaired Neurocognitive Functions

Connectionist models can be characterized within the more general framework of probabilistic graphical models, which allow to efficiently describe complex statistical distributions involving a large number of interacting variables. This integration allows building more realistic computational models of cognitive functions, which more faithfully reflect the underlying neural mechanisms at the same time providing a useful bridge to higher-level descriptions in terms of Bayesian computations. Here we discuss a powerful class of graphical models that can be implemented as stochastic, generative neural networks. These models overcome many limitations associated with classic connectionist models, for example by exploiting unsupervised learning in hierarchical architectures (deep networks) and by taking into account top-down, predictive processing supported by feedback loops. We review some recent cognitive models based on generative networks, and we point out promising research directions to investigate neuropsychological disorders within this approach. Though further efforts are required in order to fill the gap between structured Bayesian models and more realistic, biophysical models of neuronal dynamics, we argue that generative neural networks have the potential to bridge these levels of analysis, thereby improving our understanding of the neural bases of cognition and of pathologies caused by brain damage.

Dot Display Affects Approximate Number System Acuity and Relationships with Mathematical Achievement and Inhibitory Control

Much research has investigated the relationship between the Approximate Number System (ANS) and mathematical achievement, with continued debate surrounding the existence of such a link. The use of different stimulus displays may account for discrepancies in the findings. Indeed, closer scrutiny of the literature suggests that studies supporting a link between ANS acuity and mathematical achievement in adults have mostly measured the ANS using spatially intermixed displays (e.g. of blue and yellow dots), whereas those failing to replicate a link have primarily used spatially separated dot displays. The current study directly compared ANS acuity when using intermixed or separate dots, investigating how such methodological variation mediated the relationship between ANS acuity and mathematical achievement. ANS acuity was poorer and less reliable when measured with intermixed displays, with performance during both conditions related to inhibitory control. Crucially, mathematical achievement was significantly related to ANS accuracy difference (accuracy on congruent trials minus accuracy on incongruent trials) when measured with intermixed displays, but not with separate displays. The findings indicate that methodological variation affects ANS acuity outcomes, as well as the apparent relationship between the ANS and mathematical achievement. Moreover, the current study highlights the problem of low reliabilities of ANS measures. Further research is required to construct ANS measures with improved reliability, and to understand which processes may be responsible for the increased likelihood of finding a correlation between the ANS and mathematical achievement when using intermixed displays.

Effects of Presentation Type and Visual Control in Numerosity Discrimination: Implications for Number Processing?

Performance in a non-symbolic comparison task in which participants are asked to indicate the larger numerosity of two dot arrays, is assumed to be supported by the Approximate Number System (ANS). This system allows participants to judge numerosity independently from other visual cues. Supporting this idea, previous studies indicated that numerosity can be processed when visual cues are controlled for. Consequently, distinct types of visual cue control are assumed to be interchangeable. However, a previous study showed that the type of visual cue control affected performance using a simultaneous presentation of the stimuli in numerosity comparison. In the current study, we explored whether the influence of the type of visual cue control on performance disappeared when sequentially presenting each stimulus in numerosity comparison. While the influence of the applied type of visual cue control was significantly more evident in the simultaneous condition, sequentially presenting the stimuli did not completely exclude the influence of distinct types of visual cue control. Altogether, these results indicate that the implicit assumption that it is possible to compare performances across studies with a differential visual cue control is unwarranted and that the influence of the type of visual cue control partly depends on the presentation format of the stimuli.

Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: a meta-analysis

Many studies have investigated the association between numerical magnitude processing skills, as assessed by the numerical magnitude comparison task, and broader mathematical competence, e.g. counting, arithmetic, or algebra. Most correlations were positive but varied considerably in their strengths. It remains unclear whether and to what extent the strength of these associations differs systematically between non-symbolic and symbolic magnitude comparison tasks and whether age, magnitude comparison measures or mathematical competence measures are additional moderators. We investigated these questions by means of a meta-analysis. The literature search yielded 45 articles reporting 284 effect sizes found with 17,201 participants. Effect sizes were combined by means of a two-level random-effects regression model. The effect size was significantly higher for the symbolic (r = .302, 95% CI [.243, .361]) than for the non-symbolic (r = .241, 95% CI [.198, .284]) magnitude comparison task and decreased very slightly with age. The correlation was higher for solution rates and Weber fractions than for alternative measures of comparison proficiency. It was higher for mathematical competencies that rely more heavily on the processing of magnitudes (i.e. mental arithmetic and early mathematical abilities) than for others. The results support the view that magnitude processing is reliably associated with mathematical competence over the lifespan in a wide range of tasks, measures and mathematical subdomains. The association is stronger for symbolic than for non-symbolic numerical magnitude processing. So symbolic magnitude processing might be a more eligible candidate to be targeted by diagnostic screening instruments and interventions for school-aged children and for adults.

Dot comparison stimuli are not all alike: the effect of different visual controls on ANS measurement

The most common method of indexing Approximate Number System (ANS) acuity is to use a nonsymbolic dot comparison task. Currently there is no standard protocol for creating the dot array stimuli and it is unclear whether tasks that control for different visual cues, such as cumulative surface area and convex hull size, measure the same cognitive constructs. Here we investigated how the accuracy and reliability of magnitude judgements is influenced by visual controls through a comparison of performance on dot comparison trials created with two standard methods: the Panamath program and Gebuis & Reynvoet's script. Fifty-one adult participants completed blocks of trials employing images constructed using the two protocols twice to obtain a measure of immediate test-retest reliability. We found no significant correlation between participants' accuracy scores on trials created with the two protocols, suggesting that tasks employing these protocols may measure different cognitive constructs. Additionally, there were significant differences in the test-retest reliabilities for trials created with each protocol. Finally, strong congruency effects for convex hull size were found for both sets of protocol trials, which provides some clarification for conflicting results in the literature.

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.

'How many' and 'how much' dissociate in the parietal lobe

We investigated whether two features that are fundamental for quantity processing, namely numerosity and continuous quantity - or 'how many' versus 'how much' - may dissociate in the parietal lobe. Fourteen mathematically-normal participants performed a well-established numerosity discrimination task after receiving continuous theta burst transcranial magnetic stimulation (TBS) over the left or right intraparietal sulcus (IPS) or the Vertex. We performed a detailed analysis of accuracy (based on the Weber Fraction, wf), which distinguished between trials in which numerosity was anti-correlated or 'incongruent' to other continuous measures of quantity, and trials in which numerosity and other continuous features were 'congruent'. Congruent trials can be processed by integrating numerosity or continuous quantity features like cumulative area since they correlate. Instead incongruent trials can only be processed based on numerosity and requires inhibiting cumulative area or other continuous quantity features like dot size and would lead to incorrect judgment if these features are used as a proxy for numerosity. We found an increase of wf, i.e., weakened numerosity processing in incongruent but not congruent trials following left IPS-TBS, which suggests that numerosity processing was impaired while continuous quantity processing remained unchanged. Moreover, wf increased in congruent but not in incongruent trials following right IPS stimulation. We concluded that left and right parietal are respectively critical for numerosity discrimination, i.e., 'how many' or alternatively for response selection, and for integrating numerosity and continuous quantity features.

Aging and the number sense: preserved basic non-symbolic numerical processing and enhanced basic symbolic processing

Aging often leads to general cognitive decline in domains such as memory and attention. The effect of aging on numerical cognition, particularly on foundational numerical skills known as the number sense, is not well-known. Early research focused on the effect of aging on arithmetic. Recent studies have begun to investigate the impact of healthy aging on basic numerical skills, but focused on non-symbolic quantity discrimination alone. Moreover, contradictory findings have emerged. The current study aimed to further investigate the impact of aging on basic non-symbolic and symbolic numerical skills. A group of 25 younger (18-25) and 25 older adults (60-77) participated in non-symbolic and symbolic numerical comparison tasks. Mathematical and spelling abilities were also measured. Results showed that aging had no effect on foundational non-symbolic numerical skills, as both groups performed similarly [RTs, accuracy and Weber fractions (w)]. All participants showed decreased non-symbolic acuity (accuracy and w) in trials requiring inhibition. However, aging appears to be associated with a greater decline in discrimination speed in such trials. Furthermore, aging seems to have a positive impact on mathematical ability and basic symbolic numerical processing, as older participants attained significantly higher mathematical achievement scores, and performed significantly better on the symbolic comparison task than younger participants. The findings suggest that aging and its lifetime exposure to numbers may lead to better mathematical achievement and stronger basic symbolic numerical skills. Our results further support the observation that basic non-symbolic numerical skills are resilient to aging, but that aging may exacerbate poorer performance on trials requiring inhibitory processes. These findings lend further support to the notion that preserved basic numerical skills in aging may reflect the preservation of an innate, primitive, and embedded number sense.

Learning to integrate versus inhibiting information is modulated by age

Cognitive training aiming at improving learning is often successful, but what exactly underlies the observed improvements and how these differ across the age spectrum are currently unknown. Here we asked whether learning in young and older people may reflect enhanced ability to integrate information required to perform a cognitive task or whether it may instead reflect the ability to inhibit task-irrelevant information for successful task performance. We trained 30 young and 30 aging human participants on a numerosity discrimination task known to engage the parietal cortex and in which cue-integration and inhibitory abilities can be distinguished. We coupled training with parietal, motor, or sham transcranial random noise stimulation, known for modulating neural activity. Numerosity discrimination improved after training and was maintained long term, especially in the training + parietal stimulation group, regardless of age. Despite the quantitatively similar improvement in the two age groups, the content of learning differed remarkably: aging participants improved more in inhibitory abilities, whereas younger subjects improved in cue-integration abilities. Moreover, differences in the content of learning were reflected in different transfer effects to untrained but related abilities: in the younger group, improvements in cue integration paralleled improvements in continuous quantity (time and space), whereas in the elderly group, improvements in numerosity-based inhibitory abilities generalized to other measures of inhibition and corresponded to a decline in space discrimination, possibly because conflicting learning resources are used in numerosity and continuous quantity processing. These results indicate that training can enhance different, age-dependent cognitive processes and highlight the importance of identifying the exact processes underlying learning for effective training programs.

Methodological aspects to be considered when measuring the approximate number system (ANS) - a research review

According to a dominant view, the approximate number system (ANS) is the foundation of symbolic math abilities. Due to the importance of math abilities for education and career, a lot of research focuses on the investigation of the ANS and its relationship with math performance. However, the results are inconsistent. This might be caused by studies differing greatly regarding the operationalization of the ANS (i.e., tasks, dependent variables). Moreover, many methodological aspects vary from one study to the next. In the present review, we discuss commonly used ANS tasks and dependent variables regarding their theoretical foundation and psychometric features. We argue that the inconsistent findings concerning the relationship between ANS acuity and math performance may be partially explained by differences in reliability. Furthermore, this review summarizes methodological aspects of ANS tasks having important impacts on the results, including stimulus range, visual controls, presentation duration of the stimuli and feedback. Based on this review, we give methodological recommendations on how to assess the ANS most reliably and most validly. All important methodological aspects to be considered when designing an ANS task or comparing results of different studies are summarized in two practical checklists.