False Approximations of the Approximate Number System?

Prior research suggests that the acuity of the approximate number system (ANS) predicts future mathematical abilities. Modelling the development of the ANS might therefore allow monitoring of children's mathematical skills and instigate educational intervention if necessary. A major problem however, is that our knowledge of the development of the ANS is acquired using fundamentally different paradigms, namely detection in infants versus discrimination in children and adults. Here, we question whether such a comparison is justified, by testing the adult ANS with both a discrimination and a detection task. We show that adults perform markedly better in the discrimination compared to the detection task. Moreover, performance on discrimination but not detection, correlated with performance on mathematics. With a second similar experiment, in which the detection task was replaced by a same-different task, we show that the results of experiment 1 cannot be attributed to differences in chance level. As only task instruction differed, the discrimination and the detection task most likely reflect differences at the decisional level. Future studies intending to model the development of the ANS should therefore rely on data derived from a single paradigm for different age groups. The same-different task appears a viable candidate, due to its applicability across age groups

Visual stimulus parameters seriously compromise the measurement of approximate number system acuity and comparative effects between adults and children

It has been suggested that a simple non-symbolic magnitude comparison task is sufficient to measure the acuity of a putative Approximate Number System (ANS). A proposed measure of the ANS, the so-called “internal Weber fraction” (w), would provide a clear measure of ANS acuity. However, ANS studies have never presented adequate evidence that visual stimulus parameters did not compromise measurements of w to such extent that w is actually driven by visual instead of numerical processes. We therefore investigated this question by testing non-symbolic magnitude discrimination in seven-year-old children and adults. We manipulated/controlled visual parameters in a more stringent manner than usual. As a consequence of these controls, in some trials numerical cues correlated positively with number while in others they correlated negatively with number. This congruency effect strongly correlated with w, which means that congruency effects were probably driving effects in w. Consequently, in both adults and children congruency had a major impact on the fit of the model underlying the computation of w. Furthermore, children showed larger congruency effects than adults. This suggests that ANS tasks are seriously compromised by the visual stimulus parameters, which cannot be controlled. Hence, they are not pure measures of the ANS and some putative w or ratio effect differences between children and adults in previous ANS studies may be due to the differential influence of the visual stimulus parameters in children and adults. In addition, because the resolution of congruency effects relies on inhibitory (interference suppression) function, some previous ANS findings were probably influenced by the developmental state of inhibitory processes especially when comparing children with developmental dyscalculia and typically developing children

The Role of Visual Information in Numerosity Estimation

Mainstream theory suggests that the approximate number system supports our non-symbolic number abilities (e.g. estimating or comparing different sets of items). It is argued that this system can extract number independently of the visual cues present in the stimulus (diameter, aggregate surface, etc.). However, in a recent report we argue that this might not be the case. We showed that participants combined information from different visual cues to derive their answers. While numerosity comparison requires a rough comparison of two sets of items (smaller versus larger), numerosity estimation requires a more precise mechanism. It could therefore be that numerosity estimation, in contrast to numerosity comparison, might rely on the approximate number system. To test this hypothesis, we conducted a numerosity estimation experiment. We controlled for the visual cues according to current standards: each single visual property was not informative about numerosity. Nevertheless, the results reveal that participants were influenced by the visual properties of the dot arrays. They gave a larger estimate when the dot arrays consisted of dots with, on average, a smaller diameter, aggregate surface or density but a larger convex hull. The reliance on visual cues to estimate numerosity suggests that the existence of an approximate number system that can extract numerosity independently of the visual cues is unlikely. Instead, we propose that humans estimate numerosity by weighing the different visual cues present in the stimuli

Indexing the approximate number system

This is the author’s version of a work that was accepted for publication in Acta Psychologica. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published at: http://dx.doi.org/10.1016/j.actpsy.2013.11.009Much recent research attention has focused on understanding individual differences in the Approximate Number System, a cognitive system believed to underlie human mathematical competence. To date researchers have used four main indices of ANS acuity, and have typically assumed that they measure similar properties. Here we report a study which questions this assumption. We demonstrate that the Numerical Ratio Effect has poor testretest reliability and that it does not relate to either Weber fractions or accuracy on nonsymbolic comparison tasks. Furthermore, we show that Weber fractions follow a strongly skewed distribution and that they have lower test-retest reliability than a simple accuracy measure. We conclude by arguing that in future researchers interested in indexing individual differences in ANS acuity should use accuracy figures, not Weber fractions or Numerical Ratio Effects

Exploring the approximate number system in Sotos syndrome: insights from a dot comparison task

Background Sotos syndrome is a congenital overgrowth condition associated with intellectual disability and an uneven cognitive profile. Previous research has established that individuals with Sotos syndrome have relatively poor mathematical ability, but domain‐specific numeracy skills have not been explored within this population. This study investigated the approximate number system (ANS) in Sotos syndrome. Method A dot comparison task was administered to 20 participants with Sotos syndrome (mean age in years = 18.43, SD = 9.29). Performance was compared to a chronological agematched typically developing control group (n = 25) and a mental age‐matched Williams syndrome group (n = 24). Results The Sotos group did not display an ANS deficit overall when compared to chronological agematched control participants. However, for trials where the size of the individual dots and the envelope area were negatively correlated with the total number of dots (incongruent trials), the Sotos group were less accurate than the typically developing group but more accurate than the Williams syndrome group, suggesting an inhibitory control deficit. Better accuracy on incongruent trials, but not congruent trials, was associated with higher quantitative reasoning ability for participants with Sotos syndrome. Conclusion Overall, the findings suggest that ANS acuity is not impaired in Sotos syndrome but that numerical difficulties may be associated with an inhibitory control deficit for individuals with Sotos syndrome

COVID-19 outbreaks among crew on commercial ships at the Port of Rotterdam, the Netherlands, 2020 to 2021

BackgroundDuring the COVID-19 pandemic, international shipping activity was disrupted as movement of people and goods was restricted. The Port of Rotterdam, the largest port in Europe, remained operational throughout.AimWe describe the burden of COVID-19 among crew on sea-going vessels at the port and recommend improvements in future infectious disease event notification and response at commercial ports.MethodsSuspected COVID-19 cases on sea-going vessels were notified to port authorities and public health (PH) authorities pre-arrival via the Maritime Declaration of Health. We linked data from port and PH information systems between 1 January 2020 and 31 July 2021, derived a notification rate (NR) of COVID-19 events per arrival, and an attack rate (AR) per vessel (confirmed cases). We compared AR by vessel type (workship/tanker/cargo/passenger), during wildtype-, alpha- and delta-dominant calendar periods.ResultsEighty-four COVID-19 events were notified on ships, involving 622 cases. The NR among 45,030 new arrivals was 173 per 100,000 impacting 1% of vessels. Events per week peaked in April 2021 and again in July 2021, when the AR was also highest. Half of all cases were notified on workships, events occurring earlier and more frequently than on other vessels.ConclusionNotification of COVID-19 events on ships occurred infrequently, although case under-ascertainment was likely. Pre-agreed protocols for data-sharing between stakeholders locally and across Europe would facilitate more efficient pandemic response. Public health access to specimens for sequencing and environmental sampling would give greater insight into viral spread on ships.</p

Incongruence in number–luminance congruency effects

Congruency tasks have provided support for an amodal magnitude system for magnitudes that have a “spatial” character, but conflicting results have been obtained for magnitudes that do not (e.g., luminance). In this study, we extricated the factors that underlie these number–luminance congruency effects and tested alternative explanations: (unsigned) luminance contrast and saliency. When luminance had to be compared under specific task conditions, we revealed, for the first time, a true influence of number on luminance judgments: Darker stimuli were consistently associated with numerically larger stimuli. However, when number had to be compared, luminance contrast, not luminance, influenced number judgments. Apparently, associations exist between number and luminance, as well as luminance contrast, of which the latter is probably stronger. Therefore, similar tasks, comprising exactly the same stimuli, can lead to distinct interference effects

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

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

Sampling from the mental number line: How are approximate number system representations formed?

This article was published in the journal, Cognition [© Elsevier B.V.] and the definitive version is available at: http://dx.doi.org/10.1016/j.cognition.2013.06.003Nonsymbolic comparison tasks are commonly used to index the acuity of an individual’s Approximate Number System (ANS), a cognitive mechanism believed to be involved in the development of number skills. Here we asked whether the time that an individual spends observing numerical stimuli influences the precision of the resultant ANS representations. Contrary to standard computational models of the ANS, we found that the longer the stimulus was displayed, the more precise was the resultant representation. We propose an adaptation of the standard model, and suggest that this finding has significant methodological implications for numerical cognition research