An open trial assessment of "The Number Race", an adaptive computer game for remediation of dyscalculia

BACKGROUND: In a companion article [1], we described the development and evaluation of software designed to remediate dyscalculia. This software is based on the hypothesis that dyscalculia is due to a "core deficit" in number sense or in its access via symbolic information. Here we review the evidence for this hypothesis, and present results from an initial open-trial test of the software in a sample of nine 7–9 year old children with mathematical difficulties. METHODS: Children completed adaptive training on numerical comparison for half an hour a day, four days a week over a period of five-weeks. They were tested before and after intervention on their performance in core numerical tasks: counting, transcoding, base-10 comprehension, enumeration, addition, subtraction, and symbolic and non-symbolic numerical comparison. RESULTS: Children showed specific increases in performance on core number sense tasks. Speed of subitizing and numerical comparison increased by several hundred msec. Subtraction accuracy increased by an average of 23%. Performance on addition and base-10 comprehension tasks did not improve over the period of the study. CONCLUSION: Initial open-trial testing showed promising results, and suggested that the software was successful in increasing number sense over the short period of the study. However these results need to be followed up with larger, controlled studies. The issues of transfer to higher-level tasks, and of the best developmental time window for intervention also need to be addressed

Causality and the semantics of provenance

Provenance, or information about the sources, derivation, custody or history of data, has been studied recently in a number of contexts, including databases, scientific workflows and the Semantic Web. Many provenance mechanisms have been developed, motivated by informal notions such as influence, dependence, explanation and causality. However, there has been little study of whether these mechanisms formally satisfy appropriate policies or even how to formalize relevant motivating concepts such as causality. We contend that mathematical models of these concepts are needed to justify and compare provenance techniques. In this paper we review a theory of causality based on structural models that has been developed in artificial intelligence, and describe work in progress on a causal semantics for provenance graphs.Comment: Workshop submissio

Haptic subitizing across the fingers

Numerosity judgments of small sets of items (≤ 3) are generally fast and errorfree, while response times and error rates increase rapidly for larger numbers of items. We investigated an efficient process used for judging small numbers of items (known as subitizing) in active touch. We hypothesized that this efficient process for numerosity judgment might be related to stimulus properties that allow for efficient (parallel) search. Our results showed that subitizing was not possible forraised lines among flat surfaces, whereas this type of stimulus could be detected in parallel over the fingers. However, subitizing was possible when the number of fingers touching a surface had to be judged while the other fingers were lowered in mid-air. In the latter case, the lack of tactile input is essential, since subitizing was not enabled by differences in proprioceptive information from the fingers. Our results show that subitizing using haptic information from the fingers is possible only whensome fingers receive tactile information while other fingers do not

Green Urbanism and its Application to Singapore

Green urbanism has been applied to cities but not in Asia. Seven characteristics of green urbanism are outlined and then applied to Singapore. The Renewable City is not yet a concept for Singapore. The Carbon Neutral City is being developed for an island Palau Ubin and by some firms but not to significant sectors or parts of urban Singapore. The Distributed City is being developed around Singapore’s polycentric model but needs specific infrastructure plans similar to ones developed by Singapore for Tianjin Eco-City. The Biophillic City is being developed as a world first through its Skyrise Greenery initiative and urban landscaping. The Eco-Efficient City is also being demonstrated through Singapore closing the loop on their water and solid waste systems. The Place Based City is very evident in all its 22 sub centres. And the Sustainable Transport City is an Asian leader in integrated transport planning though there are signs of this becoming harder to achieve

Interdependent Infrastructure as Linked Social, Ecological, and Technological Systems (SETSs) to Address Lock‐in and Enhance Resilience

Traditional infrastructure adaptation to extreme weather events (and now climate change) has typically been techno‐centric and heavily grounded in robustness—the capacity to prevent or minimize disruptions via a risk‐based approach that emphasizes control, armoring, and strengthening (e.g., raising the height of levees). However, climate and nonclimate challenges facing infrastructure are not purely technological. Ecological and social systems also warrant consideration to manage issues of overconfidence, inflexibility, interdependence, and resource utilization—among others. As a result, techno‐centric adaptation strategies can result in unwanted tradeoffs, unintended consequences, and underaddressed vulnerabilities. Techno‐centric strategies that lock‐in today\u27s infrastructure systems to vulnerable future design, management, and regulatory practices may be particularly problematic by exacerbating these ecological and social issues rather than ameliorating them. Given these challenges, we develop a conceptual model and infrastructure adaptation case studies to argue the following: (1) infrastructure systems are not simply technological and should be understood as complex and interconnected social, ecological, and technological systems (SETSs); (2) infrastructure challenges, like lock‐in, stem from SETS interactions that are often overlooked and underappreciated; (3) framing infrastructure with a SETS lens can help identify and prevent maladaptive issues like lock‐in; and (4) a SETS lens can also highlight effective infrastructure adaptation strategies that may not traditionally be considered. Ultimately, we find that treating infrastructure as SETS shows promise for increasing the adaptive capacity of infrastructure systems by highlighting how lock‐in and vulnerabilities evolve and how multidisciplinary strategies can be deployed to address these challenges by broadening the options for adaptation

Range dependent processing of visual numerosity: similarities across vision and haptics

‘Subitizing’ refers to fast and accurate judgement of small numerosities, whereas for larger numerosities either counting or estimation are used. Counting is slow and precise, whereas estimation is fast but imprecise. In this study consisting of five experiments we investigated if and how the numerosity judgement process is affected by the relative spacing between the presented numerosities. To this end we let subjects judge the number of dots presented on a screen and recorded their response times. Our results show that subjects switch from counting to estimation if the relative differences between subsequent numerosities are large (a factor of 2), but that numerosity judgement in the subitizing range was still faster. We also show this fast performance for small numerosities only occurred when numerosity information is present. This indicates this is typical for number processing and not magnitude estimation in general. Furthermore, comparison with a previous haptic study suggests similar processing in numerosity judgement through haptics and vision

The Effect of Viewing Eccentricity on Enumeration

Visual acuity and contrast sensitivity progressively diminish with increasing viewing eccentricity. Here we evaluated how visual enumeration is affected by visual eccentricity, and whether subitizing capacity, the accurate enumeration of a small number (∼3) of items, decreases with more eccentric viewing. Participants enumerated gratings whose (1) stimulus size was constant across eccentricity, and (2) whose stimulus size scaled by a cortical magnification factor across eccentricity. While we found that enumeration accuracy and precision decreased with increasing eccentricity, cortical magnification scaling of size neutralized the deleterious effects of increasing eccentricity. We found that size scaling did not affect subitizing capacities, which were nearly constant across all eccentricities. We also found that size scaling modulated the variation coefficients, a normalized metric of enumeration precision, defined as the standard deviation divided by the mean response. Our results show that the inaccuracy and imprecision associated with increasing viewing eccentricity is due to limitations in spatial resolution. Moreover, our results also support the notion that the precise number system is restricted to small numerosities (represented by the subitizing limit), while the approximate number system extends across both small and large numerosities (indexed by variation coefficients) at large eccentricities

From 'trading zones' to 'buffer zones': Art and metaphor in the communication of psychiatric genetics to publics

Psychiatric genetics has a difficult relationship with the public given its unshakeable connection to eugenics. Drawing from a five-year public engagement programme that emerged from an internationally renowned psychiatric genetics centre, we propose the concept of the Buffer Zone to consider how an exchange of viewpoints between groups of people – including psychiatric geneticists and lay publics - who are often uneasy in one another’s company can be facilitated through the use of art and metaphor. The artwork at the exhibitions provided the necessary socio-cultural context for scientific endeavours, whilst also enabled public groups to be part of, and remain in, the conversation. Crucial to stress is that this mitigation was not to protect the science; it was to protect the discussion

Ontogeny of Numerical Abilities in Fish

Background: It has been hypothesised that human adults, infants, and non-human primates share two non-verbal systems for enumerating objects, one for representing precisely small quantities (up to 3–4 items) and one for representing approximately larger quantities. Recent studies exploiting fish’s spontaneous tendency to join the larger group showed that their ability in numerical discrimination closely resembles that of primates but little is known as to whether these capacities are innate or acquired. Methodology/Principal Findings: We used the spontaneous tendency to join the larger shoal to study the limits of the quantity discrimination of newborn and juvenile guppies. One-day old fish chose the larger shoal when the choice was between numbers in the small quantity range, 2 vs. 3 fish, but not when they had to choose between large numbers, 4 vs. 8 or 4 vs. 12, although the numerical ratio was larger in the latter case. To investigate the relative role of maturation and experience in large number discrimination, fish were raised in pairs (with no numerical experience) or in large social groups and tested at three ages. Forty-day old guppies from both treatments were able to discriminate 4 vs. 8 fish while at 20 days this was only observed in fish grown in groups. Control experiments showed that these capacities were maintained after guppies were prevented from using non numerical perceptual variables that co-vary with numerosity. Conclusions/Significance: Overall, our results suggest the ability of guppies to discriminate small numbers is innate and i

Evidence for Two Numerical Systems That Are Similar in Humans and Guppies

Background: Humans and non-human animals share an approximate non-verbal system for representing and comparing numerosities that has no upper limit and for which accuracy is dependent on the numerical ratio. Current evidence indicates that the mechanism for keeping track of individual objects can also be used for numerical purposes; if so, its accuracy will be independent of numerical ratio, but its capacity is limited to the number of items that can be tracked, about four. There is, however, growing controversy as to whether two separate number systems are present in other vertebrate species. Methodology/Principal Findings: In this study, we compared the ability of undergraduate students and guppies to discriminate the same numerical ratios, both within and beyond the small number range. In both students and fish the performance was ratio-independent for the numbers 1–4, while it steadily increased with numerical distance when larger numbers were presented. Conclusions/Significance: Our results suggest that two distinct systems underlie quantity discrimination in both humans and fish, implying that the building blocks of uniquely human mathematical abilities may be evolutionarily ancient, datin