Processing Ordinality and Quantity: The Case of Developmental Dyscalculia

In contrast to quantity processing, up to date, the nature of ordinality has received little attention from researchers despite the fact that both quantity and ordinality are embodied in numerical information. Here we ask if there are two separate core systems that lie at the foundations of numerical cognition: (1) the traditionally and well accepted numerical magnitude system but also (2) core system for representing ordinal information. We report two novel experiments of ordinal processing that explored the relation between ordinal and numerical information processing in typically developing adults and adults with developmental dyscalculia (DD). Participants made “ordered” or “non-ordered” judgments about 3 groups of dots (non-symbolic numerical stimuli; in Experiment 1) and 3 numbers (symbolic task: Experiment 2). In contrast to previous findings and arguments about quantity deficit in DD participants, when quantity and ordinality are dissociated (as in the current tasks), DD participants exhibited a normal ratio effect in the non-symbolic ordinal task. They did not show, however, the ordinality effect. Ordinality effect in DD appeared only when area and density were randomized, but only in the descending direction. In the symbolic task, the ordinality effect was modulated by ratio and direction in both groups. These findings suggest that there might be two separate cognitive representations of ordinal and quantity information and that linguistic knowledge may facilitate estimation of ordinal information

Primates do not spontaneously use shape properties for object individuation: a competence or a performance problem?

Several recent studies have documented that non-human primates can individuate objects according to property and/or kind information in much the same way as human infants do from around one year of age when they begin to acquire language. Some studies suggest, however, that only some properties are used for the individuation of food items: color, but not shape. The present study investigated whether these findings reveal a true competence problem with shape properties in the food domain or whether they merely reveal a performance problem (e.g., lack of attention to shapes). We tested 25 great apes (chimpanzees, bonobos and gorillas) in two food individuation tasks. We manipulated subjects’ experience with differences in color and shape properties of food items. Results indicated (i) that all subjects, regardless of their prior experience, solved the color-based object individuation task and (ii) that only the group with previous experience with different shape properties succeeded in the shape-based individuation task. Great apes can thus be primed to take shape into account for individuating food objects, and this results clearly speaks in favor of a performance (rather than a competence) problem in using shape for object individuation of food items

Children Base Their Investment on Calculated Pay-Off

To investigate the rise of economic abilities during development we studied children aged between 3 and 10 in an exchange situation requiring them to calculate their investment based on different offers. One experimenter gave back a reward twice the amount given by the children, and a second always gave back the same quantity regardless of the amount received. To maximize pay-offs children had to invest a maximal amount with the first, and a minimal amount with the second. About one third of the 5-year-olds and most 7- and 10-year-olds were able to adjust their investment according to the partner, while all 3-year-olds failed. Such performances should be related to the rise of cognitive and social skills after 4 years

Late Cenozoic tephrostratigraphy offshore the southern Central American Volcanic Arc: 1. Tephra ages and provenance

We studied the tephra inventory of 18 deep sea drill sites from six DSDP/ODP legs (Legs 84, 138, 170, 202, 205, 206) and two IODP legs (Legs 334 and 344) offshore the southern Central American Volcanic Arc (CAVA). Eight drill sites are located on the incoming Cocos plate and ten drill sites on the continental slope of the Caribbean plate. In total we examined ∼840 ash-bearing horizons and identified ∼650 of these as primary ash beds of which 430 originated from the CAVA. Correlations of ash beds were established between marine cores and with terrestrial tephra deposits, using major and trace element glass compositions with respect to relative stratigraphic order. As a prerequisite for marine-terrestrial correlations we present a new geochemical data set for significant Neogene and Quaternary Costa Rican tephras. Moreover, new Ar/Ar ages for marine tephras have been determined and marine ash beds are also dated using the pelagic sedimentation rates. The resulting correlations and provenance analyses build a tephrochronostratigraphic framework for Costa Rica and Nicaragua that covers the last >8 Myr. We define 39 correlations of marine ash beds to specific tephra formations in Costa Rica and Nicaragua; from the 4.15 Ma Lower Sandillal Ignimbrite to the 3.5 ka Rincón de la Vieja Tephra from Costa Rica, as well as another 32 widely distributed tephra layers for which their specific region of origin along Costa Rica and Nicaragua can be constrained

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

A review of abnormalities in the perception of visual illusions in schizophrenia

Specific abnormalities of vision in schizophrenia have been observed to affect high-level and some low-level integration mechanisms, suggesting that people with schizophrenia may experience anomalies across different stages in the visual system affecting either early or late processing or both. Here, we review the research into visual illusion perception in schizophrenia and the issues which previous research has faced. One general finding that emerged from the literature is that those with schizophrenia are mostly immune to the effects of high-level illusory displays, but this effect is not consistent across all low-level illusions. The present review suggests that this resistance is due to the weakening of top–down perceptual mechanisms and may be relevant to the understanding of symptoms of visual distortion rather than hallucinations as previously thought

Learning to represent exact numbers

This article focuses on how young children acquire concepts for exact, cardinal numbers (e.g., three, seven, two hundred, etc.). I believe that exact numbers are a conceptual structure that was invented by people, and that most children acquire gradually, over a period of months or years during early childhood. This article reviews studies that explore children’s number knowledge at various points during this acquisition process. Most of these studies were done in my own lab, and assume the theoretical framework proposed by Carey (2009). In this framework, the counting list (‘one,’ ‘two,’ ‘three,’ etc.) and the counting routine (i.e., reciting the list and pointing to objects, one at a time) form a placeholder structure. Over time, the placeholder structure is gradually filled in with meaning to become a conceptual structure that allows the child to represent exact numbers (e.g., There are 24 children in my class, so I need to bring 24 cupcakes for the party.) A number system is a socially shared, structured set of symbols that pose a learning challenge for children. But once children have acquired a number system, it allows them to represent information (i.e., large, exact cardinal values) that they had no way of representing before

Symbolic arithmetic knowledge without instruction

This article was published in the journal, Nature [© The Nature Publishing Group]. The definitive version is available at: http://dx.doi.org/10.1038/nature05850Symbolic arithmetic is fundamental to science, technology and economics, but its acquisition by children typically requires years of effort, instruction and drill. When adults perform mental arithmetic, they activate nonsymbolic, approximate number representations and their performance suffers if this nonsymbolic system is impaired. Nonsymbolic number representations also allow adults, children, and even infants to add or subtract pairs of dot arrays and to compare the resulting sum or difference to a third array, provided that only approximate accuracy is required. Here we report that young children, who have mastered verbal counting and are on the threshold of arithmetic instruction, can build on their nonsymbolic number system to perform symbolic addition and subtraction. Children across a broad socio-economic spectrum solved symbolic problems involving approximate addition or subtraction of large numbers, both in a laboratory test and in a school setting. Aspects of symbolic arithmetic therefore lie within the reach of children who have learned no algorithms for manipulating numerical symbols. Our findings help to delimit the sources of children’s difficulties learning symbolic arithmetic, and they suggest ways to enhance children’s engagement with formal mathematics

The Availability Heuristic, Intuitive Cost-Benefit Analysis, and Climate Change

Because risks are on all sides of social situations, it is not possible to be “precautionary” in general. The availability heuristic ensures that some risks stand out as particularly salient, whatever their actual magnitude. Taken together with intuitive cost-benefit balancing, the availability heuristic helps to explain differences across groups, cultures, and even nations in the assessment of precautions to reduce the risks associated with climate change. There are complex links among availability, social processes for the spreading of information, and predispositions. If the United States is to take a stronger stand against climate change, it is likely to be a result of available incidents that seem to show that climate change produces serious and tangible harm