The mathematics of sharing / Las matemáticas que realizan los niños al compartir

Abstract

The purpose of sharing is to construct equivalent sets, making it an ideal context for analysing important quantitative concepts such as counting, equivalence and cardinality. Two studies analysed how four- and five-year-olds shared blocks in equal sharing and reciprocity conditions and their number inferences about one set after counting the other. The researcher asked children to share double and single blocks between two characters. They succeeded more in building equivalent shares in an equal sharing than reciprocity condition. Most children who shared correctly also made appropriate number inferences. To examine whether perceptual cues helped children share the blocks, a second study used Canadian $1 and $2 coins. A double block is twice the size of a single, whereas there is no visual cue about the value relation between coins because they are the same size. Unexpectedly, children shared equally well with blocks and coins, and most children made number inferences.     

GLOCALIZATION: RELIGION AND SCIENCE AROUND THE WORLD

This essay explains the rationale behind a series of reviews on interactions between knowledge and values, science and religion, in different countries or regions around the world. The series will run in Zygon for the whole of 2015 and beyond. In the literature, it may seem that discussions in the United States and to a lesser extent the United Kingdom are typical of the issues, but they need not be. David Livingstone showed that the reception of evolution differed, even among Calvinists in different countries. Thus, rather than an export model, we should take time to learn from scholars rooted in different contexts how in their situation issues on knowledge and values arise and are dealt with. In this interplay of global processes and local contexts, indicated with the term glocalization, we should be alert to the migration of concepts and the transformations that ideas undergo.     

The development of numerosity estimation: Evidence for a linear number representation early in life

Several studies investigating the development of approximate number representations used the number-to-position task and reported evidence for a shift from a logarithmic to a linear representation of numerical magnitude with increasing age. However, this interpretation as well as the number-to-position method itself has been questioned recently. The current study tested 5- and 8-year-old children on a newly established numerosity production task to examine developmental changes in number representations and to test the idea of a representational shift. Modelling of the children's numerical estimations revealed that responses of the 8-year-old children approximate a simple positive linear relation between estimated and actual numbers. Interestingly, however, the estimations of the 5-year-old children were best described by a bilinear model reflecting a relatively accurate linear representation of small numbers and no apparent magnitude knowledge for large numbers. Taken together, our findings provide no support for a shift of mental representations from a logarithmic to a linear metric but rather suggest that the range of number words which are appropriately conceptualised and represented by linear analogue magnitude codes expands during development.     

Larger,smaller, odd or even? Task-specific effects of optokinetic stimulation on the mental number space

Previous studies have shown that number processing can induce spatial biases in perception and action and can trigger the orienting of visuospatial attention. Few studies, however, have investigated how spatial processing and visuospatial attention influences number processing. In the present study, we used the optokinetic stimulation (OKS) technique to trigger eye movements and thus overt orienting of visuospatial attention. Participants were asked to stare at OKS, while performing parity judgements (Experiment 1) or number comparison (Experiment 2), two numerical tasks that differ in terms of demands on magnitude processing. Numerical stimuli were acoustically presented, and participants responded orally. We examined the effects of OKS direction (leftward or rightward) on number processing. The results showed that rightward OKS abolished the classic number size effect (i.e., faster reaction times for small than large numbers) in the comparison task, whereas the parity task was unaffected by OKS direction. The effect of OKS highlights a link between visuospatial orienting and processing of number magnitude that is complementary to the more established link between numerical and visuospatial processing. We suggest that the bidirectional link between numbers and space is embodied in the mechanisms subserving sensorimotor transformations for the control of eye movements and spatial attention.     

Do phenomenal concepts misrepresent?

Many contemporary physicalists concede to dualists that conscious subjects have distinctive “phenomenal concepts” of the phenomenal qualities of their experiences. Indeed, they contend that idiosyncratic characteristics of these concepts facilitate responses to influential anti-physicalist arguments. Like some some other critics of this approach, James Tartaglia (2013 Tartaglia, J. (2013). Conceptualizing physical consciousness. Philosophical Psychology, 26(6), 817–838.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) maintains that phenomenal concepts express contents that conflict with physicalism, but as a physicalist, the moral he distinctively draws from this is that phenomenal concepts misrepresent. He contends further that the contemporary physicalists’ account cannot accommodate this feature, and that in consequence, physicalists should abandon phenomenal concepts and return to the identity theory championed by Place and Smart in the 1950s. I respond to Tartaglia by identifying lacunae in his interpretation of contemporary physicalism and arguing that phenomenal concepts as conceived by the contemporary physicalists do not express contents that support either dualist or physicalist metaphysics: they are “metaphysically neutral.”     

Concept Creep: Psychology's Expanding Concepts of Harm and Pathology

Many of psychology's concepts have undergone semantic shifts in recent years. These conceptual changes follow a consistent trend. Concepts that refer to the negative aspects of human experience and behavior have expanded their meanings so that they now encompass a much broader range of phenomena than before. This expansion takes “horizontal” and “vertical” forms: concepts extend outward to capture qualitatively new phenomena and downward to capture quantitatively less extreme phenomena. The concepts of abuse, bullying, trauma, mental disorder, addiction, and prejudice are examined to illustrate these historical changes. In each case, the concept's boundary has stretched and its meaning has dilated. A variety of explanations for this pattern of “concept creep” are considered and its implications are explored. I contend that the expansion primarily reflects an ever-increasing sensitivity to harm, reflecting a liberal moral agenda. Its implications are ambivalent, however. Although conceptual change is inevitable and often well motivated, concept creep runs the risk of pathologizing everyday experience and encouraging a sense of virtuous but impotent victimhood.     

Socio-economic and driving experience factors affecting drivers’ perceptions of traffic crash risk

Drivers are estimated to contribute an overwhelming proportion to the burden of traffic crashes, as factors that increase crash risk are frequently due to unsafe driving behaviours. The relationship between risk perceptions and people’s risky driving behaviours is still not well understood. This paper aims to further analyse the potential effect of risky driving behaviours on drivers’ perceptions of crash risk and differences in perceptions among drivers.Crash risk perceptions in an inter-city, two-way road context of 492 drivers were measured by using a Stated Preference (SP) ranking survey. Rank-ordered logit models were used to evaluate the impact on risk perception of five unsafe driving behaviours and to identify differences in drivers’ risk perceptions. The five unsafe driving behaviours considered in the analysis were respectively related to whether or not the driver follows the speed limits, the rules of passing another car and the safe distance, whether or not the driver is distracted, and whether or not she/he is driving under optimal personal conditions.All risky driving behaviours showed a significant potential effect (p < 0.001) on crash risk perceptions, and model’s results allowed to differentiate more important from less important unsafe driving behaviours based on their weight on perceived crash risk. Additionally, this paper further analyses the potential differences in risk perception of these traffic violations between drivers of different characteristics, such as driving experience, household size, income and gender.The SP technique could be applied to further analyse differences in perceptions of risky driving behaviours among drivers. Future research should consider the potential effect of driving skill on perceptions of risky driving behaviours.     

How the Abstract Becomes Concrete: Irrational Numbers Are Understood Relative to Natural Numbers and Perfect Squares

Mathematical cognition research has largely emphasized concepts that can be directly perceived or grounded in visuospatial referents. These include concrete number systems like natural numbers, integers, and rational numbers. Here, we investigate how a more abstract number system, the irrationals denoted by radical expressions like , is understood across three tasks. Performance on a magnitude comparison task suggests that people interpret irrational numbers (specifically, the radicands of radical expressions) as natural numbers. Strategy self‐reports during a number line estimation task reveal that the spatial locations of irrationals are determined by referencing neighboring perfect squares. Finally, perfect squares facilitate the evaluation of arithmetic expressions. These converging results align with a constellation of related phenomena spanning tasks and number systems of varying complexity. Accordingly, we propose that the task‐specific recruitment of more concrete representations to make sense of more abstract concepts (referential processing) is an important mechanism for teaching and learning mathematics.     

Powerful Qualities,Phenomenal Concepts,and the New Challenge to Physicalism

Defenders of the phenomenal concept strategy have to explain how both physical and phenomenal concepts provide a substantive grasp on the nature of their referents, whilst referring to the very same experience. This is the ‘new challenge’ to physicalism. In this paper, I argue that if the physicalist adopts the powerful qualities ontology of properties then a new and powerful version of the phenomenal concept strategy can be developed, which answers the new challenge.     

具身道德隐喻映射机制的双向性及其问题——基于具身效应“可重复性危机”的思考

具身认知研究虽已取得令人瞩目的进展,但某些具身效应存在可重复性较低的问题。若长期忽视这一问题,将严重损害心理学的科学性,甚至引发一定程度的“可重复性危机”。本文从道德概念清洁隐喻的两大映射方向出发,基于两大实验类型对相关研究中可能存在的问题因素分别展开分析。未来研究应关注更注重社会互动的组织道德,将道德概念具身隐喻研究引申到现实问题中,并借助认知神经科学技术更全面地考察身体经验、情绪体验和认知加工在道德清洁隐喻加工中的作用。