数字的空间特性

当要求被试对数字进行奇偶判断时,左手对小数的反应较快,而右手对大数的反应较快,该现象被称为空间数字反应编码联合效应（SNARC效应）。大量研究证实了SNARC效应的存在,该效应表明人类对数字的加工受空间表征和空间注意的影响。该文系统地回顾了SNARC效应存在及其发生阶段的证据,对比了Simon效应与SNARC效应,最后尝试着从空间注意的角度挖掘数字和空间的本质联     

The association between children's numerical magnitude processing and mental multi-digit subtraction

Children apply various strategies to mentally solve multi-digit subtraction problems and the efficient use of some of them may depend more or less on numerical magnitude processing. For example, the indirect addition strategy (solving 72–67 as “how much do I have to add up to 67 to get 72?”), which is particularly efficient when the two given numbers are close to each other, requires to determine the proximity of these two numbers, a process that may depend on numerical magnitude processing. In the present study, children completed a numerical magnitude comparison task and a number line estimation task, both in a symbolic and nonsymbolic format, to measure their numerical magnitude processing. We administered a multi-digit subtraction task, in which half of the items were specifically designed to elicit indirect addition. Partial correlational analyses, controlling for intellectual ability and motor speed, revealed significant associations between numerical magnitude processing and mental multi-digit subtraction. Additional analyses indicated that numerical magnitude processing was particularly important for those items for which the use of indirect addition is expected to be most efficient. Although this association was observed for both symbolic and nonsymbolic tasks, the strongest associations were found for the symbolic format, and they seemed to be more prominent on numerical magnitude comparison than on number line estimation.     

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.     

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.     

数字空间表征的在线建构：来自干扰情境中数字SNARC效应的证据

尽管已有研究发现数字以空间方式表征在人类记忆系统, 但是人脑如何完成数字的空间表征尚存争议。本研究两个实验在不同比例的数字字母(实验1)和不同比例的数字汉字(实验2)混合情境中考察了数字空间表征特点及其机制, 对上述争议进行了深入研究。结果发现：(1)当数字字母比例为“1 : 1”时, 数字加工中不出现SNARC效应。当数字字母比例为“1 : 6”和“6 : 1”时, 数字加工中均出现SNARC效应。即数字字母比例与数字SNARC效应之间呈倒“U”型关系。(2)数字汉字混合情境中数字汉字比例与数字SNARC效应之间同样呈倒“U”型关系。结果说明：(1)干扰刺激与数字混合呈现会影响数字SNARC效应。(2)干扰刺激加工对数字SNARC效应的影响受到数字与干扰刺激比例的调节, 且具有跨干扰材料的稳定性。研究结果意味着数字的空间表征是人类通过统计学习在线建构的, 支持了工作记忆理论。     

The left digit effect in a complex judgment task: Evaluating hypothetical college applicants

A left digit effect has been broadly observed across judgment and decision-making contexts ranging from product evaluation to medical treatment decisions to number line estimation. For example, $3.00 is judged to be a much greater cost than $2.99, and “801” is estimated strikingly too far to the right of “798” on a number line. Although the consequences of the effects for judgment and decision behavior have been documented, the sources of the effects are not well established. The goal of the current work is to extend investigations of the left digit effect to a new complex judgment activity and to assess whether the magnitude of the effect at the individual level can be predicted from performance on a simpler number skills task on which the left digit effect has also recently been observed. In three experiments (N = 434), adults completed a judgment task in which they rated the strength of hypothetical applicants for college admission and a self-paced number line estimation task. In all experiments, a small or medium left digit effect was found in the college admissions task, and a large effect was found in number line estimation. Individual-level variation was observed, but there was no relationship between the magnitudes of the effects in the two tasks. These findings provide evidence of a left digit effect in a novel multiattribute judgment task but offer no evidence that such performance can be predicted from a simple number skills task such as number line estimation.     

Quantity recognition among speakers of an anumeric language

Recent research has suggested that the Pirahã, an Amazonian tribe with a number‐less language, are able to match quantities > 3 if the matching task does not require recall or spatial transposition. This finding contravenes previous work among the Pirahã. In this study, we re‐tested the Pirahãs’ performance in the crucial one‐to‐one matching task utilized in the two previous studies on their numerical cognition, as well as in control tasks requiring recall and mental transposition. We also conducted a novel quantity recognition task. Speakers were unable to consistently match quantities > 3, even when no recall or transposition was involved. We provide a plausible motivation for the disparate results previously obtained among the Pirahã. Our findings are consistent with the suggestion that the exact recognition of quantities > 3 requires number terminology.