类比数量表征的线索:离散量还是连续量

运用Stroop研究范式,对30名成人被试的类比数量表征线索进行了研究。结果发现:在类比数量的小数和大数段上,不存在表征线索的分化;在个数任务中不出现Stroop效应,但被试在强不一致条件下的错误率显著高于强一致条件下的错误率;在累积面积任务中出现Stroop效应,且在弱不一致、强不一致条件下的反应时、错误率都显著高于强一致、弱一致条件下的反应时、错误率。以上结果表明被试在进行类比数量表征时,可以同时提取离散量线索和连续量线索,但是对离散量线索的抑制要难于对连续量线索的抑制。     

非语言情境中时间加工与空间距离加工的关系

时间加工与空间距离加工的关系主要有两种, 一种是在空距离–空时距以及动物的研究中, 时间加工影响空间距离加工, 空间距离加工影响时间加工, 两者相互影响, 存在对称的干扰, 这种关系与注意和记忆有关。另一种是在实距离–实时距中, 空间距离加工影响时间加工, 而时间加工不受空间距离加工的影响, 时间加工和空间距离加工之间具有不对称的干扰。时空关系的不对称与隐喻理论、人们的感知运动经验和时空信息的显著性有关。神经机制上, 右顶叶皮质、侧顶内区、左顶叶皮质、小脑、前额等参与时间加工和空间距离加工, 但两种加工涉及到的神经机制也有部分差异。未来可以从时间加工的分段性、不同条件下时间加工和空间距离加工的心理机制以及脑机制进行研究。     

空间量化的心理表征

空间量化(spacial quantification)是空间知觉的基础, 是对特定空间性质的表达。离散量(discrete magnitude)与连续量(continuous quantity)分别反映了空间分立和连续的性质, 二者有着相似的行为效应, 在神经表达上也有部分重叠, 这些证据暗示了二者可能有共同的表征机制——模拟表征(analog magnitude representation)。数量空间映射(number–space mappings)提供了数量与空间关系的直接证据。但空间量化的研究中还有许多未解之谜, 如：空间量化的动态表征、量化机制的普遍性、参照点问题、复杂和多维空间的量化等。在具身认知(embodied cognition)的框架下, 空间量化的心理表征研究将对空间的性质做出更深刻的回答。     

The essential moral self

It has often been suggested that the mind is central to personal identity. But do all parts of the mind contribute equally? Across five experiments, we demonstrate that moral traits—more than any other mental faculty—are considered the most essential part of identity, the self, and the soul. Memory, especially emotional and autobiographical memory, is also fairly important. Lower-level cognition and perception have the most tenuous connection to identity, rivaling that of purely physical traits. These findings suggest that folk notions of personal identity are largely informed by the mental faculties affecting social relationships, with a particularly keen focus on moral traits.     

Individual differences in children's mathematical competence are related to the intentional but not automatic processing of Arabic numerals

In recent years, there has been an increasing focus on the role played by basic numerical magnitude processing in the typical and atypical development of mathematical skills. In this context, tasks measuring both the intentional and automatic processing of numerical magnitude have been employed to characterize how children’s representation and processing of numerical magnitude changes over developmental time. To date, however, there has been little effort to differentiate between different measures of ‘number sense’. The aim of the present study was to examine the relationship between automatic and intentional measures of magnitude processing as well as their relationships to individual differences in children’s mathematical achievement. A group of 119 children in 1st and 2nd grade were tested on the physical size congruity paradigm (automatic processing) as well as the number comparison paradigm to measure the ratio effect (intentional processing). The results reveal that measures of intentional and automatic processing are uncorrelated with one another, suggesting that these tasks tap into different levels of numerical magnitude processing in children. Furthermore, while children’s performance on the number comparison paradigm was found to correlate with their mathematical achievement scores, no such correlations could be obtained for any of the measures typically derived from the physical size congruity task. These findings therefore suggest that different tasks measuring ‘number sense’ tap into different levels of numerical magnitude representation that may be unrelated to one another and have differential predictive power for individual differences in mathematical achievement.     

Judgments of discrete and continuous quantity: an illusory Stroop effect

Evidence from human cognitive neuroscience, animal neurophysiology, and behavioral research demonstrates that human adults, infants, and children share a common nonverbal quantity processing system with nonhuman animals. This system appears to represent both discrete and continuous quantity, but the proper characterization of the relationship between judgments of discrete and continuous quantity remains controversial. Some researchers have suggested that both continuous and discrete quantity may be automatically extracted from a scene and represented internally, and that competition between these representations leads to Stroop interference. Here, four experiments provide evidence for a different explanation of adults’ performance on the types of tasks that have been said to demonstrate Stroop interference between representations of discrete and continuous quantity. Our well-established tendency to underestimate individual two-dimensional areas can provide an alternative explanation (introduced here as the “illusory-Stroop” hypothesis). Though these experiments were constructed like Stroop tasks, and they produce patterns of performance that initially appear consistent with Stroop interference, Stroop interference effects are not involved. Implications for models of the construction of cumulative area representations and for theories of discrete and continuous quantity processing in large sets are discussed.     

An electro-physiological temporal principal component analysis of processing stages of number comparison in developmental dyscalculia

Developmental dyscalculia (DD) still lacks a generally accepted definition. A major problem is that the cognitive component processes contributing to arithmetic performance are still poorly defined. By a reanalysis of our previous event-related brain potential (ERP) data (Soltész et al., 2007) here our objective was to identify and compare cognitive processes in adolescents with DD and in matched control participants in one-digit number comparison. To this end we used temporal principal component analysis (PCA) on ERP data. First, PCA has identified four major components explaining the 85.8% of the variance in number comparison. Second, the ERP correlate of the most frequently used marker of the so-called magnitude representation, the numerical distance effect, was intact in DD during all processing stages identified by PCA. Third, hemispheric differences in the first temporal component and group differences in the second temporal component suggest executive control differences between DD and controls.     

Children's mappings of large number words to numerosities

Previous studies have suggested that children's learning of the relation between number words and approximate numerosities depends on their verbal counting ability, and that children exhibit no knowledge of mappings between number words and approximate numerical magnitudes for number words outside their productive verbal counting range. In the present study we used a numerical estimation task to explore children's knowledge of these mappings. We classified children as Level 1 counters (those unable to produce a verbal count list up to 35), Level 2 counters (those who were able to count to 35 but not 60) and Level 3 counters (those who counted to 60 or above) and asked children to estimate the number of items on a card. Although the accuracy of children's estimates depended on counting ability, children at all counting skill levels produced estimates that increased linearly in proportion to the target number, for numerosities both within and beyond their counting range. This result was obtained at the group level (Experiment 1) and at the level of individual children (Experiment 2). These findings provide evidence that even the least skilled counters do exhibit some knowledge of the form of the mapping between large number words and approximate numerosities.     

Quantity judgments of sequentially presented food items by capuchin monkeys (Cebus apella)

Recent assessments have shown that capuchin monkeys, like chimpanzees and other Old World primate species, are sensitive to quantitative differences between sets of visible stimuli. In the present study, we examined capuchins’ performance in a more sophisticated quantity judgment task that required the ability to form representations of food quantities while viewing the quantities only one piece at a time. In three experiments, we presented monkeys with the choice between two sets of discrete homogeneous food items and allowed the monkeys to consume the set of their choice. In Experiments 1 and 2, monkeys compared an entirely visible food set to a second set, presented item-by-item into an opaque container. All monkeys exhibited high accuracy in choosing the larger set, even when the entirely visible set was presented last, preventing the use of one-to-one item correspondence to compare quantities. In Experiment 3, monkeys compared two sets that were each presented item-by-item into opaque containers, but at different rates to control for temporal cues. Some monkeys performed well in this experiment, though others exhibited near-chance performance, suggesting that this species’ ability to form representations of food quantities may be limited compared to previously tested species such as chimpanzees. Overall, these findings support the analog magnitude model of quantity representation as an explanation for capuchin monkeys’ quantification of sequentially presented food items.

非符号数量表征和符号分数表征的关系

个体学习符号分数的一个关键是能对其数值形成准确表征。现有研究假设符号分数表征的认知基础是人类自婴幼儿期就具有的非符号数量表征(如表征两个集合各自的数量, 或两个数量的比例)。其证据包括表征非符号数量(尤其是非符号数量比例关系)和表征符号分数在行为和大脑神经活动层面上都表现出相关性。然而要说明非符号数量表征是符号分数表征的认知基础, 还需更多研究表明两者在数量概念上的独特相关和因果联系, 并阐明符号分数表征形成的认知机制。