Analog number representations in mongoose lemurs (Eulemur mongoz): evidence from a search task

A wealth of data demonstrating that monkeys and apes represent number have been interpreted as suggesting that sensitivity to number emerged early in primate evolution, if not before. Here we examine the numerical capacities of the mongoose lemur (Eulemur mongoz), a member of the prosimian suborder of primates that split from the common ancestor of monkeys, apes and humans approximately 47–54 million years ago. Subjects observed as an experimenter sequentially placed grapes into an opaque bucket. On half of the trials the experimenter placed a subset of the grapes into a false bottom such that they were inaccessible to the lemur. The critical question was whether lemurs would spend more time searching the bucket when food should have remained in the bucket, compared to when they had retrieved all of the food. We found that the amount of time lemurs spent searching was indicative of whether grapes should have remained in the bucket, and furthermore that lemur search time reliably differentiated numerosities that differed by a 1:2 ratio, but not those that differed by a 2:3 or 3:4 ratio. Finally, two control conditions determined that lemurs represented the number of food items, and neither the odor of the grapes, nor the amount of grape (e.g., area) in the bucket. These results suggest that mongoose lemurs have numerical representations that are modulated by Webers Law.     

婴儿数量表征的客体档案和类比模型

人对数量的表征及其发展是心理学研究的重要问题之一。20世纪70年代以来,国外对婴儿数量表征的研究取得了一系列理论和方法的进步。文章简要介绍了婴儿数量辨别和推理能力的研究方法,对婴儿数量表征相关的理论进行了重点讨论。大量详实的证据表明,婴儿拥有一个“天生的”数量机制,这为人数学能力的发展提供了基础。     

Memory for sequences of tone bursts in the rat: Reliance on temporal cues and evidence for an instructional ambiguity explanation of the choose-few effect

Two groups of rats were trained in a symbolic delayed matching-to-sample task with a 0-s delay to discriminate sample stimuli that consisted of sequences of tone bursts. For one group, sequences varied in number with total sequence duration controlled. For the other group, total sequence duration, sum of the tone durations, and sum of the gap durations were all controlled. The former group of rats acquired the discrimination, but the latter group of rats were not able to learn the discrimination with the additional temporal cues controlled. Retention functions for the group that acquired the discrimination exhibited a choose-many bias at the 1-s delay and a choose-few bias at the 8-s delay regardless of the similarity in the intertrial interval and delay interval illumination condition. The asymmetrical retention functions appeared to be due to instructional ambiguity which resulted from the similarity of the delay interval to temporal features of the tone burst sequence, such as the gap between tone bursts and the total duration of tone. In Experiment 2, diagnostic tests provided evidence that rats discriminated the sequences of tone bursts by timing and summing the duration of individual tone bursts rather than using an event switch to count tones. Like pigeons, rats use multiple temporal features rather than number to discriminate sequences of successive events.     

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.     

Brief non-symbolic,approximate number practice enhances subsequent exact symbolic arithmetic in children

Recent research reveals a link between individual differences in mathematics achievement and performance on tasks that activate the approximate number system (ANS): a primitive cognitive system shared by diverse animal species and by humans of all ages. Here we used a brief experimental paradigm to test one causal hypothesis suggested by this relationship: activation of the ANS may enhance children’s performance of symbolic arithmetic. Over 2 experiments, children who briefly practiced tasks that engaged primitive approximate numerical quantities performed better on subsequent exact, symbolic arithmetic problems than did children given other tasks involving comparison and manipulation of non-numerical magnitudes (brightness and length). The practice effect appeared specific to mathematics, as no differences between groups were observed on a comparable sentence completion task. These results move beyond correlational research and provide evidence that the exercise of non-symbolic numerical processes can enhance children’s performance of symbolic mathematics.     

Number processing of Arabic and Hebrew bilinguals: Evidence supporting the distance effect

In the current study, a direct assessment of the effect of language lexical‐syntactic structure and magnitude semantic access on numerical processing was made by contrasting the performance of Arabic/Hebrew bilinguals in a digital (Hindi‐digits/Arabic‐digits) and verbal numerical comparison task (Arabic, an inverted language: Units‐Decades, Hebrew, a non‐inverted language: Decades‐Units). Our data revealed in the digital presentation format (Experiment 1) a regular distance effect in Arabic language‐Hindi digits and Hebrew language‐Arabic digits, characterized by an inverse relation between reaction times and numerical distance with no difference in the mean reaction times of participants in Arabic‐L1 and Hebrew‐L2. This indicates that both lexical digits of two‐digit numbers in L1 and L2 are similarly processed and semantically accessed. However in the verbal presentation format (Experiment 2) a similar pattern of distance effect was found, but the mean reaction times in Arabic were lower than in Hebrew in each numerical distance. This indicates that the processing of two‐digit number words in L1 and L2 is semantically accessed and determined by the syntactic structure of each language.     

The understanding of die as an object that has numerical functions. A longitudinal study using two children from the ages of 24 to 36 months interacting with an adult / La comprensión del dado como objeto con funciones numéricas. Un estudio longitudinal con dos niños desde los 24 a los 36 meses en interacción con un adulto

Abstract

We investigated the process through which children understand the conventional use of numbers in interaction with an adult. We analysed previous semiotic systems that support, transform and adjust to this new semiotic system — the numerical — and we investigated the communicative-educative basis that makes it possible. We conducted an exploratory and longitudinal study with one boy and one girl at 24, 27, 30, 33 and 36 months of age in a triadic interaction (adult-child-object) with their mothers at home. We adopt the pragmatic-semiotic perspective of the object, which considers that triadic interactions are the unit of analysis of early development. Our results show a great variety of semiotic mediators used by children and adults and both children’s progressive comprehension of the meaning and use of the die as a numerical object.     

结构对称性汉字视觉识别特点的实验研究

用命名作业通过二个实验考察了结构对称性汉字的视觉识别特点,结果表明,汉字识别具有显著的结构对称性效应,识别结构对称性汉字的加工明显快于非对称性汉字,对称性效应与字频效应,笔画效应具有显著的交互作用,进一步的简单效应的分析表明,这种结构对称性效应在低频字中起作用,而在高频字中不起显著作用;在多笔画字中起作用,而在少毛画字中不起显著作用,这表明,对称性汉字中的具有冗余信息的格式塔部件促进地识别汉字的加