Do infants have a sense of numerosity? A p‐curve analysis of infant numerosity discrimination studies

Research demonstrating that infants discriminate between small (e.g., 1 vs. 3 dots) and large numerosities (e.g., 8 vs. 16 dots) is central to theories concerning the origins of human numerical abilities. To date, there has been no quantitative meta‐analysis of the infant numerical competency data. Here, we quantitatively synthesize the evidential value of the available literature on infant numerosity discrimination using a meta‐analytic tool called p‐curve. In p‐curve the distribution of available p‐values is analyzed to determine whether the published literature examining particular hypotheses contains evidential value. p‐curves demonstrated evidential value for the hypotheses that infants can discriminate between both small and large unimodal and cross‐modal numerosities. However, the analyses also revealed that the published data on infants’ ability to discriminate between large numerosities is less robust and statistically powered than the data on their ability to discriminate small numerosities. We argue there is a need for adequately powered replication studies to enable stronger inferences in order to use infant data to ground theories concerning the ontogenesis of numerical cognition.     

Neuronal changes in normal human aging and Alzheimer's disease

This article discusses age-related changes in brain weight, total number of cortical neurons, cortical dendrites, spine, and synapse density. The conclusion is that the present outlook is less grim than it was 30 years ago. Age-related reduction appears to be specific to brain region and cortical layer rather than a general feature. In addition, we describe a different pattern of changes that occur in Alzheimer's disease patients. This review concludes that the association cortices in particular are affected in aging and Alzheimer's disease and that the primary visual and somatosensory cortices are relatively spared.     

中国幼儿数数过程信息加工活动研究

探讨中国幼儿数数发展特点。实验1探讨3－5岁幼儿数数的终结点分布状况,结果表明,最大的密集终结点是“19”。实验2进一步考察幼儿在其数数范围内与范围外的起点进行数数的成绩,结果表明,数数范围为11－19的幼儿就开始有部分人可以在其数数范围外的起点进行数数,此表明他们开始应用了数列规则。据此可以认为,中国幼儿的数数活动同样包括联结学习与数列规则学习两种信息加工活动,但中国幼儿数列规则的学习活动在“11－19”数数过程开始。     

The effects of reinforcement magnitude on functional analysis outcomes

The duration or magnitude of reinforcement has varied and often appears to have been selected arbitrarily in functional analysis research. Few studies have evaluated the effects of reinforcement magnitude on problem behavior, even though basic findings indicate that this parameter may affect response rates during functional analyses. In the current study, 6 children with autism or developmental disabilities who engaged in severe problem behavior were exposed to three separate functional analyses, each of which varied in reinforcement magnitude. Results of these functional analyses were compared to determine if a particular reinforcement magnitude was associated with the most conclusive outcomes. In most cases, the same conclusion about the functions of problem behavior was drawn regardless of the reinforcement magnitude.     

On the effects of signaling reinforcer probability and magnitude in delayed matching to sample

Two experiments examined whether postsample signals of reinforcer probability or magnitude affected the accuracy of delayed matching to sample in pigeons. On each trial, red or green choice responses that matched red or green stimuli seen shortly before a variable retention interval were reinforced with wheat access. In Experiment 1, the reinforcer probability was either 0.2 or 1.0 for both red and green responses. Reinforcer probability was signaled by line or cross symbols that appeared after the sample had been presented. In Experiment 2, all correct responses were reinforced, and the signaled reinforcer durations were 1.0 s and 4.5 s. Matching was more accurate when larger or more probable reinforcers were signaled, independently of retention interval duration. Because signals were presented postsample, the effects were not the result of differential attention to the sample.     

语义信息在大小数量表征中的作用

本研究采用注意瞬脱实验范式探讨了语义信息在数量表征中的作用。结果发现：（1）在双任务方式中,字母辨认任务对大数（5及以上）的辨认产生干扰,但不影响小数（4及以下）的辨认绩效;（2）数量表征在视野上出现差异性,表现为在小数辨认时,左侧视野呈现绩效高于右侧;大数辨认正好相反,即右侧视野呈现高于左侧。结果表明,语义信息在表征小数和大数中的作用不同：小数的表征无需语言参与;而大数则更多地涉及语义信息,可能需语音回路中无声复述机制的参与。     

Further analysis of variables that affect self-control with aversive events

The purpose of this study was to examine variables that affect self-control in the context of academic task completion by elementary school children with autism. In the baseline assessment of Study 1, mathematics problem completion was shown to be an aversive event, and sensitivity to task magnitude, task difficulty, and delay to task completion were measured. The effects of manipulating values of those parameters on self-control then were assessed. For all participants, self-control increased as a function of one or more changes in task parameter values. In Study 2, the effects of a commitment response on self-control was assessed. Results indicated that for all participants, levels of self-control were higher when the opportunity to commit to the immediate aversive event was available.     

Children's representation of symbolic and nonsymbolic magnitude examined with the priming paradigm

How people process and represent magnitude has often been studied using number comparison tasks. From the results of these tasks, a comparison distance effect (CDE) is generated, showing that it is easier to discriminate two numbers that are numerically further apart (e.g., 2 and 8) compared with numerically closer numbers (e.g., 6 and 8). However, it has been suggested that the CDE reflects decisional processes rather than magnitude representation. In this study, therefore, we investigated the development of symbolic and nonsymbolic number processes in kindergartners and first, second, and sixth graders using the priming paradigm. This task has been shown to measure magnitude and not decisional processes. Our findings revealed that a priming distance effect (PDE) is already present in kindergartners and that it remains stable across development. This suggests that formal schooling does not affect magnitude representation. No differences were found between the symbolic and nonsymbolic PDE, indicating that both notations are processed with comparable precision. Finally, a poorer performance on a standardized mathematics test seemed to be associated with a smaller PDE for both notations, possibly suggesting that children with lower mathematics scores have a less precise coding of magnitude. This supports the defective number module hypothesis, which assumes an impairment of number sense.     

Transitional and steady-state choice behavior under an adjusting-delay schedule

Twelve rats made repeated choices on an adjusting-delay schedule between a smaller reinforcer (A) that was delivered immediately after a response and a larger reinforcer (B) that was delivered after a delay which increased or decreased by 20% depending on the subject's choices in successive blocks of trials. In two phases of the experiment (100 sessions and 40 sessions), reinforcer sizes were selected which enabled theoretical parameters expressing the rate of delay discounting and sensitivity to reinforcer size to be estimated from the ratio of the indifference delays obtained in the two phases. Indifference delays, calculated from adjusting delays in the last 10 sessions of each phase, were shorter when the sizes of A and B were 14 and 25 μl of a 0.6 M sucrose solution than when they were 25 and 100 μl of the same solution. The ratio of the indifference delays was significantly smaller than that predicted on the basis of an assumed linear relation between reinforcer size and instantaneous reinforcer value, consistent with a previous proposal that this relation may be hyperbolic in form. Estimates of the rate of delay discounting based on the ratio of the two indifference delays (mean, 0.08 s(-1)) were similar to values obtained previously using different intertemporal choice protocols. Estimates of the size-sensitivity parameter (mean 113 μl) were similar to estimates recently derived from performance on progressive-ratio schedules. In both phases of the experiment, adjusting delays in successive blocks of trials were analyzed using the Fourier transform. The power spectrum obtained from individual rats had a dominant frequency that corresponded to a period of oscillation of the adjusting delay between 30 and 100 trial blocks (mean, 78). Power in the dominant frequency band was highest in the early sessions of the first phase and declined with extended training. It is suggested that this experimental protocol may have utility in neurobehavioral studies of intertemporal choice.     

视觉形状知觉在近似数量系统和计算流畅性关系中的作用

已有大量研究揭示了近似数量系统与计算流畅性的相关关系, 但缺少对二者关系原因的系统检验与论证。视觉形状知觉假设有别于传统的数量领域特异性解释, 认为对形状的快速知觉是近似数量系统与计算流畅性的共同认知机制, 即视觉形状的快速知觉能力可以解释二者之间的相关关系。近似数量系统和计算流畅性在加工过程中依赖对形状的快速知觉, 二者在加工过程中都涉及了复杂视觉刺激的快速处理。视觉形状知觉假设得到了一系列研究结果的支持, 但局限在视觉形状知觉与二者关系的探讨上, 视觉形状知觉在二者关系中作用的加工机制仍不清楚。未来研究需要结合多种研究方法和技术, 多角度深入探讨视觉形状知觉在二者关系中作用的认知与脑机制, 并将研究结果应用于数学课堂教学和计算困难的干预中。