Local contrast and maintained generalization.

Pigeons received variable-interval reinforcement for key pecking during presentations of horizontal and vertical line-orientation stimuli, while pecks during five intermediate orientations were extinguished. Lowest peck rates were observed during presentations of negative stimuli adjacent to the positive orientations while peck rate during 45 degrees (the intermediate negative orientation) was relatively high, i.e., there were negative contrast shoulders. When peck rates were manipulated in the positive orientations, peck rate in neithboring orientations changed in the opposite direction. Contrast shoulders faded after prolonged training. A second type of contrast, local contrast, was correlated with similarity of preceding stimulus and different average peck rates during different stages of the discrimination process. The data suggest that sequential local contrast accompanying the formation of a discrimination contributes to the form of generalization gradients. Blough's model of stimulus control predicts the changes in gradient form described here, but may not accurately depict the underlying process responsible for gradient form.     

Stimulus control of Pavlovian facilitation

Two experiments were conducted using an autoshaping procedure with pigeons to examine whether dimensional stimulus control by a Pavlovian facilitator parallels the control established following operant discrimination training. Facilitation training consisted of the presentation of a black vertical line on a white background as the B stimulus in a feature-positive discrimination in which the A stimulus (white keylight) was followed by grain presentation only if preceded by B. In this way, B facilitates or sets the occasion for pecking at A. Subsequent testing for generalization along the line-orientation dimension produced decremental gradients when the facilitation paradigm incorporated an explicit feature-negative stimulus (B−). These results parallel the decremental control obtained following operant discrimination training and suggest that Pavlovian facilitators and instrumental discriminative stimuli are functionally equivalent.     

Time counts: Bidirectional interaction between time and numbers in human adults

Number is known for influencing time processing, but to what extent time influences number in human adults is unclear. We investigated possible bidirectional interactions (number on time and time on number) using a novel Stroop-like task; participants compared numbers or temporal durations in congruent (larger number presented for longer duration) or incongruent conditions (smaller number presented for longer duration). Time and number tasks were presented in different blocks (Experiment 1) or within the same block of trials with task instructions provided at the offset of the stimuli (Experiment 2). Analyses of response times (RTs) and their distribution revealed that number affected time from early RTs, and time affected number at late RTs – an asymmetry observed only when time and number tasks were presented in separate blocks. Thus, carefully chosen tasks and appropriate data analysis can reveal bidirectionality between time and number, consistent with shared magnitude or decision mechanisms.     

Tapping into the interplay of lexical and number knowledge using fast mapping: A longitudinal eye-tracking study with two-year-olds

Language skills and mathematical competencies are argued to influence each other during development. While a relation between the development of vocabulary size and mathematical skills is already documented in the literature, this study further examines how children’s ability to map a novel word to an unknown object as well as their ability to retain this word from memory may be related to their knowledge of number words. Twenty-five children were tested longitudinally (at 30 and at 36 months of age) using an eye-tracking-based fast mapping task, the Give-a-Number task, and standardized measures of vocabulary. The results reveal that children’s ability to create and retain a mental representation of a novel word was related to number knowledge at 30 months, but not at 36 months while vocabulary size correlated with number knowledge only at 36 months. These results show that even specific mapping processes are initially related to the acquisition of number words and they speak for a parallelism between the development of lexical and number-concept knowledge despite their semantic and syntactic differences.     

Expectations about numerical events in four lemur species (Eulemur fulvus, Eulemur mongoz, Lemur catta and Varecia rubra)

Although much is known about how some primates—in particular, monkeys and apes—represent and enumerate different numbers of objects, very little is known about the numerical abilities of prosimian primates. Here, we explore how four lemur species (Eulemur fulvus, E. mongoz, Lemur catta, and Varecia rubra) represent small numbers of objects. Specifically, we presented lemurs with three expectancy violation looking time experiments aimed at exploring their expectations about a simple 1+1 addition event. In these experiments, we presented subjects with displays in which two lemons were sequentially added behind an occluder and then measured subjects duration of looking to expected and unexpected outcomes. In experiment 1, subjects looked reliably longer at an unexpected outcome of only one object than at an expected outcome of two objects. Similarly, subjects in experiment 2 looked reliably longer at an unexpected outcome of three objects than at an expected outcome of two objects. In experiment 3, subjects looked reliably longer at an unexpected outcome of one object twice the size of the original than at an expected outcome of two objects of the original size. These results suggest that some prosimian primates understand the outcome of simple arithmetic operations. These results are discussed in light of similar findings in human infants and other adult primates.This revised version was published online in March 2005 with corrections to Fig. 6.     

Time and number discrimination in a bisection task with a sequence of stimuli: a developmental approach

Children, aged 5 and 8 years, and adults were tested in a bisection task with a sequence of stimuli in which time and number co-varied. In a counting and a non-counting condition, they were instructed either to process the duration of this sequence while ignoring the number of stimuli (temporal bisection), or to process the number of stimuli while ignoring the duration (numerical bisection). In the temporal bisection task, number interfered with the 5-year-olds' temporal performance, indicating that young children did not process time and number independently in a sequence of stimuli when they had to attend to duration. However, number interference decreased both with age and counting strategy. In contrast, in the numerical bisection task, duration did not interfere with numerical discrimination for any age group.     

Inhibitory control in number-conservation and class-inclusion tasks: A neo-Piagetian inter-task priming study

We investigated whether success in number-conservation and class-inclusion tasks relies on a general ability to inhibit misleading strategies. Two groups of 10-year-olds performed inter-task priming between computerized versions of class-inclusion and number-conservation tasks (Experiment 1). In one group, the class-inclusion task served as a prime and the number-conservation task as an assessment probe and vice versa in the other group. Response times were shorter in the number-conservation task when performed after the class-inclusion task (and vice versa in the other group) than in control prime-probe sequences in which the primes did not require the inhibition of a misleading strategy. Experiment 2 showed that these inter-task priming effects did not simply reflect that class inclusion and number conservation rely on the reversibility of concrete operations as Piaget would have hypothesized. Taken together the results are consistent with the neo-Piagetian assumption that cognitive development is rooted in both the acquisition of knowledge of incremental complexity and the ability to resist (inhibit) previous knowledge. Critically, the present finding suggests that the inhibitory ability is not domain- or strategy-specific.     

远、近空间内注意加工的分离

临床证据发现空间忽视症病人对于近处和远处空间内的注意加工存在差异,表现为空间忽视只发生于近处空间或只发生于远处空间,提示近处空间与远处空间在脑内可能是分别表征的。对健康成人的研究也发现了与之类似的近处空间和远处空间注意的分离现象,即在近处空间表现出左偏的伪忽视现象,在远处空间表现出左偏减弱或者右偏的趋势。本文综述了远、近空间内注意加工分离的实验证据以及采用线段二分任务这一主要的研究范式相关的实验结果,并且着重指出了远、近空间的划分不是绝对的,而是动态可变的研究证据。最后,指出了将来的研究需要深入考察空间参照系统在远、近空间知觉中的作用,以及关注社会交互情境下的远、近空间距离认知的动态变化。     

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.