Beginning kindergarteners' perception of number

97 children in 5 kindergarten classes when tested for perceptions of number could begin counting and 9 counted to 30, 84 counted a set of 6 correctly but when the blocks were covered 33 could say there were 6. 57 showed 1:1 correspondence but some had to count to decide. 14 showed conservation of number, but 94 recognized two sets were unequal and which one was larger. 30 pointed to the third car, but 24 could state an ordinal name for a target. Clearly the children varied greatly.     

Oculomotor bias induced by number perception

Previous research with manual response methods has found evidence for an association between numbers and space. The present study investigated whether eye movements also show this association. Eye movement responses were recorded from 15 healthy participants as they categorized the digits 0-9 as odd or even. Responses were initiated faster to the left in response to small digits and faster to the right in response to large digits. Movement amplitudes were not systematically affected by either number magnitude or parity. These results provide further evidence for a spatially oriented "mental number line".     

Creating number semantics through finger movement perception

Communication, language and conceptual knowledge related to concrete objects may rely on the sensory–motor systems from which they emerge. How abstract concepts can emerge from these systems is however still unknown. Here we report a functional interaction between a specific meaningful finger movement, such as a finger grip closing, and a concept as abstract as numerical magnitude. Participants were presented with Arabic digits to recall before or after they perceived a biological or non-biological hand movement. The results show that perceiving a grip closing slows down the processing of large magnitude numbers. Importantly, we show that this motor-to-semantic interaction differs from the reverse semantic-to-motor interaction, and that it does not result from a general movement amplitude processing as it is only observed for biological hand movements. These results demonstrate the functional link between number meaning and goal-directed finger movements, and show how abstract concept semantics can emerge from the sensory–motor circuits of the brain.     

Verbal mediation of number knowledge: evidence from semantic dementia and corticobasal degeneration

Patients with corticobasal degeneration (CBD) appear to have impaired number knowledge. We examined the nature of their number deficit while we tested the hypothesis that comprehension of larger numbers depends in part on verbal mediation. We evaluated magnitude judgments and performance on number conservation measures rooted in Piagetian theory in nonaphasic patients with CBD (n=13) and patients with a fluent form of progressive aphasia known as semantic dementia (SD; n=15). We manipulated the numbers of the arrays and the visual-spatial properties of the stimuli being compared during magnitude judgments and Piagetian conservation measures. CBD patients were consistently impaired judging the magnitudes of larger numbers (4-9), while they had minimal difficulty with smaller numbers (magnitudes < or = 3). By comparison, SD patients performed all measures of number knowledge at a ceiling level regardless of number magnitude. Neither patient group was significantly impacted by manipulations of the spatial properties of the stimuli. CBD patients' impairment with larger numbers despite minimal aphasia, and SD patients' intact performance despite an aphasia, challenge the proposal that understanding larger numbers depends on verbal mediation.     

Implicit-shape constancy as a factor in pictorial perception.

Schoolboys from the Ivory Coast and from Kenya were tested on a simple task intended to detect the effect of implicit-shape constancy. The presence of such an effect was confirmed. Comparison of two Ivorean subsamples differing in their responses to a request to build a model of a depicted structure showed that those subjects who build flat (2D) models were less influenced by the implicit-shape constancy than those subjects who built three-dimensional structures. This confirms a postulated link between the implicit constancy and perception of pictorial depth.     

Self-motion perception influences number processing: evidence from a parity task

We investigated the role of horizontal body motion on the processing of numbers. We hypothesized that leftward self-motion leads to shifts in spatial attention and therefore facilitates the processing of small numbers, and vice versa, we expected that rightward self-motion facilitates the processing of large numbers. Participants were displaced by means of a motion platform during a parity judgment task. We found a systematic influence of self-motion direction on number processing, suggesting that the processing of numbers is intertwined with the processing of self-motion perception. The results differed from known spatial numerical compatibility effects in that self-motion exerted a differential influence on inner and outer numbers of the given interval. The results highlight the involvement of sensory body motion information in higher-order spatial cognition.     

Immediate small number perception: evidence from a new numerical carry-over procedure

Evidence is presented for the immediate apprehension of exact small quantities. Participants performed a quantification task (are the number of items greater or smaller than?), and carry-over effects were examined between numbers requiring the same response. Carry-over effects between small numbers were strongly affected by repeats of pattern and number identity relative to when displays were from the same response category but contained different numbers. Carry-over effects with large items were less sensitive to both pattern and number identity, even when the numbers in the small and large categories were matched for discriminability. The data suggest that small numbers are immediately apprehended through a direct subitization process distinct from pattern recognition and the apprehension of approximate number.     

Verbal self-reports about matching to sample: effects of the number of elements in a compound sample stimulus.

Adults' self-reports about their choices in a delayed matching-to-sample task were studied as a function of the number of elements (one, two, or three) in a compound sample stimulus. Signal-detection analyses were used to examine control of self-reports by the number of sample elements, by the speed and accuracy of choices reported about, and by several events contingent on self-reports. On each matching-to-sample trial, a sample element appeared as one of two comparison stimuli. Choice of the matching element, if made within 500 ms of the onset of the comparison stimuli, produced points worth money or chances in a drawing for money, depending on the subject. After each choice, subjects pressed either a "yes" or "no" button to answer a computer-generated query about whether the choice met the point contingency. The number of sample elements in the matching-to-sample task varied across trials, and events contingent on self-reports varied across experimental conditions. In Experiment 1, the conditions were defined by different combinations of feedback messages and point consequences contingent on self-reports, but self-reports were systematically influenced only by the sample-stimulus manipulation. Self-report errors increased with the number of sample elements. False alarms (inaccurate reports of success) were far more common than misses (inaccurate reports of failure), and false alarms were especially likely after choices that were correct but too slow to meet the point contingency. Sensitivity (A') of self-reports decreases as the number of sample elements increased. In addition, self-reports were more sensitive to choice accuracy than to choice speed. All subjects showed a pronounced bias (B'H) for reporting successful responses, although the bias was reduced as the number of sample elements increased and successful choices became less frequent. Experiment 2 demonstrated that the failure of point contingencies to influence self-reports in the first experiment was not due to a general ineffectiveness of the point consequences. Rates of inaccurate self-reports decreased when they resulted in point losses and increased when they resulted in point gains.     

Verbal behavior

The recent history and current status of the area of verbal behavior are considered in terms of three major thematic lines: the operant conditioning of adult verbal behavior, learning to be an effective speaker and listener, and developments directly related to Skinner's Verbal Behavior. Other topics not directly related to the main themes are also considered: the work of Kurt Salzinger, ape-language research, and human operant research related to rule-governed behavior.     

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。     

Verbal transformations in the aged

The susceptibility of aged persons to verbal transformations was studied in an experiment with ambiguous verbal stimuli ('reversible words'). Twenty-five subjects, aged 64 to 86 years, participated in the experiment. The results indicate that the aged are somewhat less susceptible to verbal reversals than are young adults, but there seem to be no age differences in the type of illusory forms heard. These results differ from those of experiments with nonreversible words, which show a very low rate of transformation and a total absence of transformations into meaningless forms in the aged. It is hypothesized that the reversibility of repeated ambiguous patterns is a general phenomenon arising from satiation, whereas transformations of repeated unambiguous verbal stimuli, involving phonetic distortions, are based on specific speech-perception mechanisms that are absent in the aged.