数字加工任务影响时距知觉的数字效应

本研究采用复制时距和数字加工双任务,探讨数字大小影响时距知觉的机制。实验首先呈现不同时距的圆点,然后让被试按键复制圆点呈现的时距,与此同时,对屏幕上出现的数字进行命名(实验1)、奇偶数判断(实验2)、大小判断(实验3)。实验结果发现对数字进行奇偶数判断时,数字大小对时距知觉没有影响;进行数字命名和大小判断任务时,数字大小对时距知觉都产生了影响,并且时距不同,数字大小对时距知觉的影响也不同。该结果表明时距知觉的数字效应与数字加工任务和时距长短有关,呈现出动态变化的过程。     

Numerical and nonnumerical estimation in children with and without mathematical learning disabilities

There are currently multiple explanations for mathematical learning disabilities (MLD). The present study focused on those assuming that MLD are due to a basic numerical deficit affecting the ability to represent and to manipulate number magnitude (Butterworth, 1999 Butterworth, B. 1999. The mathematical brain, London, , United Kingdom: Macmillan.  [Google Scholar], 2005 Butterworth, B. 2005. “Developmental dyscalculia”. In Handbook of mathematical cognition, Edited by: Campbell, J. I. D. 455–467. New York, NY: Psychology Press.  [Google Scholar]; A. J. Wilson &; Dehaene, 2007 Wilson, A. J. and Dehaene, S. 2007. “Number sense and developmental dyscalculia”. In Human behavior, learning, and the developing brain: Atypical development, 2nd, Edited by: Coch, D., Dawson, G. and Fischer, K. 212–237. New York, NY: Guilford Press.  [Google Scholar]) and/or to access that number magnitude representation from numerical symbols (Rousselle &; Noël, 2007 Rousselle, L. and Noël, M. P. 2007. Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs non-symbolic number magnitude processing. Cognition, 102(3): 361–395. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). The present study provides an original contribution to this issue by testing MLD children (carefully selected on the basis of preserved abilities in other domains) on numerical estimation tasks with contrasting symbolic (Arabic numerals) and nonsymbolic (collection of dots) numbers used as input or output. MLD children performed consistently less accurately than control children on all the estimation tasks. However, MLD children were even weaker when the task involved the mapping between symbolic and nonsymbolic numbers than when the task required a mapping between two nonsymbolic numerical formats. Moreover, in the estimation of nonsymbolic numerosities, MLD children relied more than control children on perceptual cues such as the cumulative area of the dots. Finally, the task requiring a mapping from a nonsymbolic format to a symbolic format was the best predictor of MLD. In order to explain these present results, as well as those reported in the literature, we propose that the impoverished number magnitude representation of MLD children may arise from an initial mapping deficit between number symbols and that magnitude representation.     

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.     

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.     

发展性计算障碍儿童的数量转换缺陷

本研究拟考察发展性计算障碍儿童的认知缺陷成因。实验1要求被试在三种形式(点/点,数/数,点/数)下进行数量比较,实验2仅将点集替换为汉字数字词。结果表明障碍组和正常组在数/数、点/数和汉字/汉字比较任务上的成绩存在显著差异,而在点/点和汉字/汉字比较上没有差异。据此推论,计算障碍儿童符号加工能力受到损伤,符号与非符号数量转换能力存在缺陷,但非符号加工能力和不同符号间数量转换没有缺陷,支持语义提取缺陷假设。     

Mapping numerical magnitudes onto symbols: the numerical distance effect and individual differences in children's mathematics achievement

Although it is often assumed that abilities that reflect basic numerical understanding, such as numerical comparison, are related to children’s mathematical abilities, this relationship has not been tested rigorously. In addition, the extent to which symbolic and nonsymbolic number processing play differential roles in this relationship is not yet understood. To address these questions, we collected mathematics achievement measures from 6- to 8-year-olds as well as reaction times from a numerical comparison task. Using the reaction times, we calculated the size of the numerical distance effect exhibited by each child. In a correlational analysis, we found that the individual differences in the distance effect were related to mathematics achievement but not to reading achievement. This relationship was found to be specific to symbolic numerical comparison. Implications for the role of basic numerical competency and the role of accessing numerical magnitude information from Arabic numerals for the development of mathematical skills and their impairment are discussed.     

Desires,magnitudes, and orectic penetration

Dustin Stokes argues for the existence of orectic penetration, a phenomenon in which a desire-like state penetrates our perceptual experience. His candidate for a case of orectic penetration is the most convincing candidate presented thus far. It is argued here that his candidate and his further arguments for the existence of orectic penetration do not support the claim that orectic penetration takes place. As a result, it is concluded that there are no convincing cases of desire-like states penetrating perceptual experience.     

数量对时间知觉的影响——来自汉语数字的证据

本研究的目的在于探讨汉语数字对时间知觉的影响。采用二分试验程序,以400ms和1200ms作为标准短时间和标准长时间,三个实验中屏幕分别呈现阿拉伯数字(1、5和9),汉语小写数字(一五和九),汉语大写数字(壹伍和玖),让被试估计数字的呈现时间更接近于标准长时间还是标准短时间。结果显示三种实验条件下被试均具有低估小数字的呈现时间和高估大数字呈现时间的倾向。这个结果表明汉语数字也会对时间知觉产生影响,汉字形式的数字可以纳入到综合的数量理论体系之中。     

Sequential or parallel decomposed processing of two-digit numbers? Evidence from eye-tracking

While reaction time data have shown that decomposed processing of two-digit numbers occurs, there is little evidence about how decomposed processing functions. Poltrock and Schwartz (1984) argued that multi-digit numbers are compared in a sequential digit-by-digit fashion starting at the leftmost digit pair. In contrast, Nuerk and Willmes (2005) favoured parallel processing of the digits constituting a number. These models (i.e., sequential decomposition, parallel decomposition) make different predictions regarding the fixation pattern in a two-digit number magnitude comparison task and can therefore be differentiated by eye fixation data. We tested these models by evaluating participants' eye fixation behaviour while selecting the larger of two numbers. The stimulus set consisted of within-decade comparisons (e.g., 53_57) and between-decade comparisons (e.g., 42_57). The between-decade comparisons were further divided into compatible and incompatible trials (cf. Nuerk, Weger, & Willmes, 2001) and trials with different decade and unit distances. The observed fixation pattern implies that the comparison of two-digit numbers is not executed by sequentially comparing decade and unit digits as proposed by Poltrock and Schwartz (1984) but rather in a decomposed but parallel fashion. Moreover, the present fixation data provide first evidence that digit processing in multi-digit numbers is not a pure bottom-up effect, but is also influenced by top-down factors. Finally, implications for multi-digit number processing beyond the range of two-digit numbers are discussed.     

数量对时间知觉的影响-来自抽象数量和实际数量的证据

本研究采用抽象数量和实际数量叠加的方式呈现刺激,进一步探讨数量对时间知觉的影响。两个实验都运用时间的系列比较任务,以抽象数量和实际数量这两种数量的一致和不一致为条件,将阿拉伯数字和其字体大小叠加及阿拉伯数字和其呈现个数叠加的方式系列呈现在屏幕中央,要求被试比较判断刺激呈现的时间长短。结果显示被试均依靠实际数量的大小判断时间长短,而似乎忽略了抽象数量的存在。这一结果表明实际数量对时间知觉的影响要比抽象数量大,支持并扩展了数量理论。     

Exploring the developmental changes in automatic two-digit number processing

Even when two-digit numbers are irrelevant to the task at hand, adults process them. Do children process numbers automatically, and if so, what kind of information is activated? In a novel dot-number Stroop task, children (Grades 1-5) and adults were shown two different two-digit numbers made up of dots. Participants were asked to select the number that contained the larger dots. If numbers are processed automatically, reaction time for dot size judgment should be affected by numerical characteristics. The results suggest that, like adults, children process two-digit numbers automatically. Based on the current findings, we propose a developmental trend for automatic two-digit number processing that goes from decomposed sequential (activation of decade digit followed by that of unit digit) to decomposed parallel processing (simultaneous activation of decade and unit digits).     

Correlation between inspection time and psychometric abilities: A personal interpretation

More than 25 years of research suggests that the measure inspection time (IT) does capture low-level aspects of cognitive functioning that contribute to human intelligence. However, recent evidence does not support earlier claims that IT estimates the speed of a single mechanism like “sampling input” or “apprehension.” Rather, together with other tasks that employ pattern backward masking to limit the duration for which information is available for processing, IT is probably sensitive both to focused attentional capacities to detect organization and change under severe time constraints and to decision processes, ongoing beyond mask onset, that monitor responding. Among normal young adults, IT is correlated with the broad psychometric factor Gs (“speediness”). This mediates correlation with general intelligence. In this group, IT is not correlated with Gf. However, whether this outcome generalizes to samples of persons with an intellectual disability, to young children, or to elderly persons is not yet known. Psychological processes underpinning IT are currently only speculatively defined, but it should prove possible to unravel these by experimentation. To this end, backward masking procedures are arguably more theoretically tractable than reaction time tasks because they reduce the impact of higher-level cognitive strategies on performance. On this basis, IT may hold promise as a means for developing partial explanations for intelligence in psychological terms. However, whether this is realized depends on identifying the psychological functions that support IT.     

Relationships between three auditory inspection time tasks and processing speed

This study investigated the relationship between a spatial auditory inspection time task and previous versions of AIT, as well as the relationships of these tasks with visual inspection time (VIT) and general speediness (Gs). A total of 96 university undergraduates (age mean (M) = 20.0 years, standard deviation (SD) = 4.0 years) completed three AIT tasks, VIT, auditory reaction time (ART) and visual reaction time (VRT), and two Gs marker tests. Auditory inspection time‐spatial (AIT‐S) did not relate to VIT, but it did relate to the Gs marker tests. It also loaded moderately on a Gs factor along with VIT. Neither of the alternate AIT tasks showed any consistent relationships to reaction time (RT) or Gs measures. The AIT‐S task did, however, share substantial variance with its predecessors, suggesting that performance on all AIT tasks relies to some extent on similar processes. Further research is required to determine the nature of these processes.     

Handling time and choice in pigeons

According to optimal foraging theory, animals should prefer food items with the highest ratios of energy intake to handling time. When single items have negligible handling times, one large item should be preferred to a collection of small ones of equivalent total weight. However, when pigeons were offered such a choice on equal concurrent variable-interval schedules in a shuttlebox, they preferred the side offering many small items per reinforcement to that offering one or a few relatively large items. This preference was still evident on concurrent fixed-cumulative-duration schedules in which choosing the alternative with longer handling time substantially lowered the rate of food intake.     

Numerical and non-numerical ordinality processing in children with and without developmental dyscalculia: Evidence from fMRI

Ordinality is – beyond numerical magnitude (i.e., quantity) – an important characteristic of the number system. There is converging empirical evidence that (intra)parietal brain regions mediate number magnitude processing. Furthermore, recent findings suggest that the human intraparietal sulcus (IPS) supports magnitude and ordinality in a domain-general way. However, the latter findings are derived from adult studies and with respect to children (i.e., developing brain systems) both the neural correlates of ordinality processing and the precise role of the IPS (domain-general vs. domain-specific) in ordinality processing are thus far unknown. The present study aims at filling this gap by employing functional magnetic resonance imaging (fMRI) to investigate numerical and non-numerical ordinality knowledge in children with and without developmental dyscalculia. In children (without DD) processing of numerical and non-numerical ordinality alike is supported by (intra)parietal cortex, thus extending the notion of a domain-general (intra)parietal cortex to developing brain systems. Moreover, activation extents in response to numerical ordinality processing differ significantly between children with and without dyscalculia in inferior parietal regions (supramarginal gyrus and IPS).     

时间信息加工与信息加工时间特性双视角下的重要时间参数及其证据

时间既是人类信息加工的对象, 也是(非时间)信息加工的制约因素。数十毫秒至数秒之间的时间加工与人类日常生活关联紧密, 譬如主观计时、演奏及言语等活动。根据以往文献分析可知, 在该时间区域内, 20~ 60 ms、1/3~1 s、2~3 s是研究者关注的重要时间参数, 但是支持这些参数的证据尚存分歧。首先从“时间信息加工”和“信息加工的时间特性”的视角介绍时间参数的基本观点及其提出背景, 然后基于“时间信息加工”视角从行为学研究、脑损伤研究、神经药理学研究, 脑电研究、脑成像研究、经颅磁刺激研究、经颅直流电刺激研究等领域介评了1/3~1 s和2~3 s分界区域的证据, 接着基于“信息加工的时间特性”视角从时序知觉阈限研究、感觉运动同步研究、主观节奏研究、言语行为研究、知觉逆转研究、返回抑制研究及失匹配负波研究等领域介评了20~60 ms和2~3 s时间窗口的证据。未来研究既要注意构建基于分界区域与时间窗口的更强解释力的理论假说, 也要厘清分界区域与时间窗口的联系与区别。     

Relative reinforcer rates and magnitudes do not control concurrent choice independently

One assumption of the matching approach to choice is that different independent variables control choice independently of each other. We tested this assumption for reinforcer rate and magnitude in an extensive parametric experiment. Five pigeons responded for food reinforcement on switching-key concurrent variable-interval variable-interval schedules. Across conditions, the ratios of reinforcer rates and of reinforcer magnitudes on the two alternatives were both manipulated. Control by each independent variable, as measured by generalized-matching sensitivity, changed significantly with the ratio of the other independent variable. Analyses taking the model-comparison approach, which weighs improvement in goodness-of-fit against increasing number of free parameters, were inconclusive. These analyses compared a model assuming constant sensitivity to magnitude across all reinforcer-rate ratios with two alternative models. One of those alternatives allowed sensitivity to magnitude to vary freely across reinforcer-rate ratios, and was less efficient than the common-sensitivity model for all pigeons, according to the Schwarz-Bayes information criterion. The second alternative model constrained sensitivity to magnitude to be equal for pairs of reinforcer-rate ratios that deviated from unity by proportionately equal amounts but in opposite directions. This model was more efficient than the common-magnitude-sensitivity model for 2 of the pigeons, but not for the other 3. An analysis of variance, carried out independently of the generalized-matching analysis, also showed a significant interaction between the effects of reinforcer rate and reinforcer magnitude on choice. On balance, these results suggest that the assumption of independence inherent in the matching approach cannot be maintained. Relative reinforcer rates and magnitudes do not control choice independently.     

The relation between subitizable symbolic and non‐symbolic number processing over the kindergarten school year

A long‐standing debate in the field of numerical cognition concerns the degree to which symbolic and non‐symbolic processing are related over the course of development. Of particular interest is the possibility that this link depends on the range of quantities in question. Behavioral and neuroimaging research with adults suggests that symbolic and non‐symbolic quantities may be processed more similarly within, relative to outside of, the subitizing range. However, it remains unclear whether this unique link exists in young children at the outset of formal education. Further, no study has yet taken numerical size into account when investigating the longitudinal influence of these skills. To address these questions, we investigated the relation between symbolic and non‐symbolic processing inside versus outside the subitizing range, both cross‐sectionally and longitudinally, in 540 kindergarteners. Cross‐sectionally, we found a consistently stronger relation between symbolic and non‐symbolic number processing within versus outside the subitizing range at both the beginning and end of kindergarten. We also show evidence for a bidirectional relation over the course of kindergarten between formats within the subitizing range, and a unidirectional relation (symbolic → non‐symbolic) for quantities outside of the subitizing range. These findings extend current theories on symbolic and non‐symbolic magnitude development by suggesting that non‐symbolic processing may in fact play a role in the development of symbolic number abilities, but that this influence may be limited to quantities within the subitizing range.     

Prospective and retrospective time perception are related to mental time travel: Evidence from Alzheimer’s disease

Unlike prospective time perception paradigms, in which participants are aware that they have to estimate forthcoming time, little is known about retrospective time perception in normal aging and Alzheimer’s disease (AD). Our paper addresses this shortcoming by comparing prospective and retrospective time estimation in younger adults, older adults, and AD patients. In four prospective tasks (lasting 30 s, 60 s, 90 s, or 120 s) participants were asked to read a series of numbers and to provide a verbal estimation of the reading time. In four other retrospective tasks, they were not informed about time judgment until they were asked to provide a verbal estimation of four elapsed time intervals (lasting 30 s, 60 s, 90 s, or 120 s). AD participants gave shorter verbal time estimations than older adults and younger participants did, suggesting that time is perceived to pass quickly in these patients. For all participants, the duration of the retrospective tasks was underestimated as compared to the prospective tasks and both estimations were shorter than the real time interval. Prospective time estimation was further correlated with mental time travel, as measured with the Remember/Know paradigm. Mental time travel was even higher correlated with retrospective time estimation. Our findings shed light on the relationship between time perception and the ability to mentally project oneself into time, two skills contributing to human memory functioning. Finally, time perception deficits, as observed in AD patients, can be interpreted in terms of dramatic changes occurring in frontal lobes and hippocampus.