两位数的整体与局部加工

关于两位数的加工方式有整体加工说和局部加工说,实验证据主要来自数字数量控制/主动加工任务。本研究主要考察在数字数量自动加工任务中两位数的加工方式。实验一要求被试完成数量大小比较和物理大小比较两个任务,实验二只要求被试完成物理大小比较任务。结果是在数量比较任务和物理比较任务中都存在显著的个位十位一致性效应和数量物理一致性效应,这表明在两位数的数量主动和自动加工任务中均存在整体加工和局部加工两种方式。     

Chinese kindergartners’ automatic processing of numerical magnitude in Stroop-like tasks

Using Stroop-like tasks, this study examined whether Chinese kindergartners showed automatic processing of numerical magnitude. A total of 36 children (mean age 5 5 years 10 months) were asked to perform physical size comparison (i.e., “Which of two numbers is bigger in physical size?”) and numerical magnitude tasks (i.e., “Which of two numbers is bigger in numerical magnitude?”) on 216 number pairs. These number pairs varied in levels of congruence between numerical magnitude and physical size (for Stroop effect) and numerical distance (for distance effect). On the basis of analyses of response time and error rates, we found that Chinese kindergartners showed automatic processing of numerical magnitude. These results are significantly different from previous studies’ findings about the onset age (ranging from around the end of first grade to third grade) for automatic processing of numerical magnitude.     

Dynamic representations underlying symbolic and nonsymbolic calculation: Evidence from the operational momentum effect

When we add or subtract, do the corresponding quantities “move” along a mental number line? Does this internal movement lead to spatial biases? A new method was designed to investigate the psychophysics of approximate arithmetic. Addition and subtraction problems were presented either with sets of dots or with Arabic numerals, and subjects selected, from among seven choices, the most plausible result. In two experiments, the subjects selected larger numbers for addition than for subtraction problems, as if moving too far along the number line. This operational momentum effect was present in both notations and increased with the size of the outcome. Furthermore, we observed a new effect of spatial-numerical congruence, related to but distinct from the spatial numerical association of response codes effect: During nonsymbolic addition, the subjects preferentially selected numbers at the upper right location, whereas during subtraction, they were biased toward the upper left location. These findings suggest that approximate mental arithmetic involves dynamic shifts on a spatially organized mental representation of numbers. Supplemental materials for this study may be downloaded from app.psychonomic-journals.org/content/supplemental.     

Repetition priming across distinct contexts: Effects of lexical status,word frequency,and retrieval test

Previous studies have shown an interference of task-irrelevant numerical information with the spatial parameters of visuomotor behaviour. These findings lend support to the notion that number and space share a common metric with respect to action. Here I argue that the demonstration of the structural similarity between scales for number and space would be a more stringent test for the shared metrics than a mere fact of interference. The present study investigated the scale of number mapping onto space in a manual estimation task. The physical size of target stimuli and the magnitudes of task-irrelevant numbers were parametrically manipulated in the context of the Titchener illusion. The results revealed different scaling schemas for number and space. Whereas estimates in response to changes in stimulus physical size showed a gradual increase, the effect of number was categorical with the largest number (9) showing greater manual estimate than the other numbers (1, 3, and 7). Possible interpretations that are not necessarily incompatible with the hypothesis of shared metrics with respect to action are proposed. However, the present findings suggest that a meticulous scale analysis is required in order to determine the nature of number–space interaction.     

Approaching stimuli bias attention in numerical space

Increasing evidence suggests that common mechanisms underlie the direction of attention in physical space and numerical space, along the mental number line. The small leftward bias (pseudoneglect) found on paper-and-pencil line bisection is also observed when participants 'bisect' number pairs, estimating (without calculating) the number midway between two others. Here we investigated the effect of stimulus motion on attention in numerical space. A two-frame apparent motion paradigm manipulating stimulus size was used to produce the impression that pairs of numbers were approaching (size increase from first to second frame), receding (size decrease), or not moving (no size change). The magnitude of pseudoneglect increased for approaching numbers, even when the final stimulus size was held constant. This result is consistent with previous findings that pseudoneglect in numerical space (as in physical space) increases as stimuli are brought closer to the participant. It also suggests that the perception of stimulus motion modulates attention over the mental number line and provides further support for a connection between the neural representations of physical space and number.     

符号数量和非符号数量的空间表征:5岁儿童的SNARC效应和距离效应

对物理刺激的数量信息表征是符号数字表征的前提和基础,据此假设在儿童的SNARC效应发生的时序问题上,非符号数量(如面积)的空间表征早于符号数量(如阿拉伯数字)的空间表征。本研究邀请5岁幼儿完成数字比较和面积比较两类任务,结果发现在数字比较任务中没有出现SNARC效应,但却存在距离效应;在面积比较任务中出现了SNARC效应和距离效应。可以推断,在阿拉伯数字的空间表征出现之前,儿童已经能够对非符号数量信息进行空间表征。     

Dissociation of the distance effect and size effect in one-digit numbers

Magnitude comparison of single digits is robustly characterized by a distance effect (close numbers are more difficult to compare than numbers further apart) and a size effect (for a given distance, comparison difficulty increases with increasing size). The distance effect indicates access to the mental number line (Dehaene, 1997), and the size effect is usually interpreted as indicating that the mental number line represents larger numbers more vaguely than smaller ones. In contrast, we have argued earlier (Verguts, Fias, & Stevens, 2005) that for symbolic numbers (Arabic or verbal notation), the size effect does not originate from the mental number line but, instead, originates from mappings to relevant output components that are specific for magnitude comparison. If the latter is true, it should be possible to dissociate the distance effect from the size effect in tasks other than magnitude comparison. In two experiments, we observed a robust distance effect insame/different judgments, which implies access to the mental number line. Yet the size effect was absent. Consistent with our prediction, this finding establishes a dissociation between the size effect and the distance effect.     

Are Arabic and verbal numbers processed in different ways?

Four experiments were conducted in order to examine effects of notation--Arabic and verbal numbers--on relevant and irrelevant numerical processing. In Experiment 1, notation interacted with the numerical distance effect, and irrelevant physical size affected numerical processing (i.e., size congruity effect) for both notations but to a lesser degree for verbal numbers. In contrast, size congruity had no effect when verbal numbers were the irrelevant dimension. In Experiments 2 and 3, different parameters that could possibly affect the results, such as discriminability and variability (Experiment 2) and the block design (Experiment 3), were controlled. The results replicated the effects obtained in Experiment 1. In Experiment 4, in which physical size was made more difficult to process, size congruity for irrelevant verbal numbers was observed. The present results imply that notation affects numerical processing and that Arabic and verbal numbers are represented separately, and thus it is suggested that current models of numerical processing should have separate comparison mechanisms for verbal and Arabic numbers.     

Simon congruency effects based on stimulus and response numerosity

Three choice reaction time experiments documented a Simon-type congruence effect involving the numbers of stimuli and responses. In Experiment 1 the stimulus consisted of one or two high- or low-pitch tones, and participants were required to respond with one or two taps of a response key depending on stimulus pitch. Responses were faster when the number of tones matched the required number of response taps than when these numbers mismatched. Experiment 2 showed that a weaker version of this effect can also be obtained using visual stimuli, and Experiment 3 showed that the analogous effect can even be obtained, albeit very weakly, with bimodal stimuli. There was also evidence that the number of stimuli affected the rate of emitting the two-tap response. These results indicate that stimulus numerosity is processed automatically to the level at which it can affect the selection and possibly the execution of a varying number of responses.     

Simon congruency effects based on stimulus and response numerosity

Three choice reaction time experiments documented a Simon-type congruence effect involving the numbers of stimuli and responses. In Experiment 1 the stimulus consisted of one or two high- or low-pitch tones, and participants were required to respond with one or two taps of a response key depending on stimulus pitch. Responses were faster when the number of tones matched the required number of response taps than when these numbers mismatched. Experiment 2 showed that a weaker version of this effect can also be obtained using visual stimuli, and Experiment 3 showed that the analogous effect can even be obtained, albeit very weakly, with bimodal stimuli. There was also evidence that the number of stimuli affected the rate of emitting the two-tap response. These results indicate that stimulus numerosity is processed automatically to the level at which it can affect the selection and possibly the execution of a varying number of responses.     

Gaze orientation interferes with mental numerical representation

Number comparison tasks are characterized by distance and size effects. The distance effect reveals that the higher the distance is between two numbers, the easier their magnitude comparison is. Accordingly, people are thought to represent numbers on a spatial dimension, the mental number line, on which any given number corresponds to a location on the line. The size effect, instead, states that at any given distance, comparing two small numbers is easier than comparing two large numbers, thus suggesting that larger numbers are more vaguely represented than smaller ones. In the present work we first tested whether the participants were adopting a spatial strategy to solve a very simple numbers comparison task, by assessing the presence of the distance and the magnitude effect. Secondarily, we focused on the influence of gaze position on their performance. The present results provide evidence that gaze direction interferes with number comparisons, worsening the vague representation of larger numbers and further supporting the hypothesis of the overlapping between physical and mental spaces.     

Expanding on the mental number line: Zero is perceived as the "smallest"

The representation of 0 in healthy adults was studied with the physical comparison task. Automatic processing of numbers, as indicated by the size congruity effect, was used for detecting the basic numerical representations stored in long-term memory. The size congruity effect usually increases with numerical distance between the physically compared numbers. This increase was attenuated for comparisons to 0 or 1 (but not to 2) when they were perceived as the smallest number in the set. Furthermore, the size congruity effect was enlarged in these cases. These results indicate an end effect in automatic processing of numbers and suggest that 0, or 1 in the absence of 0, is perceived as the smallest entity on the mental number line. The implications of these findings are discussed with regard to models of number representation. (PsycINFO Database Record (c) 2012 APA, all rights reserved).     

Typical and atypical development of basic numerical skills in elementary school

Deficits in basic numerical processing have been identified as a central and potentially causal problem in developmental dyscalculia; however, so far not much is known about the typical and atypical development of such skills. This study assessed basic number skills cross-sectionally in 262 typically developing and 51 dyscalculic children in Grades 2, 3, and 4. Findings indicate that the efficiency of number processing improves over time and that dyscalculic children are generally less efficient than children with typical development. For children with typical arithmetic development, robust effects of numerical distance, size congruity, and compatibility of ten and unit digits in two-digit numbers could be identified as early as the end of Grade 2. Only the distance effect for comparing symbolic representations of numerosities changed developmentally. Dyscalculic children did not show a size congruity effect but showed a more marked compatibility effect for two-digit numbers. We did not find strong evidence that dyscalculic children process numbers qualitatively differently from children with typical arithmetic development.     

Negative numbers in simple arithmetic

Are negative numbers processed differently from positive numbers in arithmetic problems? In two experiments, adults (N?=?66) solved standard addition and subtraction problems such as 3?+?4 and 7 – 4 and recasted versions that included explicit negative signs—that is, 3 – (–4), 7?+?(–4), and (–4)?+?7. Solution times on the recasted problems were slower than those on standard problems, but the effect was much larger for addition than subtraction. The negative sign may prime subtraction in both kinds of recasted problem. Problem size effects were the same or smaller in recasted than in standard problems, suggesting that the recasted formats did not interfere with mental calculation. These results suggest that the underlying conceptual structure of the problem (i.e., addition vs. subtraction) is more important for solution processes than the presence of negative numbers.     

A memory-based, Simon-like, spatial congruence effect: Evidence for persisting spatial codes

The Simon effect refers to the finding that in a task where stimulus location is irrelevant, reaction time is faster when stimulus and response locations are congruent than when they are not. Dominant theories of the Simon effect have generally attributed this spatial congruence effect to a spatial code automatically generated upon stimulus presentation. A common assumption of these theories is that this spatial code decays in less than a few hundred milliseconds following stimulus onset. We report two working-memory experiments suggesting a reexamination of this assumption—a Simon-like spatial congruence effect persisted over a delay of as long as 2400 ms. We propose that, in addition to generating short-lived perceptual codes, spatial information may be coded in working memory as part of the context associated with stimulus events. When reactivated by cues from the original event, such information may influence response selection and produce spatial congruence effects (in this case, positive when participants made a “yes” response and negative when they made a “no” response).     

积极追随原型-特质匹配对辱虐管理的影响——基于多项式回归与响应面分析的探索

基于内隐追随理论,探索了领导者的积极追随原型(PFP)与追随者的积极追随特质(PFT)之间的匹配程度如何影响辱虐管理。对194份上下级配对数据进行多项式回归和响应面分析,结果显示:(1)相较于非匹配情形,领导者在"PFP—PFT匹配"情形下更少辱虐追随者;(2)与"PFP低—PFT低"相比,"PFP高—PFT高"情形下辱虐管理程度更低;(3)在非匹配情况下,与"PFP高—PFT低"相比,领导者在"PFP低—PFT高"时对追随者有更少的辱虐管理。以上结论能够为组织预防或减少辱虐管理提供理论指导。     

物理大小和面积的无意识空间表征

意识水平的研究发现,数字量的比较机制与物理刺激比较的机制是一样的;在无意识水平上的研究发现,数字加工存在无意识语义启动现象。我们假设,在数字的物理特性的比较任务中可能存在无意识启动效应和类SNARC效应。实验一的数字比较任务和数字的物理大小比较任务发现,在33毫秒的无意识启动条件下,数字语义比较任务和数字物理大小比较任务中都发现了类SNARC效应、启动效应以及Stroop效应。实验二的数字覆盖面积比较任务中发现,在33毫秒的启动水平,数字比较与数字覆盖面积的比较任务中均存在SNARC效应、Stroop效应和启动效应。     

Display-wide influences on figure–ground perception: The case of symmetry

Past research has demonstrated that convex regions are increasingly likely to be perceived as figures as the number of alternating convex and concave regions in test displays increases. This region-number effect depends on both a small preexisting preference for convex over concave objects and the presence of scene characteristics (i.e., uniform fill) that allow the integration of the concave regions into a background object/surface. These factors work together to enable the percept of convex objects in front of a background. We investigated whether region-number effects generalize to another property, symmetry, whose effectiveness as a figure property has been debated. Observers reported which regions they perceived as figures in black-and-white displays with alternating symmetric/asymmetric regions. In Experiments 1 and 2, the displays had articulated outer borders that preserved the symmetry/asymmetry of the outermost regions. Region-number effects were not observed, although symmetric regions were perceived as figures more often than chance. We hypothesized that the articulated outer borders prevented fitting a background interpretation to the asymmetric regions. In Experiment 3, we used straight-edge framelike outer borders and observed region-number effects for symmetry equivalent to those observed for convexity. These results (1) show that display-wide information affects figure assignment at a border, (2) extend the evidence indicating that the ability to fit background as well as foreground interpretations is critical in figure assignment, (3) reveal that symmetry and convexity are equally effective figure cues and, (4) demonstrate that symmetry serves as a figural property only when it is close to fixation.     

Language effects in magnitude comparison: small, but not irrelevant

It is assumed that number magnitude comparison is performed by assessing magnitude representation on a single analog mental number line. However, we have observed a unit-decade-compatibility effect in German which is inconsistent with this assumption (Nuerk, Weger, & Willmes, 2001). Incompatible magnitude comparisons in which decade and unit comparisons lead to different responses (e.g., 37_52 for which 3<5, but 7>2) are slower and less accurately responded to than compatible trials in which decade and unit comparisons lead to the same response (e.g., 42_57, for which 4<5 and 2<7). As overall distance was held constant, a single holistic magnitude representation could not account for this compatibility effect. However, because of the inversion property of the corresponding German two-digit number words ("einundzwanzig" ), the language-generality of the effect is questionable. We have therefore examined the compatibility effect with native English speakers. We were able to replicate the compatibility effect using Arabic notation. Thus, the compatibility effect is not language-specific. However, in cross-linguistic analyses language-specific modulations were observed not only for number words but also for Arabic numbers. The constraints imposed on current models by the verbal mediation of Arabic number comparison are discussed.     

贵州少数民族儿童青少年SNARC效应的发展

采用奇偶判断任务,考察二年级至大学阶段贵州民族儿童青少年SNARC效应的发展状况。结果显示：三年级开始出现SNARC效应（包括正确率SNARC效应）;各阶段SNARC效应无显著差异;高、低年级正确率存在显著差异,六年级以后各阶段正确率无显著差异。结论：民族儿童三年级开始形成数字的空间表征。SNARC效应的大小不因年龄而发生变化;被试对奇偶知识的掌握存在发展过程,三年级可能基本理解奇偶信息,六年级后熟练掌握奇偶信息。