The effect of working memory load on the SNARC effect: Maybe tasks have a word to say

We investigated the effect of working memory load on the SNARC (spatial–numerical association of response codes) effect under different number judgment tasks (parity judgment and magnitude comparison), using a novel dual task. Instead of exerting load over the whole block of number judgment trials, in this dual task, number judgment trials were inserted into each interstimulus interval of an n-back task, which served as the working memory load. We varied both load type (verbal and spatial) and amount (1-load, 2-load, and 3-load). The results indicated that the SNARC effect disappeared even under the 1-load condition for a parity judgment, regardless of the type of load. However, during the magnitude comparison task, the SNARC effect increased with increasing load amounts under spatial load conditions; under verbal load conditions, the SNARC effect decreased with increasing amounts of load, and disappeared during the 3-load task. The difference between the parity and magnitude tasks was not attributable to the interval stimuli or task switching. These findings confirm that different spatial–numerical associations for comparing numerical magnitudes and judgments of parity have different needs with respect to working memory resources.     

Language statistics explain the spatial–numerical association of response codes

The spatial–numerical association of response codes (SNARC) has shown that parity judgments with participants’ left hands yield faster response times (RTs) for smaller numbers than for larger numbers, with the opposite result for right-hand responses. These findings have been explained by participants perceptually simulating magnitude on a mental number line. In three RT experiments, we showed that the SNARC effect can also be explained by language statistics. Participants made parity judgments of number words (Exp. 1) and Arabic numerals (Exp. 2). Linguistic frequencies of the number words and numbers mirrored the SNARC effect, explaining aspects of processing that a perceptual simulation account could not. In Experiment 3, we investigated whether high- and low-frequency nonnumerical words would also elicit a SNARC-like effect. Again, RTs were faster for high-frequency words for left-hand responses, with the opposite result for right-hand responses. These results demonstrate that what has only been attributed to perceptual simulation should also be attributed to language statistics.     

Automaticity for numerical magnitude of two-digit Arabic numbers in children

This paper examines the automatic processing of the numerical magnitude of two-digit Arabic numbers using a Stroop-like task in school-aged children. Second, third, and fourth graders performed physical size judgments on pairs of two-digit numbers varying on both physical and numerical dimensions. To investigate the importance of synchrony between the speed of processing of the numerical magnitude and the physical dimensions on the size congruity effect (SCE), we used masked priming: numerical magnitude was subliminally primed in half of the trials, while neutral priming was used in the other half. The results indicate a SCE in physical judgments, providing the evidence of automatic access to the magnitude of two-digit numbers in children. This effect was modulated by the priming type, as a SCE only appeared when the numerical magnitude was primed. This suggests that young children needed a relative synchronization of numerical and physical dimensions to access the magnitude of two-digit numbers automatically.     

Paying attention to attention: evidence for an attentional contribution to the size congruity effect

Understanding the mechanisms supporting our comprehension of magnitude information represents a key goal in cognitive psychology. A major phenomenon employed in the pursuit of this goal has been the physical size congruity effect—namely, the observation that comparing the relative numerical sizes of two numbers is influenced by their relative physical sizes. The standard account of the physical size congruity effect attributes it to the automatic influence of the comparison of irrelevant physical magnitudes on numerical judgments. Here we develop an alternative account of this effect on the basis of the operation of attention in the typical size congruity display and the temporal dynamics of number comparison. We also provide a test of a number of predictions derived from this alternative account by combining a physical size congruity manipulation with a manipulation designed to alter the operation of attention within the typical size congruity display (i.e., a manipulation of the relative onsets of the digits). This test provides evidence consistent with an attentional contribution to the size congruity effect. Implications for our understanding of magnitude and the interactions between attention and magnitude are discussed.     

Moving the eyes along the mental number line: comparing SNARC effects with saccadic and manual responses

Bimanual parityjudgments about numerically small (large) digits are faster with the left (right) hand, even though parity is unrelated to numerical magnitude per se (the SNARC effect; Dehaene, Bossini, & Giraux, 1993). According to one model, this effect reflects a space-related representation of numerical magnitudes (mental number line) with a genuine left-to-right orientation. Alternatively, it may simply reflect an overlearned motor association between numbers and manual responses--as, for example, on typewriters or computer keyboards--in which case it should be weaker or absent with effectors whose horizontal response component is less systematically associated with individual numbers. Two experiments involving comparisons of saccadic and manual parity judgment tasks clearly support the first view; they also establish a vertical SNARC effect, suggesting that our magnitude representation resembles a number map, rather than a number line.     

The influence of time units on the flexibility of the spatial numerical association of response codes effect

The Spatial Numerical/Temporal Association of Response Codes (SNARC/STEARC) effects are considered evidence of the association between number or time and space, respectively. As the SNARC effect was proposed by Dehaene, Bossini, and Giraux in 1993, several studies have suggested that different tasks and cultural factors can affect the flexibility of the SNARC effect. This study explored the influence of time units on the flexibility of the SNARC effect via materials with Arabic numbers, which were suffixed with time units and subjected to magnitude comparison tasks. Experiment 1 replicated the SNARC effect for numbers and the STEARC effect for time units. Experiment 2 explored the flexibility of the SNARC effect when numbers were attached to time units, which either conflicted with the numerical magnitude or in which the time units were the same or different. Experiment 3 explored whether the SNARC effect of numbers was stable when numbers were near the transition of two adjacent time units. The results indicate that the SNARC effect was flexible when the numbers were suffixed with time units: Time units influenced the direction of the SNARC effect in a way which could not be accounted for by the mathematical differences between the time units and numbers. This suggests that the SNARC effect is not obligatory and can be easily adapted or inhibited based on the current context.     

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.     

The SNARC effect in the processing of second-language number words: Further evidence for strong lexico-semantic connections

We present new evidence that word translation involves semantic mediation. It has been shown that participants react faster to small numbers with their left hand and to large numbers with their right hand. This SNARC (spatial-numerical association of response codes) effect is due to the fact that in Western cultures the semantic number line is oriented from left (small) to right (large). We obtained a SNARC effect when participants had to indicate the parity of second-language (L2) number words, but not when they had to indicate whether L2 number words contained a particular sound. Crucially, the SNARC effect was also obtained in a translation verification task, indicating that this task involved the activation of number magnitude.     

The SNARC effect in the processing of second-language number words: further evidence for strong lexico-semantic connections

We present new evidence that word translation involves semantic mediation. It has been shown that participants react faster to small numbers with their left hand and to large numbers with their right hand. This SNARC (spatial-numerical association of response codes) effect is due to the fact that in Western cultures the semantic number line is oriented from left (small) to right (large). We obtained a SNARC effect when participants had to indicate the parity of second-language (L2) number words, but not when they had to indicate whether L2 number words contained a particular sound. Crucially, the SNARC effect was also obtained in a translation verification task, indicating that this task involved the activation of number magnitude.     

SNARC效应: 现状、理论与建议

SNARC效应是当对数字进行奇偶判断时,即使数的奇偶性与数的大小无关,但右手（左手）对相对大（小）的数的反应快。首先介绍SNARC效应的起源和理论解释,然后总结SNARC效应的特性,论述SNARC效应和Simon效应以及MARC 效应的关系,并对SNARC效应的脑机制进行了概述,最后提出3个有待深入研究的问题：（1）SNARC效应的加工处理机制;（2）SANRC效应的理论探索;（3）SNARC效应的本质。     

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。     

Bad–good constraints on a polarity correspondence account for the spatial–numerical association of response codes (SNARC) and markedness association of response codes (MARC) effects

Performance in numerical classification tasks involving either parity or magnitude judgements is quicker when small numbers are mapped onto a left-sided response and large numbers onto a right-sided response than for the opposite mapping (i.e., the spatial–numerical association of response codes or SNARC effect). Recent research by Gevers et al. [Gevers, W., Santens, S., Dhooge, E., Chen, Q., Van den Bossche, L., Fias, W., & Verguts, T. (2010). Verbal-spatial and visuospatial coding of number–space interactions. Journal of Experimental Psychology: General, 139, 180–190] suggests that this effect also arises for vocal “left” and “right” responding, indicating that verbal–spatial coding has a role to play in determining it. Another presumably verbal-based, spatial–numerical mapping phenomenon is the linguistic markedness association of response codes (MARC) effect whereby responding in parity tasks is quicker when odd numbers are mapped onto left-sided responses and even numbers onto right-sided responses. A recent account of both the SNARC and MARC effects is based on the polarity correspondence principle [Proctor, R. W., & Cho, Y. S. (2006). Polarity correspondence: A general principle for performance of speeded binary classification tasks. Psychological Bulletin, 132, 416–442]. This account assumes that stimulus and response alternatives are coded along any number of dimensions in terms of – and + polarities with quicker responding when the polarity codes for the stimulus and the response correspond. In the present study, even–odd parity judgements were made using either “left” and “right” or “bad” and “good” vocal responses. Results indicated that a SNARC effect was indeed present for the former type of vocal responding, providing further evidence for the sufficiency of the verbal–spatial coding account for this effect. However, the decided lack of an analogous SNARC-like effect in the results for the latter type of vocal responding provides an important constraint on the presumed generality of the polarity correspondence account. On the other hand, the presence of robust MARC effects for “bad” and “good” but not “left” and “right” vocal responses is consistent with the view that such effects are due to conceptual associations between semantic codes for odd–even and bad–good (but not necessarily left–right).     

数字空间联结的灵活性及其内在机制

数字空间联结一直是认知心理学领域研究的热点之一。探索数字空间联结的一个重要指标为空间-数字反应联合编码(spatial-numerical association of response codes, SNARC)效应(左/右手对小/大数反应更快更准确)。以往研究已验证SNARC效应的普遍性及其在方向上的灵活性, 并提出多种理论解释。此外, SNARC效应在加工阶段上也具有灵活性, 其原因可能有：(1)加因素法则的理解偏差; (2)观察的角度单一; (3)观察效标的差异; (4)使用任务的差异。结合以上因素, 提出双阶段(数量信息的空间表征、空间表征到反应选择)加工模型, 不同的操控因素分别作用于两个阶段可能是引起SNARC效应灵活变化的核心原因。未来研究可从对比任务差异、引入不同干扰因素等方面进一步验证双阶段加工模型, 并结合认知神经科学技术揭示数字空间联结灵活性的内在神经机制。     

大小判断任务中正负号及其异同对SNARC效应的影响

SNARC效应(Spatial-Numerical Association of Response Codes)是指被试对数字做按键反应时,对于较小的数字,按左键的速度快于按右键;对于较大的数字,按右键的速度快于按左键。本研究以ERP作为测量手段,采用修正的大小判断任务,旨在探究数字正负号及其异同对SNARC效应的影响。行为结果发现,在反应时上,当目标数字与基线数字正负号相同且基线数字为+5时,一致条件显著快于不一致条件。ERP结果发现,当目标数字与基线数字正负号相同时,无论基线数字为+5还是–5,在反应选择阶段,不一致都比一致条件更负且均诱发了P3。当目标数字与基线数字正负号相异时,若基线数字为+5,一致比不一致条件在刺激呈现阶段诱发了波幅显著更小的N300;若基线数字为–5,一致比不一致条件在反应执行阶段诱发了更正的LPP。无论目标数字与基线数字正负号相同还是相异,在反应选择阶段,不一致都比一致条件更负且均诱发了P3,表明出现了SNARC效应。同时,SNARC效应的出现激活了额叶头皮位置,负数加工伴随左额叶的激活,而正数加工伴随右额叶的激活,溯源分析结果进一步表明SNARC效应定位于额叶与顶叶。这些结果说明负数按实际大小表征在心理数字线上,支持了负数空间表征的个体发展论假说;表明符号捷径机制会改变SNARC效应的发生时间;同时证明了负数与正数的空间表征具有不同的优势半球。     

Implicit response-irrelevant number information triggers the SNARC effect: Evidence using a neural overlap paradigm

There is evidence from the SNARC (spatial–numerical association of response codes) effect and NDE (numerical distance effect) that number activates spatial representations. Most of this evidence comes from tasks with explicit reference to number, whether through presentation of Arabic digits (SNARC) or through magnitude decisions to nonsymbolic representations (NDE). Here, we report four studies that use the neural overlap paradigm developed by Fias, Lauwereyns, and Lammertyn (2001) to examine whether the presentation of implicit and task-irrelevant numerosity information (nonsymbolic arrays and auditory numbers) is enough to activate a spatial representation of number. Participants were presented with either numerosity arrays (1–9 circles or triangles) to which they made colour (Experiment 1) or orientation (Experiment 2) judgements, or auditory numbers coupled with an on-screen stimulus to which they made a colour (Experiment 3) or orientation (Experiment 4) judgement. SNARC effects were observed only for the orientation tasks. Following the logic of Fias et al., we argue that this SNARC effect occurs as a result of overlap in parietal processing for number and orientation judgements irrespective of modality. Furthermore, we found stronger SNARC effects in the small number range (1–4) than in the larger number range (6–9) for both nonsymbolic displays and auditory numbers. These results suggest that quantity is extracted (and interferes with responses in the orientation task) but this is not exact for the entire number range. We discuss a number of alternative models and mechanisms of numerical processing that may account for such effects.     

数字空间表征的在线建构：来自干扰情境中数字SNARC效应的证据

尽管已有研究发现数字以空间方式表征在人类记忆系统, 但是人脑如何完成数字的空间表征尚存争议。本研究两个实验在不同比例的数字字母(实验1)和不同比例的数字汉字(实验2)混合情境中考察了数字空间表征特点及其机制, 对上述争议进行了深入研究。结果发现：(1)当数字字母比例为“1 : 1”时, 数字加工中不出现SNARC效应。当数字字母比例为“1 : 6”和“6 : 1”时, 数字加工中均出现SNARC效应。即数字字母比例与数字SNARC效应之间呈倒“U”型关系。(2)数字汉字混合情境中数字汉字比例与数字SNARC效应之间同样呈倒“U”型关系。结果说明：(1)干扰刺激与数字混合呈现会影响数字SNARC效应。(2)干扰刺激加工对数字SNARC效应的影响受到数字与干扰刺激比例的调节, 且具有跨干扰材料的稳定性。研究结果意味着数字的空间表征是人类通过统计学习在线建构的, 支持了工作记忆理论。     

Implicit response-irrelevant number information triggers the SNARC effect: Evidence using a neural overlap paradigm

There is evidence from the SNARC (spatial-numerical association of response codes) effect and NDE (numerical distance effect) that number activates spatial representations. Most of this evidence comes from tasks with explicit reference to number, whether through presentation of Arabic digits (SNARC) or through magnitude decisions to nonsymbolic representations (NDE). Here, we report four studies that use the neural overlap paradigm developed by Fias, Lauwereyns, and Lammertyn (2001) to examine whether the presentation of implicit and task-irrelevant numerosity information (nonsymbolic arrays and auditory numbers) is enough to activate a spatial representation of number. Participants were presented with either numerosity arrays (1-9 circles or triangles) to which they made colour (Experiment 1) or orientation (Experiment 2) judgements, or auditory numbers coupled with an on-screen stimulus to which they made a colour (Experiment 3) or orientation (Experiment 4) judgement. SNARC effects were observed only for the orientation tasks. Following the logic of Fias et al., we argue that this SNARC effect occurs as a result of overlap in parietal processing for number and orientation judgements irrespective of modality. Furthermore, we found stronger SNARC effects in the small number range (1-4) than in the larger number range (6-9) for both nonsymbolic displays and auditory numbers. These results suggest that quantity is extracted (and interferes with responses in the orientation task) but this is not exact for the entire number range. We discuss a number of alternative models and mechanisms of numerical processing that may account for such effects.     

Developing number–space associations: SNARC effects using a color discrimination task in 5-year-olds

Human adults’ numerical representation is spatially oriented; consequently, participants are faster to respond to small/large numerals with their left/right hand, respectively, when doing a binary classification judgment on numbers, known as the SNARC (spatial–numerical association of response codes) effect. Studies on the emergence and development of the SNARC effect remain scarce. The current study introduces an innovative new paradigm based on a simple color judgment of Arabic digits. Using this task, we found a SNARC effect in children as young as 5.5 years. In contrast, when preschool children needed to perform a magnitude judgment task necessitating exact number knowledge, the SNARC effect started to emerge only at 5.8 years. Moreover, the emergence of a magnitude SNARC but not a color SNARC was linked to proficiency with Arabic digits. Our results suggest that access to a spatially oriented approximate magnitude representation from symbolic digits emerges early in ontogenetic development. Exact magnitude judgments, on the other hand, rely on experience with Arabic digits and, thus, necessitate formal or informal schooling to give access to a spatially oriented numerical representation.     

Comparing implicit and synaesthetic number–space associations: Visuospatial and verbal spatial–numerical associations of response codes

In the theory of the mental number line, number, and space are implicitly associated, giving rise to the spatial–numerical association of response codes (SNARC) effect, in which smaller numbers are more readily associated with the left side of space and larger numbers with the right, during a parity judgement task. Others, however, have argued that the SNARC effect is flexible and better explained by verbal rather than spatial associations. A few single-case studies on the SNARC effect have tested number–space synaesthetes, who make explicit associations between number and space. Here, we present data from experiments conducted on groups of synaesthetes and nonsynaesthetes on the classic SNARC parity judgement task with lateralized response keys and a modified version in which they responded to labels appearing on screen. Synaesthetes' behaviour was expected to differ from nonsynaesthetes' behaviour due to the explicit, fixed nature of their number–space associations, but both experiments show the two groups behaving in the same way, indicating that parity judgement tasks may not be tapping the same representation of number that gives rise to synaesthetic number–space experiences.     

身体形式和社会环境对SNARC效应的影响:基于具身认知观的理解

目前SNARC效应在认知心理学领域得到了广泛研究,然而较少有研究考察身体形式和社会环境对SNARC效应的影响.研究以127名在校大学生为被试,使用奇偶判断任务、Go/No-go任务以及合作情境下的Go/No-go任务依次展开了三个研究,拟揭示身体形式和社会环境对SNARC效应的影响.实验一要求被试双手完成奇偶判断任务,结果出现了经典的SNARC效应.实验二要求被试完成Go/No-go任务,并让被试单手(左手或右手)对奇数或偶数进行反应,结果SNARC效应没有出现,这表明认知主体的身体形式对SNARC效应产生了影响.实验三要求被试合作完成Go/No-go任务,该实验按照被试所坐的位置(左边和右边)和反应手(左手和右手),设计了四个条件,结果只有身体位置和反应手完全一致时出现了 SNARC 效应.以上结果一方面表明了具身认知观的合理性,另外一方面扩展了以往对SNARC效应本质的理解.