Cross-notational semantic priming between symbolic and nonsymbolic numerosity

Symbolic and nonsymbolic numerosities produce similar behavioural effects and activate the same brain areas. These results have usually been interpreted in terms of a common, notation-independent magnitude representation. However, semantic priming between symbolic and nonsymbolic inputs has been somehow elusive (e.g., Koechlin, Naccache, Block, & Dehaene, 1999 Koechlin, E., Naccache, L., Block, E. and Dehaene, S. 1999. Primed numbers: Exploring the modularity of numerical representations with masked and unmasked semantic priming. Journal of Experimental Psychology: Human Perception and Performance, 25: 1882–1905. [Crossref], [Web of Science ®] , [Google Scholar]). In Experiment 1, we looked at whether cross-notational semantic priming depends on exact numerical meaning. Dice faces and digits were mixed as prime and target. Semantic priming occurred when prime and target were in the same notation as much as when they were in different notation. In Experiment 2, we found cross-notation semantic priming even when the nonsymbolic numerosity was presented as a set of random dots. Priming, however, occurred only from sets of dots to digit, not vice versa. These data support the computational model recently proposed by Verguts and Fias (2004 Verguts, T. and Fias, W. 2004. Representation of number in animals and humans: A neural model. Journal of Cognitive Neuroscience, 16: 1493–1504. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; Verguts, Fias, & Stevens, 2005 Verguts, T., Fias, W. and Stevens, M. 2005. A model of exact small-number representation. Psychonomic Bulletin & Review, 112: 66–80.  [Google Scholar]).     

非符号数量表征和符号分数表征的关系

个体学习符号分数的一个关键是能对其数值形成准确表征。现有研究假设符号分数表征的认知基础是人类自婴幼儿期就具有的非符号数量表征(如表征两个集合各自的数量, 或两个数量的比例)。其证据包括表征非符号数量(尤其是非符号数量比例关系)和表征符号分数在行为和大脑神经活动层面上都表现出相关性。然而要说明非符号数量表征是符号分数表征的认知基础, 还需更多研究表明两者在数量概念上的独特相关和因果联系, 并阐明符号分数表征形成的认知机制。     

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.     

Children’s representation of symbolic magnitude: The development of the priming distance effect

The comparison distance effect (CDE), whereby discriminating between two numbers that are far apart is easier than discriminating between two numbers that are close, has been considered as an important indicator of how people represent magnitudes internally. However, the underlying mechanism of this CDE is still unclear. We tried to shed further light on how people represent magnitudes by using priming. Adults have been shown to exhibit a priming distance effect (PDE), whereby numbers are processed faster when they are preceded by a close number than when they are preceded by a more distant number. Surprisingly, there are no studies available that have investigated this effect in children. The current study examined this effect in typically developing first, third, and fifth graders and in adults. Our findings revealed that the PDE already occurs in first graders and remains stable across development. This study also documents the usefulness of number priming in children, making it an interesting tool for future research.     

Basic numerical skills in children with mathematics learning disabilities: a comparison of symbolic vs non-symbolic number magnitude processing

Forty-five children with mathematics learning disabilities, with and without comorbid reading disabilities, were compared to 45 normally achieving peers in tasks assessing basic numerical skills. Children with mathematics disabilities were only impaired when comparing Arabic digits (i.e., symbolic number magnitude) but not when comparing collections (i.e., non-symbolic number magnitude). Moreover, they automatically processed number magnitude when comparing the physical size of Arabic digits in an Stroop paradigm adapted for processing speed differences. Finally, no evidence was found for differential patterns of performance between MD and MD/RD children in these tasks. These findings suggest that children with mathematics learning disabilities have difficulty in accessing number magnitude from symbols rather than in processing numerosity per se.     

Children’s mapping between symbolic and nonsymbolic representations of number

When children learn to count and acquire a symbolic system for representing numbers, they map these symbols onto a preexisting system involving approximate nonsymbolic representations of quantity. Little is known about this mapping process, how it develops, and its role in the performance of formal mathematics. Using a novel task to assess children’s mapping ability, we show that children can map in both directions between symbolic and nonsymbolic numerical representations and that this ability develops between 6 and 8 years of age. Moreover, we reveal that children’s mapping ability is related to their achievement on tests of school mathematics over and above the variance accounted for by standard symbolic and nonsymbolic numerical tasks. These findings support the proposal that underlying nonsymbolic representations play a role in children’s mathematical development.     

Horses (Equus caballus) select the greater of two quantities in small numerical contrasts

The ability to select the greater numerosity over another in small sets seems to stem from the calculation of which set contains more, and has been taken as evidence of a primordial representation at the roots of the primate numerical system. We tested 56 horses (Equus caballus) in a paradigm previously used with human infants and nonhuman primates. Horses saw two quantities paired in contrasts—2 versus 1, 3 versus 2, 6 versus 4 and a control for volume, 2 versus 1 big—and had to make a choice by snout touching the container holding the numerosity selected. The horses spontaneously selected the greater of the two quantities when the numerosities were small. These results add to evidence showing spontaneous quantity assessment in a variety of species. To my brother Marcelo Uller (1964–2008), for whom the understanding of animals, through biomimetics, was the only way to understand man-made engineering.     

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.     

The relationship between non-symbolic multiplication and division in childhood

Children without formal education in addition and subtraction are able to perform multi-step operations over an approximate number of objects. Further, their performance improves when solving approximate (but not exact) addition and subtraction problems that allow for inversion as a shortcut (e.g., a?+?b???b?=?a). The current study examines children's ability to perform multi-step operations, and the potential for an inversion benefit, for the operations of approximate, non-symbolic multiplication and division. Children were trained to compute a multiplication and division scaling factor (*2 or /2, *4 or /4), and were then tested on problems that combined two of these factors in a way that either allowed for an inversion shortcut (e.g., 8*4/4) or did not (e.g., 8*4/2). Children's performance was significantly better than chance for all scaling factors during training, and they successfully computed the outcomes of the multi-step testing problems. They did not exhibit a performance benefit for problems with the a*b/b structure, suggesting that they did not draw upon inversion reasoning as a logical shortcut to help them solve the multi-step test problems.     

科学创造力与艺术创造力:启动效应及领域影响

如何有效地提升创造力,是创造力研究和实践领域的核心问题之一.而对创造力表达及其影响机制的把握则是创造力提升的必要前提.本研究计划通过实施科学创造力及艺术创造力的启动实验,以不同专业大学生为被试,来探索科学创造力和艺术创造力表达的个体心理机制,及外部影响的作用模式,从而厘清在动机启动、样例启动和自我启动之间,究竟何种启动模式对创造力的表达最为有效;进而,通过对来自理工科和艺术专业领域评分者对科学创造力及艺术创造力作品的评分比较,来考查两种创造力模式间可能存在的领域影响.经由以上的探究,试图为科学与艺术创造力的发展与促进提供科学依据和建构理论框架.     

听觉呈现条件下汉语双字词语义和语音启动的ERP研究

在词汇决定实验中研究语义启动和语音启动,材料为通过听觉呈现的汉语双字词组成的词对(间隔600ms),记录行为数据和ERP数据,结果发现：(1)启动词与目标词之间的语义联系可显著改善对目标词的加工,表现为错误率降低、反应时缩短,以及N400波幅降低;(2)启动词与目标词之间的语音一致对目标词的加工既有干扰作用,又有促进作用。表现为错误率提高,但反应时趋向缩短,N400波幅亦呈下降趋势;(3)启动词与目标词首音相同比尾音相同有更大的干扰作用。     

Comparative judgments of symbolic and non-symbolic stimuli yield different patterns of reaction times

Are different magnitudes, such as Arabic numerals, length and area, processed by the same system? Answering this question can shed light on the building blocks of our mathematical abilities. A shared representation theory suggested that discriminability of all magnitudes complies with Weber's law. The current work examined this suggestion. We employed comparative judgment tasks to investigate different types of comparisons — conceptual comparison of numbers, physical comparison of numbers and physical comparison of different shapes. We used 8 different size ratios and plotted reaction time as a function of these ratios. Our findings suggest that the relationship between discriminability and size ratio is not always linear, as previously suggested; rather, it is modulated by the type of comparison and the type of stimuli. Hence, we suggest that the representation of magnitude is not as rigid as previously suggested; it changes as a function of task demands and familiarity with the compared stimuli.     

词汇的语义表征及其启动效应研究现状与问题

语义启动是研究语义表征的主要范式。在过去的30年里,通过对语义启动效应的研究,词汇的语义表征理论也从符号联结发展到神经联结,其影响因素也逐步重视多方面的交互作用。究其问题,已有研究还存在很多不一致的结论,对语义内在的表征机制和学习机制缺乏深入了解,对影响语义表征的个体因素考虑不多。     

A matter of design: Priming context and person perception

A matter of considerable debate is whether people spontaneously use categorical knowledge (i.e., stereotypes) to guide their interactions with others. Despite initial evidence for the unconditional automaticity of category activation, recent research has identified a range of factors that moderate this process. Extending this line of inquiry, the current investigation explored the extent to which contextual influences—specifically the order in which priming stimuli are presented to participants—may modulate person categorization. Using a standard semantic-priming paradigm to index category and stereotype activation, participants were presented with priming stimuli that were either intermixed or blocked by sex. The results revealed that: (i) category and stereotype activation are moderated by the order in which priming stimuli are presented; and (ii) priming effects decrease monotonically as a function of category repetition. The theoretical implications of these findings are considered.     

Production and Identification Repetition Priming in AmnesticMild Cognitive Impairment

ABSTRACT

The experiment reported here examined implicit memory function, as measured through repetition priming, in amnestic mild cognitive impairment (MCI) to examine whether impairments exist in this aspect of memory function. Young adults, healthy older controls, Alzheimer's disease patients, and MCI participants were asked to perform two types of implicit memory tests (word stem completion and threshold identification repetition priming tasks), as well as a recognition test for studied items. As expected, young adults performed better than the other participants on the recognition test and the word stem completion task; there was equivalent priming across groups on the word identification task. While both the older control and MCI participants showed lower levels of priming on the word stem completion task relative to the young adults, the magnitude of priming was equivalent for these two groups, and reliably greater than that of the dementia participants. These results suggest that not all aspects of memory function are impaired in MCI relative to healthy aging.     

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.     

Modes of spatial coding in the Simon task*

Many models of the Simon effect assume that categorical spatial representations underlie the phenomenon. The present study tested this assumption explicitly in two experiments, both of which involved eight possible spatial positions of imperative stimuli arranged horizontally on the screen. In Experiment 1, the eight stimulus locations were marked with eight square boxes that appeared at the same time during a trial. Results showed gradually increasing Simon effects from the central locations to the outer locations. In Experiment 2, the eight stimulus locations consisted of a combination of three frames of spatial reference (hemispace, hemifield, and position relative to the fixation), with each frame appearing in different timings. In contrast to Experiment 1, results showed an oscillating pattern of the Simon effect across the horizontal positions. These findings are discussed in terms of grouping factors involved in the Simon task. The locations seem to be coded as a single continuous dimension when all are visible at once as in Experiment 1, but they are represented as a combination of the lateral categories (“left” vs. “right”) with multiple frames of reference when the reference frames are presented successively as in Experiment 2.     

The Effect of Feedback Schedule Manipulation on Speech Priming Patterns and Reaction Time

Speech priming tasks are frequently used to delineate stages in the speech process such as lexical retrieval and motor programming. These tasks, often measured in reaction time (RT), require fast and accurate responses, reflecting maximized participant performance, to result in robust priming effects. Encouraging speed and accuracy in responding can take many forms, including verbal instructions and feedback, and often involves visually displayed RT feedback. However, it is uncertain how manipulation of the schedule of this RT feedback influences speech RT speed and, ultimately, the priming effect. This experiment examined the effect of visually presented RT feedback schedules on priming patterns in 20 older healthy adults. Results suggested that feedback schedule manipulation had a differential effect on reaction time, depending on the interstimulus interval between the prime and the target, but no effect on response priming patterns.