从数量表征到数表征：具身认知视角下的人类数能力获得

数能力是数学认知的基本成分。与动物所具有的基本数能力不同,人类不仅具备数量表征能力,更重要的是还拥有对数概念进行表征的数表征能力。虽然具身认知与离身认知都对数概念的表征问题进行了解释,但二者却存在明显理论分歧。具身认知观点主要从具身数量表征和数能力发展的具身认知机制两方面为人类独特数能力的获得提供了理论支撑及实证证据。这启示人们需要重视具身学习在数能力形成实践中的关键作用,重视具身数量表征在数学教学中的作用,仍需进一步揭示其内在的心理和神经基础。     

数量表征的符号特异性和符号非特异性

数量表征(numerical representation)指与特定数量相联系的心理表征。长期以来抽象的数量表征假说占据主导地位, 但随着自动化加工范式和脑成像技术的发展, 数量表征存在符号特异性的证据已不断涌现。其中, 最近有两个理论认为数量表征可能同时存在符号特异性和符号非特异性。计算的模型假说提出非符号数量和符号数字在总和编码阶段具有符号特异性, 而在之后的位置编码阶段具有符号非特异性。双重编码的延伸假说则认为数量表征在自动编码阶段具有符号特异性, 然后在有意编码阶段, 受任务要求影响, 数量表征向实时的抽象表征过渡。已有大量行为和神经基础研究为以上假说提供了证据, 但数量表征动态变化的内在机制和脑区还有待探索, 未来应该在发展、跨文化、自动加工范式与神经成像相结合、单细胞记录技术等方向继续开展数量表征研究。     

4～5岁儿童对书面数符号的表征和理解能力的发展

本研究对61名中班儿童的书面数符号表征和理解能力进行了跟踪调查。一年中三次个别面试的结果表明,约40％的4岁儿童已能运用1—10的书面数符号表征数量。至中班末期,大多数5岁儿童能够较熟练地运用至少1一17的书面数符号来表征数量,尽管其中有人在两位数的表征和数字的正确写法上有困难。儿童的书面数符号表征与他们的基数概念发展水平密切相关。大学附属幼儿园4—5岁儿童的书面数符号表征能力好于为工人家庭服务的幼儿园儿童的能力。     

多元表征假设：概念表征机制的新观点

传统的认知主义认为概念表征是与主体的感知系统无关的抽象符号。而具身理论则认为,概念表征以主体的感觉、知觉运动系统为基础的,感知系统在概念表征中具有中心作用。然而,具身性假设无法恰当的解释抽象概念表征这一问题。这种局限性说明主体的概念系统可能具有多元表征机制：既包括感知表征以加工与身体经验相关的具体知识,也包括抽象符号表征以加工与身体经验无关的抽象知识。来自病理学、认知神经科学和行为实验的实证研究证明了不同类型的概念会涉及不同的表征机制,证实了多元表征存在的合理性。今后的研究应探讨各种表征机制之间的关系等问题。     

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。     

具身概念表征的研究及理论述评

具身认知强调认知在本质上是具身的, 身体在认知的实现中发挥着关键作用。传统的符号加工理论认为, 概念表征独立于主体的知觉运动系统并以抽象符号的形式储存于语言记忆中。概念表征的具身理论则认为, 概念表征与知觉运动系统具有共同的神经基础, 概念在本质上是主体经验客体时知觉与运动体验的神经记录, 而概念加工的基本形式则是身体经验的模拟与还原。关于该理论的实证研究主要集中于概念加工引发的知觉动作变化、身体动作对概念加工的影响、抽象概念加工的具身特征等领域。今后的研究应关注符号加工理论与具身理论的整合等。     

知觉符号理论及其研究范式

知觉符号理论是第二代认知科学的核心理论之一, 研究者采用多种实验范式、在各个领域对该理论进行了探讨。分析以往的研究发现, 大量的研究主要探讨语言表征、概念获得、具身情绪、推理过程、社会认知和知觉符号发展等科学问题。本文对此领域的发展进行了简要梳理, 特别是以实验范式发展为主线详细介绍了知觉符号理论的发展, 并在此基础上提出了多元表征的思考。最后, 对知觉符号理论的发展提出了展望。     

手指的感知、运动以及数量表征对数字认知的促进作用

手指是儿童在习得数字符号之前最常使用的表征数量的工具,大量研究都表明手指在数字认知中具有促进作用。但是,目前仍不清楚手指在数字认知中的作用机制。综述从手指感知、手指运动以及手指数量表征三个方面总结了手指在数字认知中所起的作用。手指感知可能通过影响儿童的数量表征能力间接地影响其它数学能力;与表征量有关的手指运动可能促进了数量大小的加工。关于手指数量表征在数字认知中的作用存在两种有争议的观点：一种认为手指数量表征促进了儿童由非符号数量表征向符号数量表征的转化;另一种认为手指数量表征可能是一种数量语义表征方式。未来应该在发展、作用机制、性别差异等方向继续开展研究,进一步探讨手指在数字认知中所起的作用。     

情境模型的实质：命题符号与知觉符号之争

阅读理解中情境模型的建构是当今阅读研究的热点。传统命题符号理论认为情境模型是组相关命题,是非模式符号系统;随着知识表征理论的发展,知觉符号理论认为情境模型的建构包括模式符号系统,即含有知觉符号。文章对比了两种理论对情境模型的不同解释,并介绍了相关的实证研究,最后对未来验证两种理论的研究方向进行了展望。     

5～6岁儿童对书面数符号的表征和理解能力的发展

本研究对54名大班儿童的书面数符号表征和理解能力进行了跟踪调查。一年中三次面试结果表明,约85%的儿童(M=5:10)能运用书面数符号来表征30个以上的物体的数量。至大班末,94%的儿童(M=6:4)能运用书面数符号来表征100个以上物体的数量。大班末儿童对20以内书面加法运算成绩好于20以上书面减法运算,他们在遇到需进位和借数的加减运算时会有困难。6岁儿童在对加减运算式表征中的符号-实物的转换上有困难,儿童书面数符号表征、书面加减运算及对书面加减运算式的表征之间有显著正相关。大学附属幼儿园儿童的书面数符号表征能力在大班上学期好于为一般居民服务的幼儿园儿童,但无显著差异;在大班末期,为一般居民服务的幼儿园儿童的得分反超大学附属幼儿园儿童的得分,但无显著差异。     

Learning and development of embodied numerosity

Recent empirical evidence indicates that seemingly abstract numerical cognitions are rooted in sensory and bodily experiences. In particular in finger counting finger-based representations reflect a specific case of embodied cognition, we termed embodied numerosity. Furthermore, we suggest that finger-based representations should be considered a distinct representation of number (magnitude) and argue that this representation is activated automatically whenever we encounter a number. We discuss in what way such a theoretical framework can account for the associations of fingers and numbers observed so far. In the final part, we evaluate whether the concept of embodied numerosity should be generalized beyond finger-based representations with particular focus on whether bodily-sensory experiences (such as moving the whole body along the mental number line) may corroborate numerical capabilities. In a series of intervention studies, we consistently observed more pronounced training effects for our embodied numerosity trainings for different age groups, different digital media, different number ranges, and different control conditions. Taken together, we conclude that embodied representations of number (magnitude) exist, are not limited to finger-based representations, and influence number processing in a systematic and functional way that can be used to foster the efficiency of numerical trainings.     

Two-digit number processing: holistic,decomposed or hybrid? A computational modelling approach

Currently, there are three competing theoretical accounts concerning the nature of two-digit number magnitude representation: a holistic, a strictly decomposed, and a hybrid model. Observation of the unit-decade compatibility effect (Nuerk et al. in Cognition 82:B25–B33, 2001) challenged the view of two-digit number magnitude to be represented as one integrated entity. However, at the moment there is no study distinguishing between the decomposed and the hybrid model. The present study addressed this issue using a computational modelling approach. Three network models complying with the constraints of all three theoretical models were programmed and trained on two-digit number comparison. Models were compared as to how well they accounted for empirical effects in the most parsimonious way. Generally, this evaluation indicated that the empirical data were simulated best by the strictly decomposed model. Implications of these results for our understanding of the nature of human number magnitude representation are discussed.     

Resilience in the Workplace: A Multilevel Review and Synthesis

In an increasingly dynamic business environment, the concept of resilience is fundamental to understanding how employees successfully handle adversity. Yet, the operationalisation of the concept, the factors which lead to its development, and how and why it influences outcomes of interest to organisations are issues still under debate in the literature. In this article, we address these debates by undertaking a critical review of research on resilience in the workplace at both the individual and team levels. We pinpoint different conceptualisations of resilience and highlight how resilience has been measured in extant quantitative work. Further, we provide a systematic literature review of empirical work on the antecedents and outcomes of resilience at the individual and team levels, as well as conduct a review of work that has introduced resilience as a moderator or mediator. In doing so, we highlight theoretical approaches that have been adopted to study resilience in the workplace. Based on our review of the extant empirical work on resilience, we develop a roadmap for future research. In particular, we pinpoint relevant theoretical approaches that help us understand the mechanisms underlying the development and outcomes of resilience and highlight opportunities for empirical advancement of the literature.     

3~5岁幼儿一位数大小比较的信息加工模式

主要探讨我国幼儿对数量大小比较的信息加工模式。实验1探讨幼儿对一位数大小比较的发展状况及其心理表征特点,被试为3岁、4岁与5岁幼儿各20人,要求被试对1-9两两进行大小比较,然后对不同年龄幼儿对比成绩进行比较与聚类分析。实验2进一步探讨幼儿对数字的语义编码情况及其与数的大小比较的关系,被试与实验1相同,要求被试对1-9每个数字作出大、中或小的编码,然后分析数字的语义编码成绩与大小比较成绩的关系。实验3采用因果设计,探讨幼儿关于数字的语义编码对他们关于数的大小判断的影响,被试为30名4岁幼儿,随机分成训练组与控制组,对训练组被试进行数字语义编码训练,然后比较两组被试大小比较的成绩。结果表明：(1)幼儿一位数大小比较直接受其对数的语义表征的影响;(2)随着年龄的增长,幼儿对数的表征逐步表现出离散聚类模式,相应地,对一位数大小比较的信息加工过程就表现为由无序的、随机的过程逐步发展成为层次编码比较的过程。     

Social interaction and cognitive growth: Possible causal mechanisms

The causal role of social interaction in the promotion of cognitive development has recently emerged as an important issue in developmental psychology. Two dominant theoretical orientations are currently guiding the empirical studies. The Piagetian perspective has influenced studies conducted to measure operational advances in cognitive functioning as a result of conflict between children. Vygotsky's developmental framework has provoked interest in the ontogenesis of self-regulatory abilities in children through an analysis of social problem solving. Both seek to explain cognitive development through social processes. Theoretical and empirical links between the two approaches are explored, and the possible role of linguistic processes as causal mechanisms examined.     

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。     

4~8年级学生分数数量表征的准确性及形式

在分数学习中,分数数量表征是非常重要的方面。本研究利用数字线估计任务对四到八年级学生分数数量表征的情况进行探索。研究结果表明：随着年级升高,被试分数数量表征的准确性也随之提高;被试对单位分数和非单位分数表征的准确性存在显著差异,表现为对单位分数表征的准确性显著高于对非单位分数的表征,这种差异在低年级显著,随着年级的增长,差异逐渐消失;四到八年级学生在0~3数字线上,对分数数量的表征表现为线性形式而非对数形式,且这种线性表征形式是在六年级开始出现并随着年龄增长逐渐发展起来的。中西方儿童在分数数量表征的准确性和形式上有相似的发展路径,但是在表征准确性上中国儿童更高、线性形式出现年级上中国儿童可能更早。     

The development of numerosity estimation: Evidence for a linear number representation early in life

Several studies investigating the development of approximate number representations used the number-to-position task and reported evidence for a shift from a logarithmic to a linear representation of numerical magnitude with increasing age. However, this interpretation as well as the number-to-position method itself has been questioned recently. The current study tested 5- and 8-year-old children on a newly established numerosity production task to examine developmental changes in number representations and to test the idea of a representational shift. Modelling of the children's numerical estimations revealed that responses of the 8-year-old children approximate a simple positive linear relation between estimated and actual numbers. Interestingly, however, the estimations of the 5-year-old children were best described by a bilinear model reflecting a relatively accurate linear representation of small numbers and no apparent magnitude knowledge for large numbers. Taken together, our findings provide no support for a shift of mental representations from a logarithmic to a linear metric but rather suggest that the range of number words which are appropriately conceptualised and represented by linear analogue magnitude codes expands during development.     

Relationships between number and space processing in adults with and without dyscalculia

A large body of evidence indicates clear relationships between number and space processing in healthy and brain-damaged adults, as well as in children. The present paper addressed this issue regarding atypical math development. Adults with a diagnosis of dyscalculia (DYS) during childhood were compared to adults with average or high abilities in mathematics across two bisection tasks. Participants were presented with Arabic number triplets and had to judge either the number magnitude or the spatial location of the middle number relative to the two outer numbers. For the numerical judgment, adults with DYS were slower than both groups of control peers. They were also more strongly affected by the factors related to number magnitude such as the range of the triplets or the distance between the middle number and the real arithmetical mean. By contrast, adults with DYS were as accurate and fast as adults who never experienced math disability when they had to make a spatial judgment. Moreover, number–space congruency affected performance similarly in the three experimental groups. These findings support the hypothesis of a deficit of number magnitude representation in DYS with a relative preservation of some spatial mechanisms in DYS. Results are discussed in terms of direct and indirect number–space interactions.