儿童数量表征与数概念的发展特点及机制

对儿童数量表征和数概念的研究是当前数认知领域的两个重点研究方向。我们在这一领域通过理论及实证研究进行了广泛且深入的探索,系统分析了大小数量、符号与非符号数量表征的机制,深入考察了数量表征线索的发展、线性数量表征的发展特点及形成机制等问题;并对数概念的发展及其影响机制、数量表征与数概念的关系进行了理论梳理和实证研究。这些探索为进一步探明数量表征与数概念的发展特点及机制提供了基础。     

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。     

抽象概念表征的具身认知观

抽象概念是否通过感知经验来表征以及如何被感知经验表征是具身认知面临的一大问题.在抽象概念表征是否具有感知经验基础的问题上,具身认知理论认为抽象概念通过情境模拟或隐喻与感知经验发生联系.在抽象概念如何与感知经验表征发生联系的问题上,概念模拟理论强调情景或运动模拟在抽象概念表征中的直接作用;概念隐喻理论则侧重具体经验或具体经验与抽象概念之间的共同结构关系在抽象概念表征中的间接作用.未来研究应改变概念表征的稳定的心理实体观,从语言和抽象表征的关系、正常儿童和特殊群体的抽象概念表征差异入手,整合不同的具身认知观点.     

感知运动信息在概念表征中的作用

研究概念的表征问题对理解概念的本质非常重要,传统认知和具身认知视角下的概念表征理论争议的焦点在于感觉运动信息在表征中的作用。传统认知视角下的离身认知认为感知觉运动信息会转化成抽象的符号,概念表征不包含感知觉运动信息。概念表征的具身观点认为感知觉运动信息是概念表征的基础。对感知运动信息在概念表征中起作用这一命题已经达成共识。未来研究应该关注感知运动信息起作用的机制,以及抽象概念表征等问题,进一步完善发展概念表征理论。     

中小学数学教师数感内隐观的调查研究

该研究以131名中小学数学教师为被试,采用调查分析的方法,编制了数感结构选项表,考察了中小学数学教师的数感结构内隐观。结果显示：中小学数学教师的数感结构内隐观所涉及的范围广泛,经因素分析可以把它概括为6个因素。它们分别是：数学运算、数学认知因素、非书面计算能力、理解数与运算的意义、对数的认识与直觉、数符号表征能力。     

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。     

4-6岁儿童数学认知中的多元表征研究

本研究以早期儿童数学认知中的数、数运算以及模式三个维度为切入点,对来自上海市的120名4-6岁儿童采用个别面试法考察其数学认知中的多元表征,采用描述性统计、多元方差分析、卡方检验等方法探查儿童多元表征的发展特点、相互关系及影响因素。结果表明：4-6岁儿童已具备初步的数、数运算、模式的多元表征能力,其中数的多元表征能力最好;4-6岁儿童在数、模式的多元表征中未出现明显的年龄差异与性别差异,在数运算多元表征中有明显的年龄差异,无性别差异;儿童使用的表征形式数量随年龄增长相应增加,且更倾向于使用描绘性表征中的实物情境表征与教具模型表征;4-6岁儿童数、数运算、模式的多元表征能力之间存在一定的相关;除年龄之外,已有学习经验、学习材料的呈现样式也是影响儿童多元表征的可能性因素。     

语义表征具身理论:情绪在概念表征中的作用

概念如何被表征是认知科学的热点问题,其中抽象概念如何表征是当前具身认知最具争议性的话题之一。与前期概念隐喻理论(强调意象图式)和知觉符号理论(强调情境内省信息)的观点不同,语义表征具身理论强调情绪经验信息在抽象概念表征和加工中的作用。具体而言,具体概念的表征主要来自感觉运动信息,而抽象概念的表征主要来自情绪经验信息和语言信息。研究证明,抽象概念的高情绪经验信息能够促进词汇的加工,且这一促进作用受词汇情绪效价的调节。未来研究应进一步考虑影响情绪经验信息发挥作用的因素,比如语言信息的丰富性、情绪唤醒或个体的情绪状态等。     

生成认知与具身机能主义的比较——表征的取舍

在具身认知不同的思潮中,生成认知以其激进的观点反对表征和计算主义,可以称之为是具身认知思潮中的最为激进的一部分。另一方面,由于标准认知中表征和计算的解释力和影响力,具身认知诞生出各种不同程度上的“妥协”性理论,其中,以克拉克为代表的具身的“机能主义”为目前具身认知的主流观点。表征尽管在当前阶段中表现出强大的生命力,但依然无法在所有领域中都得到运用。随着表征的改造与发展,未来的激进具身认知工作者应该将更多的精力投入到具身认知与更多学科的融合研究中。     

适应性表征:架构自然认知与人工认知的统一范畴

作为一门新兴交叉学科,认知科学目前业已发展出计算表征、联结网络和动态耦合说明等研究理论,以及具身认知、嵌入认知、延展认知、生成认知和情境认知等研究纲领。是否存在一种可以统摄这些不同认知理论和纲领的统一范畴或概念框架,这是迄今为止认知科学及其哲学面临的关键性难题。"适应性表征"概念似乎具有统摄各种认知理论和纲领的共通性,能够为复杂的认知现象提供一种方法论,能够合理地说明认知在语境中的形成与演化机制。原因在于,刻画认知的计算、表征、联结、耦合、具身、嵌入、延展、生成、情景化等概念均是语境依赖的,即是在特定语境中对认知现象的不同方面的描述。这种依赖语境的认知说明它们在本质上是适应性表征。     

Numerical ordering ability mediates the relation between number-sense and arithmetic competence

What predicts human mathematical competence? While detailed models of number representation in the brain have been developed, it remains to be seen exactly how basic number representations link to higher math abilities. We propose that representation of ordinal associations between numerical symbols is one important factor that underpins this link. We show that individual variability in symbolic number-ordering ability strongly predicts performance on complex mental-arithmetic tasks even when controlling for several competing factors, including approximate number acuity. Crucially, symbolic number-ordering ability fully mediates the previously reported relation between approximate number acuity and more complex mathematical skills, suggesting that symbolic number-ordering may be a stepping stone from approximate number representation to mathematical competence. These results are important for understanding how evolution has interacted with culture to generate complex representations of abstract numerical relationships. Moreover, the finding that symbolic number-ordering ability links approximate number acuity and complex math skills carries implications for designing math-education curricula and identifying reliable markers of math performance during schooling.     

Mathematical symbols as epistemic actions

Recent experimental evidence from developmental psychology and cognitive neuroscience indicates that humans are equipped with unlearned elementary mathematical skills. However, formal mathematics has properties that cannot be reduced to these elementary cognitive capacities. The question then arises how human beings cognitively deal with more advanced mathematical ideas. This paper draws on the extended mind thesis to suggest that mathematical symbols enable us to delegate some mathematical operations to the external environment. In this view, mathematical symbols are not only used to express mathematical concepts??they are constitutive of the mathematical concepts themselves. Mathematical symbols are epistemic actions, because they enable us to represent concepts that are literally unthinkable with our bare brains. Using case-studies from the history of mathematics and from educational psychology, we argue for an intimate relationship between mathematical symbols and mathematical cognition.     

Representation and cognitive science

‘Representation’ is a concept which occurs both in cognitive science and philosophy. It has common features in both settings in that it concerns the explanation of behaviour in terms of the way the subject categorizes and systematizes responses to its environment. The prevailing model sees representations as causally structured entities correlated on the one hand with elements in a natural language and on the other with clearly identifiable items in the world. This leads to an analysis of representation and cognition in terms of formal symbols and their relations. But human perception and cognition use multiple informational constraints and deal with unsystematic and messy input in a way best explained by Parallel Distributed Processing models. This undermines the claim that a formal representational theory of mind is ‘the only game in town’. In particular it suggests a radically different model of brain function and its relation to epistemology from that found in current representational theories.     

近似数量系统敏锐度与数学能力的关系

近年来,来自认知发展、比较认知、跨文化认知和神经生物学的研究证据都表明近似数量系统的存在,并且相较于一般认知能力,它更可能是决定个体数学能力差异最为重要的因素。本文综述了有关近似数量系统敏锐度与数学能力相互关系的横断研究、纵向研究、训练研究及认知神经科学的研究成果,分析了影响二者关系的因素,包括个体年龄、数学能力高低、抑制控制等,并总结了多种理论对二者间显著正相关关系的解释。未来研究需要在确定更具信效度的测量范式的基础上探讨近似数量系统与数学能力各维度的关系,以及这种相互关系背后的原因,并将研究结论运用于数学教学及计算障碍个体的干预。     

Being Human: Experiencing and Communicating

Haye’s article Living being and speaking being highlights a confusion that the traditional cognitive science has been making between cognition and representation, reducing semantics (meaning) to the syntax (computation with symbols). This traditional view cannot fully grasp the dependence of meaning on the relational context, opening space for the need to take into account the Bakhtinian notions of responsivity and addressivity to an other as defining features of the communicational social act. Socialized signs are conceived here as central tools to our relation to the world and to the others. We pursue some of the implications of this radical dialogical commitment specifying their implications to an ontological level of human beings: relationships are the ground for the depiction of human beings and otherness as a necessary complementarity of our own existence.     

两种数量表征系统

数量表征是人类数学能力的基础,数量表征研究中的一个争论焦点在于是否存在两种不同的数量表征系统：对小数的精确表征系统和对大数的近似表征系统。通过综述不同研究领域对数量表征的研究,总结了支持两种表征系统分离的证据：对1~3范围内小数的表征受数量大小的限制,基于指向物体本身的注意,更依赖于物体的知觉特征,对物体及其数量进行精确表征;而对4以上的数量的近似表征系统则受韦伯定律的限制,基于指向数量的模拟幅度的表征,而不依赖单个物体的知觉特征,是对数量的近似的、心理的表征。fMRI、PET和ERP的脑成像研究结果迄今尚无定论,但认知神经科学研究的深入开展将最终阐明数量表征的机制     

Varieties of numerical abilities.

This paper provides a tutorial introduction to numerical cognition, with a review of essential findings and current points of debate. A tacit hypothesis in cognitive arithmetic is that numerical abilities derive from human linguistic competence. One aim of this special issue is to confront this hypothesis with current knowledge of number representations in animals, infants, normal and gifted adults, and brain-lesioned patients. First, the historical evolution of number notations is presented, together with the mental processes for calculating and transcoding from one notation to another. While these domains are well described by formal symbol-processing models, this paper argues that such is not the case for two other domains of numerical competence: quantification and approximation. The evidence for counting, subitizing and numerosity estimation in infants, children, adults and animals is critically examined. Data are also presented which suggest a specialization for processing approximate numerical quantities in animals and humans. A synthesis of these findings is proposed in the form of a triple-code model, which assumes that numbers are mentally manipulated in an arabic, verbal or analogical magnitude code depending on the requested mental operation. Only the analogical magnitude representation seems available to animals and preverbal infants.     

Representation recovers information

Early agreement within cognitive science on the topic of representation has now given way to a combination of positions. Some question the significance of representation in cognition. Others continue to argue in favor, but the case has not been demonstrated in any formal way. The present paper sets out a framework in which the value of representation use can be mathematically measured, albeit in a broadly sensory context rather than a specifically cognitive one. Key to the approach is the use of Bayesian networks for modeling the distal dimension of sensory processes. More relevant to cognitive science is the theoretical result obtained, which is that a certain type of representational architecture is necessary for achievement of sensory efficiency. While exhibiting few of the characteristics of traditional, symbolic encoding, this architecture corresponds quite closely to the forms of embedded representation now being explored in some embedded/embodied approaches. It becomes meaningful to view that type of representation use as a form of information recovery. A formal basis then exists for viewing representation not so much as the substrate of reasoning and thought, but rather as a general medium for efficient, interpretive processing.     

Symbolic Representation by Pigeons

The capacity for symbolic representation is a prerequisite for the development of human language because words, the basic units of language, are symbols that represent things. But symbolic representation may also serve a nonlinguistic role of organizing events into categories having the same meaning, and such a capacity could have considerable survival value for many species. In a number of experiments, my co-workers and I have found that pigeons that are trained to treat two different stimuli similarly also learn that those stimuli are commonly represented and, thus, that they have the same meaning. We have demonstrated evidence for such common representations in a number of ways, but perhaps the most convincing is when pigeons learn a new association involving one of the presumed commonly represented stimuli, and without further training demonstrate that they have learned a similar association involving the other stimulus. Furthermore, we have found that when pigeons are trained to treat two stimuli similarly, one of those stimuli is represented in terms of the other. These results have implications not only for the generality of cognitive processes across species, but also for the generality of symbolic representation beyond language use.     

Does finger sense predict addition performance?

The impact of fingers on numerical and mathematical cognition has received a great deal of attention recently. However, the precise role that fingers play in numerical cognition is unknown. The current study explores the relationship between finger sense, arithmetic and general cognitive ability. Seventy-six children between the ages of 5 and 12 participated in the study. The results of stepwise multiple regression analyses demonstrated that while general cognitive ability including language processing was a predictor of addition performance, finger sense was not. The impact of age on the relationship between finger sense, and addition was further examined. The participants were separated into two groups based on age. The results showed that finger gnosia score impacted addition performance in the older group but not the younger group. These results appear to support the hypothesis that fingers provide a scaffold for calculation and that if that scaffold is not properly built, it has continued differential consequences to mathematical cognition.