人类数能力的演化基础——数能力比较研究的启示

人类的数能力可以发展到很高的抽象水平,但大量研究表明,人类婴儿和非人灵长类也具有基本的数表征和数推理能力。文章从表征内容和表征形式两个方面系统地比较了人类婴儿和非人灵长类的数能力,并对比了成人和非人灵长类数表征的生理基础。人类和非人灵长类在这三方面存在的相似性揭示了他们可能享有相同的数表征系统。在今后的研究中,进一步探讨这两者相似的数表征核心系统,可以加深我们对人类数能力起源和本质的理解     

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。     

不同手指表征方式对数量表征能力的影响

采用距离启动范式,考察中国文化背景下不同手指表征方式对数量表征能力的影响。实验首先验证单手表征中不同手指数量表征方式对小数字（1～5）认知表征的影响;实验2则进一步采用中国人特有的单手手指表征,考察其对大数字（5～9）认知表征的影响。结果表明,小数字中出现了标准手指表征方式语义层面的位置编码、非标准手指表征方式知觉层面总和编码的激活;但大数字中两种手指表征方式均出现了语义层面位置编码的激活。此结果与计算模型理论一致,说明当手指数量从少到多变化时,标准手指表征方式为语义性的符号数量表征;而非标准手指表征方式由知觉性的非符号向语义性符号数量表征过渡。     

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。     

语言与数量认知关系的新认识

数量认知研究近年有长足发展。文章从新近提出的独立于语言的两个数量表征核心系统,语言与精确数量运算,语言与算术事实的储存,语言对儿童早期数概念发展的影响,语言与数量认知关系的最新脑科学证据,以及语言在数量认知模型中的角色等方面,介绍和评述了人类存在依赖和不依赖语言的两级数量能力的新认识。对于是否还存在其它不依赖语言的理解数量的系统,以及这些非语言数量表征系统的认知机制,文章认为有待进一步研究     

0―1.5岁婴儿表征能力的研究概述

就0-1.5岁婴儿的知识表征方面,该文主要介绍了国外的一些研究成果,指出婴儿的表征能力由感知表征向意义表征发展.即使很小的婴儿都已经有了相当复杂的表征能力,能初步感知典型的变化,识别不同种类物体的物体,表征事物与事物之间的空间关系、数量关系、因果关系等,对动因有一定的理解,并逐渐形成概念和图示     

3～6年级儿童整数数量表征与分数数量表征的关系

研究主要探讨了整数数量表征和分数数量表征的关系以及年级对两者关系的影响。实验对155名三至六年级儿童进行0~1分数数字线估计任务和0~1000整数数字线估计任务的测量。结果发现:(1)对于整数数字线估计,所有年级儿童均主要采取了线性表征;(2)对于分数数字线估计,五六年级儿童主要采取了线性表征,三四年级儿童没有明显的线性表征或对数表征的倾向;(3)整数数量表征和分数数量表征呈显著正相关,不过年级对两者的关系产生了影响,表现在只有五六年级儿童的整数数字线估计对分数数字线估计有显著预测作用。     

婴儿的数认知核心系统

在简要回顾双系统假设产生过程的基础上,重点分析了双系统理论的要点、工作机理、实验依据,具体包括小数量精确表征系统和大数量近似表征系统的实验依据.最后讨论了婴儿数量认知的行为和脑生理机制研究中的问题和争论点以及数量认知研究中的矛盾结果和方法局限,并探讨了婴儿数认知是独立的系统还是需要多系统联合参与等七个亟待解决的课题.     

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     

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。     

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.     

Core systems of number

What representations underlie the ability to think and reason about number? Whereas certain numerical concepts, such as the real numbers, are only ever represented by a subset of human adults, other numerical abilities are widespread and can be observed in adults, infants and other animal species. We review recent behavioral and neuropsychological evidence that these ontogenetically and phylogenetically shared abilities rest on two core systems for representing number. Performance signatures common across development and across species implicate one system for representing large, approximate numerical magnitudes, and a second system for the precise representation of small numbers of individual objects. These systems account for our basic numerical intuitions, and serve as the foundation for the more sophisticated numerical concepts that are uniquely human.     

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。     

Chronometric studies of numerical cognition in five-month-old infants

Developmental research suggests that some of the mechanisms that underlie numerical cognition are present and functional in human infancy. To investigate these mechanisms and their developmental course, psychologists have turned to behavioral and electrophysiological methods using briefly presented displays. These methods, however, depend on the assumption that young infants can extract numerical information rapidly. Here we test this assumption and begin to investigate the speed of numerical processing in five-month-old infants. Infants successfully discriminated between arrays of 4 vs. 8 dots on the basis of number when a new array appeared every 2 s, but not when a new array appeared every 1.0 or 1.5 s. These results suggest alternative interpretations of past findings, provide constraints on the design of future experiments, and introduce a new method for probing infants' enumeration process. Further experiments using this method provide initial evidence that infants' enumeration mechanism operates in parallel and yields increasingly accurate numerical representations over time, as does the enumeration mechanism used by adults in symbolic and non-symbolic tasks.     

Number-space associations without language: Evidence from preverbal human infants and non-human animal species

It is well known that humans describe and think of numbers as being represented in a spatial configuration, known as the ‘mental number line’. The orientation of this representation appears to depend on the direction of writing and reading habits present in a given culture (e.g., left-to-right oriented in Western cultures), which makes this factor an ideal candidate to account for the origins of the spatial representation of numbers. However, a growing number of studies have demonstrated that non-verbal subjects (preverbal infants and non-human animals) spontaneously associate numbers and space. In this review, we discuss evidence showing that pre-verbal infants and non-human animals associate small numerical magnitudes with short spatial extents and left-sided space, and large numerical magnitudes with long spatial extents and right-sided space. Together this evidence supports the idea that a more biologically oriented view can account for the origins of the ‘mental number line’. In this paper, we discuss this alternative view and elaborate on how culture can shape a core, fundamental, number–space association.     

Infants perceive human point-light displays as solid forms

While five-month-old infants show orientation-specific sensitivity to changes in the motion and occlusion patterns of human point-light displays, it is not known whether infants are capable of binding a human representation to these displays. Furthermore, it has been suggested that infants do not encode the same physical properties for humans and material objects. To explore these issues we tested whether infants would selectively apply the principle of solidity to upright human displays. In the first experiment infants aged six and nine months were repeatedly shown a human point-light display walking across a computer screen up to 10 times or until habituated. Next, they were repeatedly shown the walking display passing behind an in-depth representation of a table, and finally they were shown the human display appearing to pass through the table top in violation of the solidity of the hidden human form. Both six- and nine-month-old infants showed significantly greater recovery of attention to this final phase. This suggests that infants are able to bind a solid vertical form to human motion. In two further control experiments we presented displays that contained similar patterns of motion but were not perceived by adults as human. Six- and nine-month-old infants did not show recovery of attention when a scrambled display or an inverted human display passed through the table. Thus, the binding of a solid human form to a display in only seems to occur for upright human motion. The paper considers the implications of these findings in relation to theories of infants' developing conceptions of objects, humans and animals.     

TOWARD A MENTALISTIC ACCOUNT OF EARLY PSYCHOLOGICAL REASONING

Recent investigations of early psychological understanding have revealed three key findings. First, young infants attribute goals and dispositions to any entity they perceive as an agent, whether human or non-human. Second, when interpreting an agent's actions in a scene, young infants take into account the agent's representation of the scene, even if this representation is less complete than their own. Third, at least by the second year of life, infants recognize that agents can hold false beliefs about a scene. Together, these findings support a system-based, mentalistic account of early psychological reasoning.     

数形联觉——数字空间表征研究“新”取向

数字空间表征是人类对数字进行表征的重要方式。数形联觉（number-form synesthesia）是一种数字可以有意识地引起空间知觉的独特现象,与此类似的是非联觉者中广泛存在的无意识的心理数字线（mental number line）现象。两者在行为和脑机制上存在着很多重叠,也存在着值得思考的差异。数形联觉的研究能够提供实质性的行为和脑机制数据,用以解决数字空间表征研究中出现的问题,加强对于数字空间表征的理解;也为更加全面深入地开展进一步研究提供了新的启示,成为数字空间表征研究中值得推崇的新取向。     

数字加工的认知神经基础

数学作为人类最重要的发明,越来越引起认知神经科学家的重视与关注,究竟什么才是人类数学知识的脑基础？脑成像的研究已经证实了一个参与数学运算加工的神经网络,包括顶叶皮质、侧前额叶皮质、内前额叶皮质、和小脑。实验证明：人脑对于数字具有一种模拟表达,类似于将数量在脑内部作为一种内心的数字线上的点来操作。神经心理学的研究证实数字加工的这种数量表达分布于两半球,其优势区位于下顶叶皮质区。