语义信息在大小数量表征中的作用

本研究采用注意瞬脱实验范式探讨了语义信息在数量表征中的作用。结果发现：（1）在双任务方式中,字母辨认任务对大数（5及以上）的辨认产生干扰,但不影响小数（4及以下）的辨认绩效;（2）数量表征在视野上出现差异性,表现为在小数辨认时,左侧视野呈现绩效高于右侧;大数辨认正好相反,即右侧视野呈现高于左侧。结果表明,语义信息在表征小数和大数中的作用不同：小数的表征无需语言参与;而大数则更多地涉及语义信息,可能需语音回路中无声复述机制的参与。     

不同注意条件下大数与小数的加工差异

考察在注意（注视点）与非注意（非注视点）条件下数字加工的距离效应和符号效应。采用小数（1－4）和大数（6－9）的中文与阿拉伯数字为材料,以判断数字是否大于5为任务。实验结果表明：⑴ 在注意条件下,大小数都出现了距离效应;而在非注意条件下,只有小数出现距离效应;⑵ 在注意条件下,大小数都没有出现符号效应;而在非注意条件下,只有小数出现符号效应,中文数字绩效显著好于阿拉伯数字。     

Is there really a link between exact‐number knowledge and approximate number system acuity in young children?

Although everyone perceives approximate numerosities, some people make more accurate estimates than others. The accuracy of this estimation is called approximate number system (ANS) acuity. Recently, several studies have reported that individual differences in young children's ANS acuity are correlated with their knowledge of exact numbers such as the word ‘six’ (Mussolin et al., 2012, Trends Neurosci. Educ., 1, 21; Shusterman et al., 2011, Connecting early number word knowledge and approximate number system acuity; Wagner & Johnson, 2011, Cognition, 119, 10; see also Abreu‐Mendoza et al., 2013, Front. Psychol., 4, 1). This study argues that this correlation should not be trusted. It seems to be an artefact of the procedure used to assess ANS acuity in children. The correlation arises because (1) some experimental designs inadvertently allow children to answer correctly based on the size (rather than the number) of dots in the display and/or (2) young children with little exact‐number knowledge may not understand the phrase ‘more dots’ to mean numerically more. When the task is modified to make sure that children respond on the basis of numerosity, the correlation between ANS acuity and exact‐number knowledge in normally developing children disappears.     

Number comparison and number ordering as predictors of arithmetic performance in adults: Exploring the link between the two skills,and investigating the question of domain-specificity

Recent evidence has highlighted the important role that number-ordering skills play in arithmetic abilities, both in children and adults. In the current study, we demonstrated that number comparison and ordering skills were both significantly related to arithmetic performance in adults, and the effect size was greater in the case of ordering skills. Additionally, we found that the effect of number comparison skills on arithmetic performance was mediated by number-ordering skills. Moreover, performance on comparison and ordering tasks involving the months of the year was also strongly correlated with arithmetic skills, and participants displayed similar (canonical or reverse) distance effects on the comparison and ordering tasks involving months as when the tasks included numbers. This suggests that the processes responsible for the link between comparison and ordering skills and arithmetic performance are not specific to the domain of numbers. Finally, a factor analysis indicated that performance on comparison and ordering tasks loaded on a factor that included performance on a number line task and self-reported spatial thinking styles. These results substantially extend previous research on the role of order processing abilities in mental arithmetic.     

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。     

数字线和离散物体任务训练对儿童整数偏向的影响

通过数字线任务和离散物体任务对81名拥有错误整数偏向的儿童进行干预,再进行分数比较任务,以考查不同干预对错误整数偏向的影响以及分数在心理数字线上的表征方式。结果表明：（1）离散物体组儿童在干预任务中表现较好,在分数比较任务中得分也显著高于数字线组儿童,但反应时要慢于数字线组儿童。（2）正确比较分数时,两组均出现正确整数偏向,但错误的整数偏向依然存在,二者在整数系统扩展到有理数系统这个过渡期同时存在。     

分数认知的“整数偏向”研究:理论与方法

整数偏向普遍存在于分数认知中,它指儿童在应用分数知识时,常使用先前形成的有关整数的独立单元计数图式来解释分数的倾向。学者们提出了先天约束假设、未分化量假设和学习的负迁移假设分别从先天和后天角度对其成因做了解释。以往研究常采用纸笔测验或口语报告揭示它的存在,近年来有研究采用了心理数字线假设的相关效应考查了成人的整数偏向,使其研究方法和被试得以扩展。在该领域,今后应在定义、理论解释、研究方法以及教学干预方面加强研究。     

内源性注意与外源性注意对数字加工的不同影响

分别采用内源性注意和外源性注意实验范式,材料为小数（1－4）和大数（6－9）的中文与阿拉伯数字,任务为判断数字是否大于5,考察在注意与非注意条件下不同大小数字加工的距离效应和符号效应。结果发现：⑴在内源性线索和外源性线索的注意条件下,大小数都出现了距离效应;但在非注意条件下,内源性线索时的大小数都出现了距离效应,而外源性线索时只有小数出现了距离效应,大数的距离效应明显减弱或消失。⑵在内源性线索和外源性线索的注意条件下,大小数都没有出现符号效应;但在非注意条件下,大数没有出现符号效应,而小数出现了符号效应（阿拉伯数字的绩效比中文数字差）,并且内源性线索时的符号效应强度小于外源性线索。     

An axiomatization of family resemblance

We invoke concepts from the theory of hypergraphs to give a measure of the closeness of family resemblance, and to make precise the idea of a composite likeness. It is shown that for any positive integer m, for any general term possessing any extent of family resemblance strictly greater than m, there is a taxonomical representation of the term whereby each subordinate taxon has an extent of family resemblance strictly greater than m.     

壮族大学生一位数字词的SNARC效应

本研究以壮族大学生为被试,要求他们对壮语、汉语听觉数字词(实验一)或汉语、英语视觉数字词(实验二)进行奇偶判断。结果发现：(1)壮族大学生对汉语、壮语听觉数字词以及汉语、英语视觉数字词都表现出了SNARC效应。(2)数字词在听觉条件下和视觉条件下产生的SNARC效应的强度相当。(3)书写习惯也影响到壮语听觉数字的SNARC效应的方向。     

情境对序数的空间表征之影响

通过设置垂直维度上不同的情境,本研究采用“奇偶判断任务”探讨了情境对序数空间表征的影响。结果发现,只有序数的情况下,被试对小数的上键反应或下键反应、对大数的上键反应或下键反应都没有显著差异;在楼层情境下,被试对小数的下键反应更快,对大数的上键反应更快;在家谱情境下,被试对小数的上键反应更快,对大数的下键反应更快。以上结果表明,垂直维度上序数的空间表征受到情境的影响,这说明在垂直维度上数字的空间表征具有动态性,且受到具体和情境的调节。     

Spontaneous mapping of number and space in adults and young children

Mature representations of space and number are connected to one another in ways suggestive of a ‘mental number line’, but this mapping could either be a cultural construction or a reflection of a more fundamental link between the domains of number and geometry. Using a manual bisection paradigm, we tested for number line representations in adults, young school children, and preschool children. Non-symbolic numerical displays systematically distorted localization of the midpoint of a horizontal line at all three ages. Numerical and spatial representations therefore are linked prior to the onset of formal instruction, in a manner that suggests a privileged relation between spatial and numerical cognition.     

大小数量加工机制分离现象的ERP研究

大量行为研究表明,个体对4以上非符号数量的加工存在加工机制分离现象,但是相关的神经机制研究还很少。本研究选取21名大学生被试,结合ERP技术和数量判断任务,以数量比率效应为指标,比较4以上不同大小数量加工的神经反应模式。结果显示,大小数量加工条件下数量比率效应对P2p成分幅值的调节模式存在显著差异。这支持了小数量加工基于数量属性,大数量加工基于非数量属性的观点。     

Numerosity discrimination in deep neural networks: Initial competence,developmental refinement and experience statistics

Both humans and non‐human animals exhibit sensitivity to the approximate number of items in a visual array, as indexed by their performance in numerosity discrimination tasks, and even neonates can detect changes in numerosity. These findings are often interpreted as evidence for an innate ‘number sense’. However, recent simulation work has challenged this view by showing that human‐like sensitivity to numerosity can emerge in deep neural networks that build an internal model of the sensory data. This emergentist perspective posits a central role for experience in shaping our number sense and might explain why numerical acuity progressively increases over the course of development. Here we substantiate this hypothesis by introducing a progressive unsupervised deep learning algorithm, which allows us to model the development of numerical acuity through experience. We also investigate how the statistical distribution of numerical and non‐numerical features in natural environments affects the emergence of numerosity representations in the computational model. Our simulations show that deep networks can exhibit numerosity sensitivity prior to any training, as well as a progressive developmental refinement that is modulated by the statistical structure of the learning environment. To validate our simulations, we offer a refinement to the quantitative characterization of the developmental patterns observed in human children. Overall, our findings suggest that it may not be necessary to assume that animals are endowed with a dedicated system for processing numerosity, since domain‐general learning mechanisms can capture key characteristics others have attributed to an evolutionarily specialized number system.     

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。     

Infants recognize counting as numerically relevant

Children do not understand the meanings of count words like “two” and “three” until the preschool years. But even before knowing the meanings of these individual words, might they recognize that counting is “about” the dimension of number? Here in five experiments, we asked whether infants already associate counting with quantities. We measured 14‐ and 18‐month olds’ ability to remember different numbers of hidden objects that either were or were not counted by an experimenter before hiding. As in previous research, we found that infants failed to differentiate four hidden objects from two when the objects were not counted—suggesting an upper limit on the number of individual objects they could represent in working memory. However, infants succeeded when the objects were simply counted aloud before hiding. We found that counting also helped infants differentiate four hidden objects from six (a 2:3 ratio), but not three hidden objects from four (a 3:4 ratio), suggesting that counting helped infants represent the arrays’ approximate cardinalities. Hence counting directs infants’ attention to numerical aspects of the world, showing that they recognize counting as numerically relevant years before acquiring the meanings of number words.     

3~6岁儿童数感发展的研究

从上海两所中等水平幼儿园以年龄班分层随机抽取180名3~6岁儿童为被试,采用个别测查法考察其数感发展状况。结果表明:(1)3~6岁儿童的数感发展存在显著年龄差异,无性别差异;(2)顺数、实物比较和数符号辨认是其表现较好的三项技能,而倒数和序数却表现较差;(3)数感各组成部分发展不同步,倒数,序数和数符号在中班到大班期间发展迅速,而顺数,基数概念,加减理解却在小班到中班期间发展较快。     

幼儿在集合比较中运用数数的实验研究

本研究中运用了两个实验探讨数数干预和测查条件对儿童在集合比较中运用数数的影响。干预对3岁儿童(M=3：9)没有影响。在平均年龄为4岁4个月时．干预组儿童比控制组儿童更倾向于用数数比较集合．自然组儿童也比传统组更倾向于用数数。许多4岁儿童在无干预时不用数数可能是因为,1)不知数数比视觉性比较更有效,或2)他们在集合比较中的数数极易受测查情景因素的影响。儿童在集合比较中的数数运用与他们的数数水平密切关联。