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。     

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。     

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。     

小学生近似数量系统敏锐度的发展趋势及其与数学能力的关系：抑制控制的中介作用

采用测量法和问卷法考察了172名小学生近似数量系统敏锐度的发展,以及抑制控制在近似数量系统敏锐度与数学能力关系中的中介效应。结果表明：(1)随着年龄增长,小学生的近似数量系统敏锐度逐渐提高;(2)近似数量系统敏锐度(负相关序列中的韦伯系数)和抑制控制均能显著正向预测小学生的数学能力;(3)抑制控制在小学生近似数量系统敏锐度(负相关序列中的韦伯系数)与数学能力的关系中起部分中介作用。     

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.     

The influence of instructional intervention on children's understanding of fractions

An experimental instructional program based mainly on an equal-whole schema in fractions was given to two fourth-grade classes of a Japanese elementary school. As a control, conventional teaching based on a traditional Japanese textbook was given to another fourth-grade class. The study tested the hypothesis that students given the experimental program would understand order and magnitude as central characteristics of fractions better than those who were instructed using the traditional textbook. Students in the experimental group showed better understanding of both the order of fractions and the representation of the sizes of fractions than did the textbook group. However, there were no differences between the experimental and textbook groups in the performance of assessment tasks which were less related to the equal-whole schema. These results are discussed in view of the important instructional aim of having students understand fractions.     

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。     

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.