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。     

小学生在非符号材料上的分数表征方式

以小学三到六年级学生117人作为被试,采用非符号性分数材料探讨小学生的分数表征方式,以确定他们能否表征分数值。以心理数字线假设为理论基础,分析被试完成分数比较任务的距离效应和反应编码中的“空间—数字关联”效应（SNARC效应）。结果表明：小学三到六年级学生能够对分数进行整体表征,并且表征效率随年级上升而显著提高。至少从三年级开始,小学生已能够根据分数的值,按从小到大的顺序自左至右地将分数表征在心理数字线上。     

不同数字线下儿童与成人分数估计的表征模式

以44名小学六年级儿童与40名大学生为被试,通过0~1和1/100~1/10两种数字线的NP（数字位置）和PN（位置数字）估计任务系统考察儿童与成人的分数估计的表征方式。结果显示：（1）儿童和成人在0~1数字线的NP和PN任务上都呈线性表征,但在1/100~1/10数字线下,两组被试在NP任务上却呈对数表征,在PN任务上呈指数表征;（2）NP任务的错误百分比均高于PN任务,且儿童在两数字线下的准确性均明显低于成人。     

儿童数字估计的表征模式与发展

探讨中国儿童数字估计的表征模式与发展趋势。包括两个实验,均采用数字线估计任务,实验一以92名幼儿园、一年级及二年级儿童为被试,考察其在0~100范围的数字估计,结果显示,幼儿园儿童在数字估计更多地采用对数表征,而一二年级的儿童在数字估计中更多地采用线性表征;实验二以86名一、三、五年级儿童为被试,考察其在0~1000范围的数字估计,结果显示,一年级儿童有一半采用对数表征,另一半采用线性表征,而三五年级儿童大多采用线性表征。中国儿童的数字估计表现出与美国儿童相同的发展模式,都是由不精确的对数表征逐步向精确的线性表征发展;人的数表征有多种形式,即使在同一年龄阶段,也会因任务难度的不同而选择不同的表征模式。中国儿童精确数字估计能力的出现要早于美国儿童。     

数字表征的表象赋义效应:来自数字线估计任务的证据

已有研究中数字线估计任务几乎都使用纯数字。本研究以二到六年级儿童为被试,采用纯数字任务和赋义数字任务来探索赋义表象对数字表征形式的影响。结果表明,对0~1000的数字赋义后,对数模型的解释力上升,而线性模型的解释力下降;表象大小对于赋义数字的估计影响显著,大表象赋义提高了对数模型解释力而降低了数字估计的准确性,小表象的影响比较微弱。     

儿童数字线表征的发展——心理长度的影响

探讨儿童在数字线估计任务中心理长度的发展及其对数量表征模式的影响.选取7~9岁儿童共109名进行数字线估计任务测试,设置了10cm和20cm两种长度条件,要求儿童完成根据位置判断数字任务(position to number,PN任务).结果表明儿童在数字线PN任务中存在心理长度,且7岁儿童心理长度的范围超过10,随着儿童年龄的增长,他们的心理长度范围不断缩小;心理长度范围影响儿童的表征模式,随着心理长度范围的缩小,儿童的数字线表征出现从指数模式到线性模式的变化趋势;与表征模式的发展趋势一致,儿童估计的精确性随年龄增长逐渐提高.     

时间赋义对数字空间表征的影响：来自数字线估计任务的证据

数字线估计任务的大量研究以纯数字为研究对象而忽视了赋义数字。本研究以Siegler等的数字线估计任务为原型,探讨在对数字时间赋义条件下小学二、四和六年级儿童的数字表征形式是否发生变化。结果表明,小学二年级是0-1000范围内数字表征从对数形式转换为线性形式的转折点,对数字赋予时间含义后,三个年级均出现了赋义效应。在线性模型和对数模型中时间赋义的作用相反,时间赋义表现出抑线升对（抑制线性模型提升对数模型解释力）的效果。     

心理长度对二年级儿童数字线估计表征的影响

从心理长度的角度探讨二年级儿童在0~100和0~1000数字范围存在不同表征方式的原因。实验一要求二年级儿童完成长度均为10cm,范围分别为0~100和0~1000的数字线估计任务。实验二要求儿童对长度分别为10cm和18cm,范围均为0~1000的数字线进行估计。结果发现在两个实验中二年级儿童的估计均存在心理长度,但与以往研究的一年级儿童相比,心理长度的范围有所缩小。随着数字范围的增大或长度的减小,儿童的表征方式出现了从线性表征向对数表征的转变趋势。这些结果表明不精确的表征方式可能与心理长度策略的使用有关,心理长度在一定程度上影响了二年级儿童的估计表征方式。     

心理长度对二年级儿童数字线估计表征的影响

从心理长度的角度探讨二年级儿童在0~100和0~1000数字范围存在不同表征方式的原因。实验一要求二年级儿童完成长度均为10cm,范围分别为0~100和0~1000的数字线估计任务。实验二要求儿童对长度分别为10cm和18cm,范围均为0~1000的数字线进行估计。结果发现在两个实验中二年级儿童的估计均存在心理长度,但与以往研究的一年级儿童相比,心理长度的范围有所缩小。随着数字范围的增大或长度的减小,儿童的表征方式出现了从线性表征向对数表征的转变趋势。这些结果表明不精确的表征方式可能与心理长度策略的使用有关,心理长度在一定程度上影响了二年级儿童的估计表征方式。     

儿童数字估计中的心理长度

从儿童对数字属性的认识角度探讨一年级儿童在不同数字范围中采用不同表征形式的根本原因。两个实验均采用数字线估计任务,实验一测量一年级儿童在15cm数字线长度下0～100与0～1000两种范围上的数字估计;实验二测量一年级儿童对0～1000范围10cm和20cm数字线长度的估计。结果显示,无论在不同的数字范围还是在不同的数字线长度下,儿童对低端数字的估计均存在心理长度,即儿童倾向于将低端数字与固定的线段长度对应起来,且这种对应关系不随数字范围与数字线长度的变化而变化。心理长度的存在是儿童在不同数字范围和不同数字线长度中采用不同数字表征形式的根本原因,也是儿童对数概念的认识发展到等距水平时出现的一种独特特点。     

Developmental changes in the whole number bias

Many students’ knowledge of fractions is adversely affected by whole number bias, the tendency to focus on the separate whole number components (numerator and denominator) of a fraction rather than on the fraction's magnitude (ratio of numerator to denominator). Although whole number bias appears early in the fraction learning process and under speeded conditions persists into adulthood, even among mathematicians, little is known about its development. Performance with equivalent fractions indicated that between fourth and eighth grade, whole number bias decreased, and reliance on fraction magnitudes increased. These trends were present on both fraction magnitude comparison and number line estimation. However, analyses of individual children's performance indicated that a substantial minority of fourth graders did not show whole number bias and that a substantial minority of eighth graders did show it. Implications of the findings for development of understanding of fraction equivalence and for theories of numerical development are discussed.     

Association between basic numerical abilities and mathematics achievement

Various measures have been used to investigate number processing in children, including a number comparison or a number line estimation task. The present study aimed to examine whether and to which extent these different measures of number representation are related to performance on a curriculum‐based standardized mathematics achievement test in kindergarteners, first, second, and sixth graders. Children completed a number comparison task and a number line estimation task with a balanced set of symbolic (Arabic digits) and non‐symbolic (dot patterns) stimuli. Associations with mathematics achievement were observed for the symbolic measures. Although the association with number line estimation was consistent over grades, the association with number comparison was much stronger in kindergarten compared to the other grades. The current data indicate that a good knowledge of the numerical meaning of Arabic digits is important for children's mathematical development and that particularly the access to the numerical meaning of symbolic digits rather than the representation of number per se is important.     

Cross-sex best friendship influences on early adolescent cigarette and alcohol expectancies and use

In this study, the author investigates the influences of cross-sex best friends in early adolescence in regard to cigarettes and alcohol. Specific goals include determining the prevalence of cross-sex best friendships, investigating expectancies and perceived approval of the use of cigarettes and alcohol, and examining substance use levels. A group of urban sixth, seventh, and eighth graders completed a survey that addressed these issues. Results indicate the presence of cross-sex best friendships in the sample. Significant findings on cross-sex best friends' influence include positive expectancies for alcohol in sixth (p = .006) grade, the perception of seventh graders that the best friend's attitudes about smoking (p = .003) and drinking (p = .001) are less negative, and higher levels of cigarette use in sixth (p = .001) and eighth (p = .024) grade and alcohol use in sixth (p = .008), seventh (p = .002), and eighth grades (p = .039).     

On the Meaning of Time in Later Life

Fourth-, sixth-, and eighth-grade subjects participated in a free-recall experiment to test the relative power of two Taxonomic, two Semantic Differential, and two Sense Impression word classes in facilitating recall. Findings show that across all grades children exhibited a significantly greater tendency to recall and cluster Taxonomic and Semantic Differential over Sense Impression word classes. Further, sixth and eighth graders recalled more words over all word classes than fourth graders. It was also found that girls recalled more words than boys across all three grade levels and all six word classes. Finally, there was no grade or sex effect for clustering. An interpretation of this difference was offered     

CPQ personality factors of upper elementary gifted students

The results of administering the Children's Personality Questionnaire (CPQ) to gifted students in the fourth, fifth, and sixth grades indicated that they had personality profiles similar to the norm group. Gifted males were more controlled, socially precise, self-disciplined, and compulsive than females, described as more casual and careless of social rules. Also, gifted females were more assertive and independent than males who had scores suggesting a more obedient, mild, or conforming personality. In comparing personality factors across grades, fourth graders had profiles significantly different from sixth graders.     

The development of numerical estimation: evidence for multiple representations of numerical quantity

Abstract - We examined children's and adults' numerical estimation and the representations that gave rise to their estimates. The results were inconsistent with two prominent models of numerical representation: the logarithmic-ruler model, which proposes that people of all ages possess a single, logarithmically spaced representation of numbers, and the accumulator model, which proposes that people of all ages represent numbers as linearly increasing magnitudes with scalar variability. Instead, the data indicated that individual children possess multiple numerical representations; that with increasing age and numerical experience, they rely on appropriate representations increasingly often; and that the numerical context influences their choice of representation. The results, obtained with second graders, fourth graders, sixth graders, and adults who performed two estimation tasks in two numerical contexts, strongly suggest that one cause of children's difficulties with estimation is reliance on logarithmic representations of numerical magnitudes in situations in which accurate estimation requires reliance on linear representations.     

分数的数量表征

分数数量表征已成为当前数学认知研究的重要主题之一。基于该领域近10年来的研究发现, 总结了分数数量表征研究的新进展。首先概述分数数量表征的发展, 然后着重介绍分数数量的不同表征方式并系统分析制约数量表征的任务及背景因素。此外, 还深入探究了分数数量表征与整数、小数数量表征的区别与联系。未来研究者应注意在分数数量表征的个体差异、跨文化以及干预等方面加强考察。