3-6年级数学学习困难儿童与正常儿童空间能力的比较

选取3-6年级数学学习困难和数学学习正常的儿童共458名,比较了两类儿童空间能力的发展特点。结果表明:(1)正常儿童的空间能力优于数困儿童,二者空间视觉化能力均优于空间定向能力;(2)正常儿童与数困儿童的空间能力均随年龄增长而提高,但二者不同空间能力快速发展的时间点不同;(3)单纯数困儿童的空间能力优于混合数困儿童,后者空间定向能力发展滞后;(4)正常儿童的空间能力在发展过程中对数学成绩的作用量为26.17%,数困儿童为28.43%。     

数学学习不良儿童视觉-空间表征与数学问题解决

采用临床访谈的方法,考察了30名数学学习不良(MD)儿童和31名一般儿童的数学问题解决、视觉-空间表征策略和空间视觉化能力。结果发现：图式表征能促进数学问题的解决,图像表征则起妨碍作用;空间视觉化能力与解题正确率及图式表征策略有显著正相关,与图像表征策略有显著负相关。MD儿童的解题正确率以及使用图式表征策略的程度显著低于一般儿童,使用图像表征策略的程度则显著高于一般儿童。在解题正确率和图式表征策略这两个变量上,MD儿童和一般儿童的年级发展趋势相同,都随年级的升高而提高。但在图像表征策略的使用上,一般儿童有随年级的升高而下降的趋势,MD儿童却没有下降的趋势。两类儿童的空间视觉化能力都随年级的升高而提高。     

数学学习不良的研究及趋势

认知心理学、神经心理学的研究发现了数学学习不良(MD)儿童的3种基本算术技能障碍:语义记忆型MD、程序型MD、视觉空间型MD,并对它们的机制和特征做了考察.近年来对MD儿童较高级数学问题解决的研究呈现如下特点:参与到该研究的领域很多;研究所涉及的认知和非认知因素增多;教学干预研究大量出现.目前MD研究在辨别MD儿童、缺陷的概念以及神经心理学解释上面临挑战.因此该研究领域的趋势是从发展的、整体的视角来考察影响MD的各种因素,并注意各种方法的革新和结合.     

学习不良儿童与一般儿童认知发展、学习动机和家庭资源的比较

运用认知测验法和问卷法,综合考察了167名学习不良儿童和161名一般儿童的认知发展、学习动机和家庭资源的特点,结果表明:与一般儿童相比,学习不良儿童认知发展的速度比较缓慢,对于较简单的认知能力,其年龄差异显着,而对于较复杂的认知能力,年龄差异较小;学习不良儿童的学习动机显着低于一般儿童,但其学习动机与其认知水平呈显着的正相关;学习不良儿童的家庭资源配置与一般儿童相比差异明显.     

数学学业不良儿童的估算情感特点研究

运用自编估算测试材料,通过与学优生相比较,考察了数学学业不良儿童的估算情感特点及与估算能力的关系,被试为40名小学六年级学生。结果表明:1.学业不良儿童的估算情感总分明显低于学优儿童,学业不良儿童在数学自信心和估算情感认同这两个维度上表现较为消极。2.学业不良儿童的估算情感认同与他们的估算成绩之间关系更为密切。     

学龄早期Asperger综合症儿童行为问题和注意、行为抑制功能研究

研究采用Achenbach儿童行为量表(父母用表)和注意、行为抑制及动作协调性行为任务对12名学龄早期的Asperger综合征儿童与29名在年龄及智力水平上与之匹配的正常儿童在行为问题、注意、行为抑制及动作协调等方面进行了比较.结果发现,在控制了年龄和智力因素后:1)Asperger综合征儿童的社会能力与正常儿童相比明显较差,同时常伴随有交往不良、社交退缩、焦虑、忧郁、强迫性、攻击性和多动等一系列行为问题;2)Asperger综合征儿童表现出一定的注意和行为抑制障碍,动作的协调性和灵活性较差.     

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。     

数学不良儿童的书写运动控制特征

选取小学生47名,其中23名为数学不良,24名为一般儿童,使用数码写字板,测试二者在自然和双任务条件下,书写一条横线的速度、加速度。结果发现：（1）自然条件下书写,MD儿童的速度、加速度与一般儿童相一致,两者的差异均不显著。（2）双任务条件下书写,MD儿童的总体平均速度、加速度明显慢于一般儿童的,两者的差异均显著。     

儿童早期工作记忆与数学学习的关系

以往研究认为工作记忆对数学学习很重要,但是以往工作记忆和早期数学学习的关系研究结果并不一致。本研究运用元分析的方法回顾了33篇独立研究,含307项相关系数作为效应值,总被试量为42423名平均年龄3~8岁的儿童,旨在探讨工作记忆的3个主成分PL(语音回路)、VSSP(视觉空间画板)、CE(中央执行)与数学学习不同方面之间的关系,以及样本年龄对工作记忆和数学学习相关程度的调节作用。结果显示:工作记忆与数学学习确实存在强相关,工作记忆子成分中,CE与数学学习平均相关的程度最强。并且,CE与数学学习不同方面之间的相关程度不存在显著差异,PL、VSSP与数运算的相关程度比数概念更强,存在显著差异。样本年龄对CE、PL与数学学习之间相关关系存在显著调节作用,对VSSP与数学学习之间的相关关系不存在显著调节作用。文献梳理还发现,以往研究对数学学习的考察,大都聚焦数概念、数运算的内容,未来研究需要关注几何与空间、测量等方面内容。     

简单心算中数学学习困难儿童的数字距离效应

采用事件相关电位(ERP)方法,以阿拉伯数字的简单心算为任务,考察数学学习困难儿童(MD)的数字距离效应。行为数据的结果表明:MD组没有出现数字距离效应,对照组儿童出现了数字距离效应。事件相关电位数据显示:与对照组相比,MD组N270的潜伏期更长;两组被试在N270的波幅和潜伏期上都没有表现出数字距离效应。研究结果表明:MD儿童对数量信息的空间表征存在缺陷。     

Relation of cognitive operational performance to comprehension and production of dimensional adjectives

This study compared normal developing children, aged 34 to 51 mo., on comprehension and production of relative dimensional adjectives using object manipulations in a close elicitation procedure and on Piagetian operational tests of conservation of continuous quantity, length, reversibility and seriation. Analysis indicated a significant difference on the expressive language performance of the transitional and the concrete operational children over the preoperational children, but no significant differences occurred between the first two groups. Children who performed better on seriation were significantly better on expressive language performance. Children classified as operational for length performed better on all language measures than those classified as nonoperational. Reversibility and conservation of a continuous quantity did not differentiate children.     

Judgments of quantity and conservation of quantity: the area of a rectangle

This study examines the relationships between perceptive judgment of quantity and conservation judgment of quantity with regard to the concept of area. Twenty children who passed an area conservation task (mean age = 8) and 20 children who failed it (mean age = 6, 7) were administered an area judgment task. This task was a replication of Anderson and Cuneo's study (1978, Journal of Experimental Psychology: General, 107, 335-378). The conserving children generally appeared to apply an additive rule (the height and width rule) observed by Anderson and Cuneo in 5 year olds. The nonconserving children in contrast generally presented patterns suggesting centration on one of the two dimensions. The implications for Anderson's and Piaget's conceptions of conservation development are discussed.     

Cognitive Analysis of Children's Mathematics Difficulties

The aim of the study is to investigate the informal and formal mathematical knowledge of children suffering from "mathematics difficulty" (MD). The research involves comparisons among three groups: fourth-grade children performing poorly in mathematics but normal in intelligence; fourth-grade peers matched for intelligence but experiencing no apparent difficulties in mathematics; and a randomly selected group of third graders. These children were individually presented with a large number of tasks designed to measure key mathematical concepts and skills. The findings suggest that: (1) MD children are not seriously deficient in key informal mathematical concepts and skills; (2) MD children seem to have elementary concepts of base ten notation but experience difficulty in related enumeration skills, particularly when large numbers are involved; (3) MD children's calculational errors often result from common error strategies; (4) MD children display severe difficulty in recalling common addition facts; and (5) in the area of problem solving, MD children are capable of "insightful" solutions and can solve simple forms of word problems, but experience difficulty with complex word problems. MD children are in many respects similar to normal, younger peers; an hypothesis of "essential cognitive normality" is advanced. The only and dramatic exception occurs in the area of number facts. While clinical experience corroborates this finding, its explanation is not evident.     

A developmental comparison of identity and equivalence conservations

The developmental priority of identity conservation as contrasted with equivalence conservation theorized by Elkind (1967) was investigated using quantity and number conservation tasks. Subjects were 60 four-, five-, and six-year-old children of middle socioeconomic class background. All children received a battery of tasks which included qualitative identity, quantitative identity, and equivalence conservation of quantity and number problems. For the quantity battery, under the without justification condition, conditional probabilities and significant performance differences in the mean number of trials passed indicated that the order of acquisition of quantity tasks did conform to the hypothesized sequence: qualitative identity, quantitative identity, and equivalence conservation. No significant performance differences for number concepts were noted for both justification and without justification conditions. Scalogram analyses performed upon the combined quantity number task array indicated a scale or quasi-scale in the predicted order of difficulty. It was concluded that identity concepts develop prior to equivalence concepts when the content area is quantity conservation. In contrast, clear-cut conclusions cannot be made about number conservation.     

Counting knowledge and skill in cognitive addition: a comparison of normal and mathematically disabled children.

The relationship between counting knowledge and computational skills (i.e., skill at counting to solve addition problems) was assessed for groups of first-grade normal and mathematically disabled (MD) children. Twenty-four normal and 13 MD children were administered a series of counting tasks and solved 40 computer-administered addition problems. For the addition task, problem-solving strategies were recorded on a trial-by-trial basis. Performance on the counting tasks suggested that the MD children were developmentally delayed in the understanding of essential and unessential features of counting and were relatively unskilled in the detection of certain forms of counting error. On the addition task, the MD children committed many more computational errors and tended to use developmentally immature counting procedures. The immature counting knowledge of the MD children, combined with their relatively poor skills at detecting counting errors, appeared to underlie their poor computational skills on the addition task. Suggestions for future research are presented.     

How to think about informal proofs

It is argued in this study that (i) progress in the philosophy of mathematical practice requires a general positive account of informal proof; (ii) the best candidate is to think of informal proofs as arguments that depend on their matter as well as their logical form; (iii) articulating the dependency of informal inferences on their content requires a redefinition of logic as the general study of inferential actions; (iv) it is a decisive advantage of this conception of logic that it accommodates the many mathematical proofs that include actions on objects other than propositions; (v) this conception of logic permits the articulation of project-sized tasks for the philosophy of mathematical practice, thereby supplying a partial characterisation of normal research in the field.     

The performance of attention-deficit-disordered and normal children on conservation tasks

The present study was designed to investigate whether a specific subgroup of learning-disabled children (attention-deficit-disordered, ADD) differed from their normal counterparts on Piagetian tasks of conservation. The subjects were 34 third-and fourth-grade children. Seventeen children had been diagnosed as ADD; the remaining half were designated as normal. The two groups were equivalent in chronological age, mental age, and intelligence. The results indicated significant differences between the two groups on tasks tapping conservation of substance and number. These results may support the theory of a lag in the development of conservation in children with specific learning disabilities (ADD). Implications of the present research for therapeutic and remedial programs that serve ADD children are also discussed.     

The Performance of Attention-Deficit-Disordered and Normal Children on Conservation Tasks

The present study was designed to investigate whether a specific subgroup of learning-disabled children (attention-deficit-disordered, ADD) differed from their normal counterparts on Piagetian tasks of conservation. The subjects were 34 third- and fourth-grade children. Seventeen children had been diagnosed as ADD; the remaining half were designated as normal. The two groups were equivalent in chronological age, mental age, and intelligence. The results indicated significant differences between the two groups on tasks tapping conservation of substance and number. These results may support the theory of a lag in the development of conservation in children with specific learning disabilities (ADD). Implications of the present research for therapeutic and remedial programs that serve ADD children are also discussed.     

Quantity judgments and individuation: evidence that mass nouns count

Three experiments explored the semantics of the mass-count distinction in young children and adults. In Experiments 1 and 2, the quantity judgments of participants provided evidence that some mass nouns refer to individuals, as such. Participants judged one large portion of stuff to be "more" than three tiny portions for substance-mass nouns (e.g. mustard, ketchup), but chose according to number for count nouns (e.g. shoes, candles) and object-mass nouns (e.g. furniture, jewelry). These results suggest that some mass nouns quantify over individuals, and that therefore reference to individuals does not distinguish count nouns from mass nouns. Thus, Experiments 1 and 2 failed to support the hypothesis that there exist one-to-one mappings between mass-count syntax and semantics for either adults or young children. In Experiment 3, it was found that for mass-count flexible terms (e.g. string, stone) participants based quantity judgments on number when the terms were used with count syntax, but on total amount of stuff when used with mass syntax. Apparently, the presence of discrete physical objects in a scene (e.g. stones) is not sufficient to permit quantity judgments based on number. It is proposed that object-mass nouns (e.g. furniture) can be used to refer to individuals due to lexically specified grammatical features that normally occur in count syntax. Also, we suggest that children learning language parse words that refer to individuals as count nouns unless given morpho-syntactic and referential evidence to the contrary, in which case object-mass nouns are acquired.