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.     

MD儿童与正常儿童早期数学认知差异的研究

该研究采用测验法,考察数学学习不良(MD)儿童的早期数学认知能力,包括计数、数守恒、时空概念、逻辑、计算和操作等方面。被试为城市幼儿园34名MD儿童和30名正常儿童,平均年龄约6.0岁。结果发现:学习不良儿童早期数学能力在逻辑、计算和空间保持上有缺陷,与Johnson、Ginsburg等人的研究结果一致。与以往研究有所不同的是:在计数能力上,MD儿童与正常儿童间差异不明显;在数守恒能力上,MD儿童明显低于正常儿童;空间保持缺陷表现突出,表现为书写数字时的镜像反应、图形的错误表征等。     

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。     

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。     

西方心理分离的研究回顾

近几十年来,家庭对儿童青少年心理发展的影响受到众多研究者的关注,国外家庭研究和治疗领域的许多研究者进行了大量有关心理分离的研究。心理分离即个体与家庭在心理上的分离并形成个体化的程度。文章从心理分离的界定、心理分离的理论背景（Mahler发展阶段理论、Bowen家庭系统理论）、心理分离的测量方法、心理分离研究现状这几方面对现有研究进行了综述,并做了简要评述,最后阐述了西方心理分离的研究对我国家庭研究与治疗的启示,并对未来的研究进行了展望     

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。     

关于市场经济与伦理道德关系的几个问题

关于市场经济与伦理道德关系的几个问题廖申白在《哲学研究》１９９５年６期上撰文《市场经济与伦理道德讨论中的几个问题》,认为这场讨论中讨论较多的一个问题是市场经济的建立与发展对社会伦理道德的影响问题,从“代价论”、“滑坡论”与“爬坡论”,到市场经济对社会...     

论数学能力的研究与认知理论的关系

本文对关于数学能力的实质的心理学研究作了历史的回顾,其中包括心理计量学、认知科学和心理学中的认知发展等几个领域的研究工作。文中揭示了在这几个领域的研究中存在着的几个共同问题。作者认为需要假借这些不同的研究领域中的研究方法,创造新的信息加工的方法以揭示数学能力及其发展的实质。     

发展的价值基础追思

纵观发展观念的演革,不难发现,人们对发展所蕴涵的价值基础、对发展所达求的理想目标的认识日渐丰富。依笔者之见,这种认识与发展的机制分析是深化发展问题的哲学研究的两大基本方面。本文试图探讨的就是价值基础这一方面的几个问题。     

双语与认知发展关系的近期研究进展

双语与认知发展的关系一直是心理学家关注的一个重要问题。该文从双语的概念入手,介绍了双语的几种重要的分类、双语和认知发展及元语言意识发展的关系、相关的理论解释以及双语儿童认知优势的内在机制,最后对已有研究进行了评述并提出了需要进一步研究的问题。     

The cognitive profile of Chinese children with mathematics difficulties

This study examined how four domain-specific skills (arithmetic procedural skills, number fact retrieval, place value concept, and number sense) and two domain-general processing skills (working memory and processing speed) may account for Chinese children’s mathematics learning difficulties. Children with mathematics difficulties (MD) of two age groups (7-8 and 9-11 years) were compared with age-matched typically achieving children. For both age groups, children with MD performed significantly worse than their age-matched controls on all of the domain-specific and domain-general measures. Further analyses revealed that the MD children with literacy difficulties (MD/RD group) performed the worst on all of the measures, whereas the MD-only group was significantly outperformed by the controls on the four domain-specific measures and verbal working memory. Stepwise discriminant analyses showed that both number fact retrieval and place value concept were significant factors differentiating the MD and non-MD children. To conclude, deficits in domain-specific skills, especially those of number fact retrieval and place value understanding, characterize the profile of Chinese children with MD.     

Basic number processing in children with specific learning disorders: Comorbidity of reading and mathematics disorders

As well as being the hallmark of mathematics disorders, deficits in number processing have also been reported for individuals with reading disorders. The aim of the present study was to investigate separately the components of numerical processing affected in reading and mathematical disorders within the framework of the Triple Code Model. Children with reading disorders (RD), mathematics disorders (MD), comorbid deficits (RD + MD), and typically developing children (TD) were tested on verbal, visual-verbal, and nonverbal number tasks. As expected, children with MD were impaired across a broad range of numerical tasks. In contrast, children with RD were impaired in (visual-)verbal number tasks but showed age-appropriate performance in nonverbal number skills, suggesting their impairments were domain specific and related to their reading difficulties. The comorbid group showed an additive profile of the impairments of the two single-deficit groups. Performance in speeded verbal number tasks was related to rapid automatized naming, a measure of visual-verbal access in the RD but not in the MD group. The results indicate that deficits in number skills are due to different underlying cognitive deficits in children with RD compared to children with MD: a phonological deficit in RD and a deficit in processing numerosities in MD.     

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.     

Basic numerical skills in children with mathematics learning disabilities: a comparison of symbolic vs non-symbolic number magnitude processing

Forty-five children with mathematics learning disabilities, with and without comorbid reading disabilities, were compared to 45 normally achieving peers in tasks assessing basic numerical skills. Children with mathematics disabilities were only impaired when comparing Arabic digits (i.e., symbolic number magnitude) but not when comparing collections (i.e., non-symbolic number magnitude). Moreover, they automatically processed number magnitude when comparing the physical size of Arabic digits in an Stroop paradigm adapted for processing speed differences. Finally, no evidence was found for differential patterns of performance between MD and MD/RD children in these tasks. These findings suggest that children with mathematics learning disabilities have difficulty in accessing number magnitude from symbols rather than in processing numerosity per se.     

Can we predict mathematical learning disabilities from symbolic and non‐symbolic comparison tasks in kindergarten? Findings from a longitudinal study

Background. The ability to compare numbers, as the most basic form of number sense, has been related to arithmetical achievement. Aims. The current study addressed the predictive value of non‐symbolic and symbolic (number word (NW) and Arabic number (AN)) comparison for arithmetics by means of a longitudinal design. Sample. Sixteen children with mathematical disabilities (MD), 64 low achievers (LA), and 315 typical achieving (TA) children were followed from kindergarten till grade 2. Method. The association of comparison skills with arithmetical skills in grades l and 2 was studied. The performances of MD, LA and TA children were compared. Results. Regression analyses showed that non‐symbolic skills in kindergarten were predictively related to arithmetical achievement 1 year later and fact retrieval 2 years later. AN comparison was predictively related to procedural calculation 2 years later. In grade 2, there was an association between both symbolic tasks and arithmetical achievement. Children with MD already had deficits in non‐symbolic and symbolic AN comparison in kindergarten, whereas in grade 2 the deficits in processing symbolic information remained. Conclusions. The combination of non‐symbolic and symbolic deficits represents a risk of developing MD.     

数学困难儿童的数学估计能力

对数学困难儿童(简称数困)的数学估计进行探讨有助于理解数困的成因和寻找适当的干预措施。本文在简要回顾数困和估计的概念基础上, 重点对近年来国内外关于数困儿童数学估计(主要是估算和估数)的表现及影响因素、神经基础和相关的干预研究进行了回顾和梳理, 并强调未来对数困儿童的数学估计研究应注重从选取被试、扩展研究范围和加强干预方案设计等方面开展探讨。     

Numerical and arithmetical cognition: a longitudinal study of process and concept deficits in children with learning disability

Based on the stability and level of performance on standard achievement tests in first and second grade (mean age in first grade = 82 months), children with IQ scores in the low-average to high-average range were classified as learning disabled (LD) in mathematics (MD), reading (RD), or both (MD/RD). These children (n = 42), a group of children who showed variable achievement test performance across grades (n = 16), and a control group of academically normal peers (n = 35) were administered a series of experimental and psychometric tasks. The tasks assessed number comprehension and production skills, counting knowledge, arithmetic skills, working memory, the ease of activation of phonetic representations of words and numbers, and spatial abilities. The children with variable achievement test performance did not differ from the academically normal children in any cognitive domain, whereas the children in the LD groups showed specific patterns of cognitive deficit, above and beyond the influence of IQ. Discussion focuses on the similarities and differences across the groups of LD children.