两种类型数学困难儿童的执行水平

使用Crack the Code任务考察单纯型与混合型数学困难小学儿童的执行水平,结果发现:单纯型数学困难儿童在对认知资源要求较高的任务上的执行水平显著低于数学优良生,但在认知要求较低的任务上二者之间没有显著差异;混合型数学困难儿童执行水平最低,在两个难度水平执行任务上的表现均显著差于数学优良生、单纯型数学困难儿童.小学儿童执行水平年级差异似乎主要表现在认知负荷较高的任务上,1年级学生与3、5年级学生的执行水平存在显著差异.     

数学学习困难儿童的编码加工特点:基于PASS理论的研究

同时加工和继时加工是PASS模型中的两类编码加工,二者在数学学习中发挥重要作用。使用基于PASS理论的认知评估系统（DN：CAS）单纯型数学困难、混合型数学困难和正常小学生进行两类编码加工的测评,比较研究发现,两类困难学生的两类编码加工水平均显著低于正常儿童,两类困难学生间的同时加工差异不显著,而混合型困难学生的继时加工水平显著低于单纯型困难学生。较低的同时加工水平似乎是两类数学困难的共同特征,继时加工水平的差异则似可作为单纯型与混合型困难的区分指标之一。     

不同亚型数学学习困难儿童应用题问题表征过程的研究

采用自编数学应用题解决能力测验题对小学四年级单纯型数困儿童、混合型数困儿童和普通儿童问题理解阶段、问题整合阶段的差异,以及问题表征能力与数学问题解决之间的关系进行探究。结果表明：（1）单纯型与混合型数困儿童有效识别信息的能力弱,难于利用相关信息和排除干扰信息。（2）单纯型数困儿童比混合型数困儿童更擅于运用图式表征策略。（3）图式表征策略能促进数困儿童应用题的解决。     

听障儿童抑制控制能力特点及其与数学基本能力的关系

采用Flanker实验范式与中国小学生数学基本能力测试量表,以97名听障儿童与97名健听儿童为被试,考察听障儿童抑制控制能力与其数学基本能力的关系。结果发现：（1）听障儿童抑制控制能力水平显著低于健听儿童;（2）听障儿童数学基本能力显著低于健听儿童;（3）听障儿童抑制控制能力与数学基本能力之间相关显著,且抑制控制能力能够预测听障儿童的逻辑思维与空间–视觉能力。     

数学学习困难初中生的中央执行系统特点

为揭示数学学习困难学生的认知过程加工特点,筛选上海111名初中生（男生46名,女生68名,平均年龄11.97岁）比较数学困难学生（55名）与数学优秀学生（56名）的中央执行系统的表现差异,通过反应停止任务和Flanker任务考察抑制能力以及注意控制能力。结果发现各种抑制和注意控制条件下,数困组学生的正确率低于数优组;在具有干扰的情况的成绩更能有效预测数学成绩;中央执行系统能力在初中总体具有上升发展趋势,数困生的发展具有波动性。因此,数学学习困难在中央执行系统中的缺损主要是对抗干扰的能力不足,而非简单的加工速度。     

儿童执行功能对数学能力的预测模型

使用数点数广度任务(C-span)、Stroop任务、威斯康星卡片分类任务(WCST)测查儿童的执行功能,用《小学儿童数学能力测查量表》(一年级)、《韦克斯勒儿童智力测量》分别测查儿童的数学能力和智力,对64名小学一年级儿童的执行功能(抑制、转换、刷新)和数学能力的关系进行了研究,相关分析和回归分析发现,数学能力与执行功能任务测量都有显著相关,抑制、转换和刷新都分别对数学能力存在显著回归效应;在此基础上,建立了执行功能及其对儿童数学能力的预测模型。结果表明,抑制控制、转换和刷新都能对数学能力产生直接影响,但抑制控制还通过转换和刷新对数学能力产生间接影响。说明儿童数学能力的认知差异,主要在于抑制控制能力的差异,而抑制控制的差异又导致转换和刷新能力表现的差异。     

5～6岁不同数学能力水平儿童的执行功能差异研究

为了考察不同数学能力水平儿童的执行功能差异,根据331名学前儿童的数学能力得分选取了潜在数学学习困难儿童组、低分组、典型发展儿童组和数学优秀组等4个实验组。首先分析了各组儿童的执行功能差异特点,之后使用判别分析进一步探索了各执行功能子结构对儿童早期数学能力差异分组的贡献。结果表明:相对于典型发展儿童组,潜在数学学习困难儿童在执行功能的更新、抑制和转换方面普遍缺损;低分组儿童则仅表现出数字更新能力不足;数学优秀组在数字更新和有时间要求的认知转换方面比典型发展组有明显优势。进一步判别分析表明,对早期数学能力差异分组贡献最大的并非独立执行功能子结构,而是更新和转换的共同因素结构。     

小学低年级儿童的计算流畅性与数学焦虑:基于变量为中心与个体为中心的分析

为考察计算流畅性对小学低年级儿童数学焦虑的影响及作用机制,对592名小学二年级儿童的计算流畅性、数学学习兴趣、教师支持和数学焦虑进行测查。结果发现:(1)计算流畅性不仅通过数学学习兴趣间接影响数学焦虑,也可通过数学学习兴趣进而通过教师支持间接影响数学焦虑;(2)对计算流畅性和数学学习兴趣得分进行潜剖面分析,可将儿童区分为三种类型:低能力-低兴趣型、高能力-高兴趣型和低能力-高兴趣型;(3)低能力-低兴趣型儿童的数学焦虑得分显著高于其他两类,而低能力-高兴趣型和高能力-高兴趣型儿童的数学焦虑得分则无显著差异。上述结果表明计算流畅性、数学学习兴趣和教师支持在预防和干预小学低年级儿童的数学焦虑中具有重要作用。     

小学低年级儿童的计算流畅性与数学焦虑:基于变量为中心与个体为中心的分析

为考察计算流畅性对小学低年级儿童数学焦虑的影响及作用机制,对592名小学二年级儿童的计算流畅性、数学学习兴趣、教师支持和数学焦虑进行测查。结果发现:(1)计算流畅性不仅通过数学学习兴趣间接影响数学焦虑,也可通过数学学习兴趣进而通过教师支持间接影响数学焦虑;(2)对计算流畅性和数学学习兴趣得分进行潜剖面分析,可将儿童区分为三种类型:低能力-低兴趣型、高能力-高兴趣型和低能力-高兴趣型;(3)低能力-低兴趣型儿童的数学焦虑得分显著高于其他两类,而低能力-高兴趣型和高能力-高兴趣型儿童的数学焦虑得分则无显著差异。上述结果表明计算流畅性、数学学习兴趣和教师支持在预防和干预小学低年级儿童的数学焦虑中具有重要作用。     

数学学习困难儿童的加工速度与工作记忆

以数学学习困难儿童为研究对象,系统考察了数学学习困难儿童与控制组的加工速度和工作记忆,比较了工作记忆和加工速度对数学学习困难影响的相对贡献.结果发现,与控制组相比,数学学习困难儿童在工作记忆和加工速度方面均存在明显的不足,但加工速度不能解释不同能力组之间的差异,数学学习困难儿童的缺陷在于工作记忆能力的下降.工作记忆缺陷在于数字工作记忆、视空间工作记忆和中央执行功能的整体不足,中央执行功能对数学学习困难儿童影响的解释量最大.     

Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties

This study examined numerical magnitude processing in first graders with severe and mild forms of mathematical difficulties, children with mathematics learning disabilities (MLD) and children with low achievement (LA) in mathematics, respectively. In total, 20 children with MLD, 21 children with LA, and 41 regular achievers completed a numerical magnitude comparison task and an approximate addition task, which were presented in a symbolic and a nonsymbolic (dot arrays) format. Children with MLD and LA were impaired on tasks that involved the access of numerical magnitude information from symbolic representations, with the LA children showing a less severe performance pattern than children with MLD. They showed no deficits in accessing magnitude from underlying nonsymbolic magnitude representations. Our findings indicate that this performance pattern occurs in children from first grade onward and generalizes beyond numerical magnitude comparison tasks. These findings shed light on the types of intervention that may help children who struggle with learning mathematics.     

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.     

Numerical and nonnumerical estimation in children with and without mathematical learning disabilities

There are currently multiple explanations for mathematical learning disabilities (MLD). The present study focused on those assuming that MLD are due to a basic numerical deficit affecting the ability to represent and to manipulate number magnitude ( Butterworth, 1999 , 2005 ; A. J. Wilson & Dehaene, 2007 ) and/or to access that number magnitude representation from numerical symbols ( Rousselle & No?l, 2007 ). The present study provides an original contribution to this issue by testing MLD children (carefully selected on the basis of preserved abilities in other domains) on numerical estimation tasks with contrasting symbolic (Arabic numerals) and nonsymbolic (collection of dots) numbers used as input or output. MLD children performed consistently less accurately than control children on all the estimation tasks. However, MLD children were even weaker when the task involved the mapping between symbolic and nonsymbolic numbers than when the task required a mapping between two nonsymbolic numerical formats. Moreover, in the estimation of nonsymbolic numerosities, MLD children relied more than control children on perceptual cues such as the cumulative area of the dots. Finally, the task requiring a mapping from a nonsymbolic format to a symbolic format was the best predictor of MLD. In order to explain these present results, as well as those reported in the literature, we propose that the impoverished number magnitude representation of MLD children may arise from an initial mapping deficit between number symbols and that magnitude representation.     

数学学业不良初中生的工作记忆特点：领域普遍性还是特殊性?

研究选取上海111名(男生48名, 女生63名, 平均年龄11.97岁)初中学生(数学学业不良学生55名与数学学业优秀学生56名), 根据国家数学课程标准, 将数学划分为数与代数、空间与几何两部分, 又从空间与几何领域中选取初一数学学业知识点—— 轴对称和中心对称图形, 分析在不同内容知识领域的解答过程中所涉及的工作记忆成分。结果发现：(1)数与代数学习需要中央执行系统、视觉-空间模板、语音环路三个成分的共同作用; 空间与几何学习主要受到视觉-空间模板和中央执行系统的影响, 但不存在语音环路的影响。(2)对轴对称与中心对称图形任务的成绩影响最大的是视觉-空间模板, 其次是中央执行系统, 语音环路对该任务作用不明显。两个研究说明工作记忆在初中不同年级的各类数学学业任务中具有不同的作用, 中央执行系统和视觉-空间模板相对更具有普遍性作用, 语音环路具有特殊性作用, 并且随着年龄增高, 视觉－空间模板对数学学业任务的作用更为突显。     

How does the severity of a learning disability affect working memory performance?

Working memory performance was examined in children aged 11-12 years who had borderline, mild, and moderate learning disabilities. Comparisons with children of average abilities were used to determine whether those with more severe learning disabilities had greater impairments in working memory. Seven measures of working memory span were used to assess temporary phonological short-term storage (digit span, word span), temporary visuo-spatial short-term storage (pattern span, spatial span), and temporary short-term storage with additional processing, or central executive, demands (listening span. odd one out span, reverse digit span). Children with mild and moderate learning disabilities were impaired on all measures of working memory compared to children of average abilities. Children with borderline learning disabilities were just as good as children with average abilities on visuo-spatial and complex span tasks, but showed an impairment on phonological span tasks. Children with moderate learning disabilities were indistinguishable from children with mild learning disabilities on simple span tasks, but were significantly poorer than the mild group on the more demanding complex span tasks. For the group as a whole, working memory was strongly related to mental age.     

How does the severity of a learning disability affect working memory performance?

Working memory performance was examined in children aged 11-12 years who had borderline, mild, and moderate learning disabilities. Comparisons with children of average abilities were used to determine whether those with more severe learning disabilities had greater impairments in working memory. Seven measures of working memory span were used to assess temporary phonological short-term storage (digit span, word span), temporary visuo-spatial short-term storage (pattern span, spatial span), and temporary short-term storage with additional processing, or central executive, demands (listening span, odd one out span, reverse digit span). Children with mild and moderate learning disabilities were impaired on all measures of working memory compared to children of average abilities. Children with borderline learning disabilities were just as good as children with average abilities on visuo-spatial and complex span tasks, but showed an impairment on phonological span tasks. Children with moderate learning disabilities were indistinguishable from children with mild learning disabilities on simple span tasks, but were significantly poorer than the mild group on the more demanding complex span tasks. For the group as a whole, working memory was strongly related to mental age.     

Sensitivity to general and specific numerical features in typical achievers and children with mathematics learning disability

We examined the development of sensitivity to general and specific numerical features in typical achievers and in 6th and 8th graders with mathematics learning disability (MLD), using two effects in mental multiplication: operand-relatedness (i.e., difficulty in avoiding errors that are related to the operands via a shared multiplication row) and decade-consistency (i.e., difficulty in avoiding errors that are operand related and also share a decade with the true result). Responses to decade-consistent products were quick but erroneous. In line with the processing sequence in adults, children first became sensitive to the general numerical feature of operand-relatedness (typical achievers—from 3rd grade; children with MLD in 8th grade) and only later to the specific feature of decade-consistency (typical achievers—from 4th grade, but only from 6th grade in a mature pattern). Implications of the numerical sensitivity in children with MLD are discussed.