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。     

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。     

A Negationless Interpretation of Intuitionistic Theories. I

The present work contains an axiomatic treatment of some parts of the restricted version of intuitionistic mathematics advocated by G. F. C. Griss, also known as negationless intuitionistic mathematics. Formal systems NPC, NA, and FIM ^N for negationless predicate logic, arithmetic, and analysis are proposed. Our Theorem 4 in Section 2 asserts the translatability of Heyting's arithmetic HAinto NA. The result can in fact be extended to a large class of intuitionistic theories based on HAand their negationless counterparts. For instance, in Section 3 this is shown for Kleene's system of intuitionistic analysis FIMand our FIM ^N . This revised version was published online in June 2006 with corrections to the Cover Date.     

学科领域知识与数学学习的知识表征研究

根据领域知识的结构特点对初中数学学科知识作出改编和重组,形成数学学科领域知识单元进行教学实验,以215名普通初中二年级学生为被试,通过自编问卷和深度访谈考察学科领域知识对知识表征的影响,并探讨了知识表征与数学学业成绩之间的关系。研究发现:(1)学科领域知识可以显著提高学生数学陈述性知识表征全面性和总体水平;(2)学科领域知识可以显著提高学生的程序性知识表征全面性、自动化、组织性和总体水平;(3)认知结构三要素、陈述性知识表征及程序性知识表征与数学成绩显著相关;(4)学优生的陈述性知识表征准确性、总体水平和程序性知识表征组织性、总体水平显著高于中等生和学困生。     

数学学习困难与工作记忆关系研究的现状与前瞻

工作记忆是一种对信息进行暂时加工和贮存的能量有限的记忆系统,在许多复杂的认知活动中起重要作用,工作记忆缺陷是造成数学学习困难的根本原因。数学学习困难儿童都存在视觉空间模板、语音回路以及中央执行器功能等方面的缺陷,工作记忆的各成分对数学困难者的影响不同。今后研究将以整体的、发展的视角,不断改进研究方法,将行为研究和神经加工机制研究相结合。     

Racing dragons and remembering aliens: Benefits of playing number and working memory games on kindergartners' numerical knowledge

Sources that contribute to variation in mathematical achievement include both numerical knowledge and general underlying cognitive processing abilities. The current study tested the benefits of tablet‐based training games that targeted each of these areas for improving the mathematical knowledge of kindergarten‐age children. We hypothesized that playing a number‐based game targeting numerical magnitude knowledge would improve children's broader numerical skills. We also hypothesized that the benefits of playing a working memory (WM) game would transfer to children's numerical knowledge given its important underlying role in mathematics achievement. Kindergarteners from diverse backgrounds (n = 148; 52% girls; M_age = 71.87 months) were randomly assigned to either play a number‐based game, a WM game, or a control game on a tablet for 10 sessions. Structural equation modeling was used to model children's learning gains in mathematics and WM across time. Overall, our results suggest that playing the number game improved kindergarten children's numerical knowledge at the latent level, and these improvements remained stable as assessed 1 month later. However, children in the WM group did not improve their numerical knowledge compared to children in the control condition. Playing both the number game and WM game improved children's WM at the latent level. Importantly, the WM group continued to improve their WM for at least a month after playing the games. The results demonstrate that computerized games that target both domain‐specific and domain‐general skills can benefit a broad range of kindergarten‐aged children.     

First demonstration of effective spatial training for near transfer to spatial performance and far transfer to a range of mathematics skills at 8 years

There is evidence that spatial thinking is malleable, and that spatial and mathematical skills are associated (Mix et al. [2016] Journal of Experimental Psychology: General, 145, 1206; Mix et al. [2017] Journal of Cognition and Development, 18, 465; Uttal et al. [2013] Psychological Bulletin, 139, 352). However, few studies have investigated transfer of spatial training gains to mathematics outcomes in children, and no known studies have compared different modes of spatial instruction (explicit vs. implicit instruction). Based on a sample of 250 participants, this study compared the effectiveness of explicit and implicit spatial instruction in eliciting near transfer (to the specific spatial skills trained), intermediate transfer (to untrained spatial skills) and far transfer (to mathematics domains) at age 8. Spatial scaling and mental rotation skills were chosen as training targets as previous studies have found, and proposed explanations for, associations between these skills and mathematics in children of this age (Journal of Experimental Psychology: General, 145, 2016 and 1206). In this study, spatial training led to near, intermediate and far transfer of gains. Mental visualization and proportional reasoning were proposed to explain far transfer from mental rotation and spatial scaling skills respectively. For most outcomes, except for geometry, there was no difference in the effectiveness of implicit (practice with feedback) compared to explicit instruction (instructional videos). From a theoretical perspective, the study identified a specific causal effect of spatial skills on mathematics skills in children. Practically, the results also highlight the potential of instructional videos as a method of introducing spatial thinking into the classroom.     

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。     

Who benefits the most? Teacher expectations and their relation with students’ achievement in mathematics in primary school

Over the past 50 years, many studies have investigated the impact of teacher expectations on student achievement and indicated small to moderate effects. Currently, it is still unclear which student-related factors (e.g. socioeconomic status, or gender) moderate the expectation effect. There is still a need to gain a better understanding of the relation between teacher expectations and students' characteristics. The present study aims to examine the accuracy of teacher expectations as well as student-related moderators of the expectation effects on students' achievement. The analyses are based on data from a longitudinal study including 28 primary school teachers and their students (N = 509). The results show that high expectations of teachers correlated positively with student achievement in mathematics, although no significant moderating effects were found. These findings strengthen the importance of ensuring high teacher expectations for all students.     

数学焦虑对儿童加减法认知策略选择和执行的影响

根据数学焦虑量表测查结果,随机选取90名小学1~3年级的儿童为被试,每个年级30人(高、低数学焦虑者各15人).采用实验法、观察法和口语报告法相结合的方式,探讨不同数学焦虑水平儿童加减法认知策略选择和执行情况.结果发现:(1)从策略选择上看,高数学焦虑儿童使用出声策略和手势策略较多;使用对位策略较少.(2)从策略执行上看,高数学焦虑儿童出声策略、手势策略和拆十策略执行的正确率较高;竖式策略和对位策略执行的正确率较低;(3)随着儿童年级的增长,数学焦虑对其策略选择的影响越来越显著.