数学概念的理解问题

对数学概念的理解问题是数学学习理论中的重要理论问题．就刻划数学概念理解的重要概念——数学概念的心理表征和数学概念理解的认知基础进行分析，从而对数学概念的理解问题有更深入的认识。     

数学概念表征缺失引起的理解障碍探析

数学概念学习中,概念理解是首要的;认知心理学研究表明,学生数学概念的获得是一个对概念心理表征的构建过程;相关的数学概念表征的调查研究也证明了数学概念表征与概念理解是相互促进、相互制约的;根据学生在数学概念学习中,对因概念表征缺失引起的概念理解障碍进行认知分析。     

坐标运算法,平面向量的一种另解

向量是近代数学中重要和基本的数学概念之一,它是沟通代数、几何与三角函数的一种工具,有着极其丰富的实际背景.但是学生对平面向量与平面几何图形综合的题目感到害怕,其主要原因是学生对平面向量的概念理解不够全面、不够透彻,对平面向量的二维性及平面向量基本定理的理解应用不熟练.对于这样的试题,可另辟蹊径,采用坐标云算法.     

平面向量“数形”之美——以平行四边形为内核的一类平面向量问题

引入平面向量的概念后,几何图形与代数运算得以交融,图形语言的直观美与向量语言的简洁美融会贯通.中学生对平面向量之所以"望而生畏"往往是由于对平面向量的双属性理解不透.通过对以平行四边形为内核的一类平面向量问题进行深入分析,能让学生更好地理解平面向量的数形之美.     

基于Pirie-Kieren数学理解模型的高中数学概念教学策略初探——以"弧度制"教学为例

Pirie-Kieren数学理解模型直观地描述了学生数学理解的过程和本质,是从认知的观点全面认识数学理解的理论.本文从创设问题背景,引发积极理解意向;创设探究活动,促进产生概念表象;创设反思对比,引导认识概念本质;创设应用问题,促使获得理性认识这四个方面,阐述如何运用Pirie-Kieren数学理解模型设计弧度制的教学,拟对高中数学概念的教学策略进行探讨,从而构建促进关系性理解的数学课堂.     

形成数学概念体系对掌握数学概念的作用

提出数学概念体系的特点。运用现代认知同化理论,分析了数学概念体系对数学概念的理解、保持及运用的作用,并得出了这一过程的结构关系。     

基于“学为中心”的概念教学优化策略

<正>数学概念是反映现实世界的空间形式和数量关系的本质属性的思维形式,是进行数学思维的基本单位.众所周知,学生获得概念的方式有两种:一种是由学生从大量同类事物的不同例证中独立发现其共同的关键属性,叫做概念形成;一种是用定义的方式向学生直接揭示,学生利用已有认知结构中的有关知识来理解新概念,叫做概念同化.无论是哪一种概念获得方式,对学生而言,概念都是抽象的,要让学生顺利获得概念、理解概念、应用概念,就需要教师以"学为     

平面向量的概念与平面向量的基本定理

平面向量是初等数学的重要概念,它集数、形于一体,是沟通代数、几何与三角函数的一种重要工具.本文通过对平面向量的概念及线性运算、平面向量基本定理的认识和理解,把相关内容进行归纳整理,以便同学们在复习中能系统掌握这一知识.     

用数学思想解决平面向量问题

向量是重要而基本的数学概念之一，它是沟通代数、几何与三角函数的一种工具，有着极其丰富的实际背景，向量也是近年高考必考的内容．同学们在学习这部分知识时，应注意理解向量问题中渗透的数学思想方法，有意识地运用向量解决相应问题．下面对平面向量中的几种常用思想方法举例说明．     

数学概念教学“六环节”的设计

<正>教学实践证明,数学概念教学应包括以下六个环节:概念的引入—概念的形成—概括概念—明确概念—应用概念—形成认知.本文就此"六环节"的教学设计进行简要概述,与同行交流探讨.1.概念的引入概念的引入通常有两类:一类是从数学概念体系的发展过程引入,另一类是从实际问题引入.(1)从数学概念体系的发展过程引入.例如:在讲分数指     

理查德·梅耶多媒体学习的理论基础

梅耶的多媒体学习理论是建立在坚实的理论基础和可靠的实证经验基础上的科学体系。多媒体学习的认知理论是理解多媒体学习的关键。双重通道假设、容量有限假设和主动加工假设是梅耶构建多媒体学习认知理论的基石,也是整个多媒体学习科学体系的逻辑起点。这三大假设赖以成立的理论前提正是双重编码理论、工作记忆模型、生成学习理论和认知负荷理论,由此构成了多媒体学习的理论基础。具体而言,双重编码理论和工作记忆模型为多媒体学习的认知理论构建提供了关键概念与元素;生成学习理论则为多媒体学习的认知理论构建提供了基本的解释性框架;多媒体学习的认知理论正是由这些关键概念、元素和解释性框架整合而成;而认知负荷理论则以多媒体学习的认知理论为基础,进而为多媒体教学的系列设计原理提供了关键支撑。     

图形-背景论框架下的英语分裂句再认识

图形-背景理论是一种认知观,1915年由丹麦心理学家鲁宾(Rubin)首先提出,后由完形心理学家借鉴来研究知觉(主要是视觉和听觉)及描写空间组织的方式,再后来被认知语言学家用来研究语言结构的意义.图形-背景分离原则是空间组织的一个基本认知原则,同时也是语言组织概念内容的一个基本认知原则.确定“背景“和“目标“是主客观结合的结果,但最终以主观为准.本文从图形-背景论的基本思想出发,对英语分裂句(it-clefts)进行了重新认识.     

Model based learning as a key research area for science education

A framework is presented for thinking about cognitive factors involved in model construction in the classroom that can help us organize the research problems in this area and the articles in this issue. The framework connects concepts such as: expert consensus model, target model, intermediate models, preconceptions, learning processes, and natural reasoning skills. By connecting and elaborating on these major areas, the articles in this issue have succeeded in moving us another step toward having a theory of conceptual change that can provide guidance to teachers in the form of instructional principles. Taken together, the articles remind us that individual cognition, while not the only factor in learning, is a central determining feature of learning. However, we must work to further develop the present partial theory of conceptual change to fill in the missing cognitive core of the present shell.     

APOS理论下高职化工专业高等数学概念教学方法探究

美国数学教育家杜宾斯基提出的APOS理论是一种建构主义的数学学习理论,他将数学概念的建构分为Action、Process、Object、Scheme四个阶段.在对该理论的认识基础上,结合高职学生数学学习认知的心理特点,对化工专业高等数学概念的教学进行探讨,并就如何进行数学概念教学设计作了探索,使学生主动建构其概念体系.     

Mathematics and learning disabilities

Between 5% and 8% of school-age children have some form of memory or cognitive deficit that interferes with their ability to learn concepts or procedures in one or more mathematical domains. A review of the arithmetical competencies of these children is provided, along with discussion of underlying memory and cognitive deficits and potential neural correlates. The deficits are discussed in terms of three subtypes of mathematics learning disability and in terms of a more general framework for linking research in mathematical cognition to research in learning disabilities.     

An exploration of interrelationships among presence indicators of a community of inquiry in a 3D game-like environment for high school programming courses

The combination of Open Sim and Scratch4OS can be a worthwhile innovation for introductory programming courses, using a Community of Inquiry (CoI) model as a theoretical instructional design framework. This empirical study had a threefold purpose to present: (a) an instructional design framework for the beneficial formalization of a virtual community, by utilizing a CoI model which consisted of 81 high school students and (b) the results of linear correlations to amplify the interrelationships among presence indicators (cognitive, social, and teaching) of a CoI model to learn basic programming concepts via a 3D multi-user game-like environment underpinned by Papert‘s theory of constructionism. The findings indicated that social presence (communication and cohesiveness of a group) had not only a direct correlation with the cognitive presence (learning process for the construction of knowledge), but also had a positive association with teaching presence (organization, planning, and guidance of learning activities), reinforcing them as well.     

连接主义理论框架下的母语迁移研究

连接主义是认知心理学的核心理论。该理论很好地解释了大脑中的认知机制,极大地促进了二语习得的研究。母语迁移作为二语习得研究中的根本性问题,近半个世纪来引起了各个理论学派的关注。论文从连接主义理论基础出发,解释了二语习得中的母语迁移现象。     

Teachers’ Attitudes Towards Their Pupils’ Mathematical Errors

This article is mainly concerned with the didactical and the epistemological approach towards pupils’ errors in mathematics. The findings of an investigation into a representative sample of Cypriot teachers’ attitudes of errors in mathematics are presented. Although teachers draw on behaviourism as a way of understanding pupils’ errors, a considerable number of teachers seem to be influenced by both cognitive science error theory and the obstacle theory. Inferential statistical analysis revealed that teachers’ attitudes of errors are mainly associated with the attendance of a specialised INSET course in mathematics. Teachers who attended the INSET course in mathematics are generally more influenced by the cognitive science theory and the obstacle theory. Implications for the development of policy on teacher training are discussed. It is argued that with appropriate training teachers will be able to adopt a model of interpreting errors in mathematics based on the didactical and the epistemological approaches.     

Mathematical practices in a technological workplace: the role of tools

This paper investigates the role of tools in the formation of mathematical practices and the construction of mathematical meanings in the setting of a telecommunication organization through the actions undertaken by a group of technicians in their working activity. The theoretical and analytical framework is guided by the first-generation activity theory model and Leont’ev’s work on the three-tiered explanation of activity. Having conducted a 1-year ethnographic research study, we identified, classified, and correlated the tools that mediated the technicians’ activity, and we studied the mathematical meanings that emerged. A systemic network was generated, presenting the categories of tools such as mathematical (communicative, processes, and concepts) and non-mathematical (physical and written texts). This classification was grounded on data from three central actions of the technicians’ activity, while the constant interrelation and association of these tools during the working process addressed the mathematical practices and supported the construction of mathematical meanings that this group developed from the researchers’ perspective. Technicians’ emerging mathematical meanings referred to place value, spatial, and algebraic relations and were expressed through personal algorithms and metaphorical and metonymic reasoning. Finally, the educational implications of the findings are discussed.