数学符号与数学理解的关系

对数学符号、数学语言及数学理解之间的关系进行探讨，给出了用符号思想理解学习数学新概念(续创概念、新创概念)的方法。     

On Some Mathematical Aspects of Magnetohydro-and Plasma-Dynamics

The author presents a review of some mathematical aspects of magnetohydrodynamics and plasma-dynamics, and the fields of mathematics required and used in those domains are briefly discussed. The last section is devoted to the discussion of adjusting the mathematical program of a university, from the point of view of engineering, physics and mathematics, so that a greater number of students in those disciplines will be prepared for graduate courses in magnetohydrodynamics and plasma-dynamics.     

元认知开发与数学问题解决

元认知包括元认知知识、元认知检验和元认知监控三个成分。元认知的实质是主体对认知活动的自我意识和自我调节。根据学习的认知理论，数学学习过程是一个数学认知过程，教学教育的根本任务是发展学生的数学认知结构。数学问题解决是创造性的教学思维活动，创造心理活动本身就是人类心智活动的最高形式。因此，与其它较为低级的心理活动相比，数学问题解决更需要元认知的统摄、调节和监控。     

Representational Tools and Mathematical Understanding

Understanding how cultural mediators and social interaction promote meaningful learning requires that each student's perspective, reasoning, and construction processes be taken into account. In my analysis of the classroom episodes, I consider individual students' progress as they use tools, discuss data distributions, and interact with their teachers and their peers. I argue that data display tools provide a partial context for discussions but do not constrain the students' interpretations or the way they reason about the data. Students' approaches to the mathematical relations discussed in the classroom result rather from the meaning they attribute to the different features of the displays, the teachers' questions, and the evolving interaction with their peers.     

温度梯度的数学理解

借助数学中的梯度概念,指出了热学教材中温度梯度的定义实质上只是温度梯度的模,而不是温度梯度。     

数学问题错解的感悟

深刻剖析了数学问题错解的根源,指出预防错误的具体对策是深化数学基本概念和基本方法．     

侗族数学文化面面观

侗族鼓楼、民居、民间工艺、服饰及刺绣等都蕴涵着丰富的数学文化。侗族从日常生活中的基本运算到生产实践的数学应用所表现出来的古朴的数学思想方法具有鲜明的文化特征,古老的侗族传承着人类古老的数学文化。     

数学理解水平评定方法及其数学模型构建研究

数学理解的水平可以用量来刻画,而且是一个连续量,是一个模糊量。数学理解的因素一般由事实、计算、联系、分辨、表达、转化、推理、应用构成。结合数学学科和数学理解的特点提出了评价数学理解水平的定性和定量相结合的方法——加权求和法。     

企业伦理建设认识上的三个误区

伦理建设已成为企业在国际竞争中提升竞争力的重要手段。我国不少企业对企业伦理漠视 ,对企业目标片面理解 ,看不到企业伦理对企业经济目标实现的作用。澄清企业伦理问题上的片面错误的认识 ,是推进我国企业伦理建设首先要解决的问题。     

中学生对函数概念的理解——历史相似性初探

高一新生和高三学生用自己的语言对函数的描述涵盖了从17世纪莱布尼兹到20世纪布尔巴基学派诸多数学家的各种定义,他们的理解与历史上数学家的理解有着高度的相似性.在中学,课本上函数的抽象定义不易于理解和记忆,学生也往往不从定义出发来理解函数;函数概念历史发展过程中的认识论障碍也会成为课堂上学生的认知障碍.在函数概念的教学中,应该恰当地借鉴历史,以帮助学生更好地理解该概念.     

Statistical and Mathematical Aspects of Ranking: Lessons from Poland

This paper presents both the formal and methodological variety of ranking approaches, and asks whether a really objective ranking is possible. A ranking represents compiled information, provided according to a criterion or set of criteria. Its purpose is to highlight real or perceived differences in quality. Ranking methodology refers to its criteria, the features allowing for measurement. Methods of aggregation, which focus on weightings, and different means of classification, suggest that a single, objective ranking could not exist.     

零起点学生对俄语动词体的认知与理解

在俄语学习实践中,动词是最丰富、最复杂的一种词类。俄语动词分为完成体动词和未完成体动词两种形式。动词体是零起点学生最难理解和掌握的一项语法知识。从动词体的概述及体的对偶,两体的基本意义和一些实践用法四个方面对动词体进行全方位、详细的介绍,以帮助零起点学生对俄语动词体有一个正确的认知与了解。     

重新认识第二次数学危机

深入讨论了数学分析中“x→0”的数量形式，分析了无穷小方法、标准分析方法、非标准分析方法这三代数学分析理论的本质及之间的异同点，得出明确的结论：三百多年来无穷小悖论悬而未决，第二次数学危机名亡实存，是现有数学基础理论中所存在的“有穷－无穷”理论体系及相关的数量体系中的本质性缺陷使人们不具备认识数学中所有“x→0”的数量形式的能力，不具备解决第二次数学危机的能力。     

Aspects of a Practical Understanding: Heidegger at the workplace

This article aims to clarify some of our pre‐conceived assumptions when we address issues of learning in practice. It argues that we need to develop an understanding of practice based on its own premises. For this purpose the German philosopher Martin Heidegger's (1889–1976) understanding of practice and learning is introduced. Heidegger emphasises the use of equipment as crucial for a practical understanding. This perspective is contrasted with an intellectualistic approach to learning in practice exemplified by the work of Donald Schön. Heidegger and Schön's perspectives on learning in practice are evaluated and discussed throughout the article. Examples from studies of apprenticeship are used to illustrate Heidegger's comprehension of learning in practice. Especially learning through the use of tools and equipment, learning in context, learning as a consequence of making mistakes and learning as a matter of developing a sense of familiarity are types of learning emphasised in this article.     

Metacognition,General Ability,and Mathematical Understanding

The purpose of the present study was threefold: (a) to examine the extent to which kindergarten children acquire metacognitive knowledge related to mathematics; (b) to investigate the relationships between children's metacognitive knowledge and general ability; and (c) to examine the relative roles of general ability and metacognition in facilitating word problem solutions. Participants were 32 kindergarten children. Results showed that preschoolers acquired a substantial metacognitive knowledge about mathematical word problems. That knowledge was highly correlated with mathematics performance, even after general ability was controlled. The study further shows that metacognition explained more of the variance in mathematics performance than general ability. The theoretical and practical implications of the study are discussed.     

关于数学素养及其培养的若干认识

数学素养是数学教育改革的目标,是提高数学教育质量的关键.在数学课程改革不断深化的今天,准确理解数学素养的概念内涵,认真分析数学素养的培养策略具有十分重要的意义.国外对数学素养研究聚焦的层面并不完全相同,作为一种评价研究,PISA没有涉及数学素养培养的对策研究,对我国数学教育的指导具有一定的局限性.国内关于数学素养的研究主要集中在数学素养内涵讨论、数学素养构成要素探析、数学素养培养策略指导等方面.从数学活动的视角进行分析,应当充分认识不同数学成分所对应数学素养的特殊内涵,并因此做好相关方面的工作.从全球教育的视角进行分析,数学教育应当积极响应并落实科学发展观,积极推进创新培养和实施全球化概念的数学素养教育.     

Metacognition, General Ability, and Mathematical Understanding

The purpose of the present study was threefold: (a) to examine the extent to which kindergarten children acquire metacognitive knowledge related to mathematics; (b) to investigate the relationships between children's metacognitive knowledge and general ability; and (c) to examine the relative roles of general ability and metacognition in facilitating word problem solutions. Participants were 32 kindergarten children. Results showed that preschoolers acquired a substantial metacognitive knowledge about mathematical word problems. That knowledge was highly correlated with mathematics performance, even after general ability was controlled. The study further shows that metacognition explained more of the variance in mathematics performance than general ability. The theoretical and practical implications of the study are discussed.     

小学四年级学生对平均数概念理解的发展过程

利用Pirie和Kieren提出的数学理解发展模型,分析了3名小学四年级学生对平均数概念理解的发展过程.结果表明:学生对平均数概念的理解经历了初步了解、产生表象、形成表象、关注性质和形式化等5个水平.在理解发展过程中,当学生发现他的思想和行动与自己所面临的问题不一致时,他就要折返回内层水平来扩展自己目前的活动能力和活动空间.而教师的干预则激发了学生的折返,为学生提供了独立建构或修正个人表象的机会.     

数学理解及理解障碍的探究

理解在数学学习中占有重要的地位，因此数学理解障碍是数学学习障碍中的一种重要障碍．如果不注重学生是否具有理解的意向，不了解学生的认知水平，就不能帮助学生克服障碍．在教学上，可以通过创设恰当、有趣的教学情境、帮助学生生成正确的数学表象、注重数学交流等途径来排除理解障碍．     

对提高中学数学教师数学修养的思考和尝试

提高中学数学教师的数学修养在塑造人的过程中具有不可替代的作用.在实际调查中我们发现:一方面,教师们对提高自身数学修养水平的热情很高;另一方面,在涉及到具体数学知识时,教师们又往往把自己的眼光仅局限在个人所讲授或熟悉的具体中学课程中,而对关系“较远”的内容则倾向于采取回避和应付的态度.提高教师自身的数学修养是解决目前数学教育中种种弊端的关键.在实际教学中可采用如下方法加强数学教育中数学类课程:(1)加强对数学内容的数学思想和方法论的讲解;(2)加强数学计算和论证的训练;(3)加强与中学数学课程的结合.