认清问题，把握原则，有效发挥口诀的作用

为使学生对数学知识的理解和应用更深刻和灵活，广大的数学教学工作者在长期的数学教学实践中，总结出的数学口诀对提高数学课堂教学效果起到了积极的作用。但在实际教学中，由于学生思维的开阔性和有些数学问题的特殊性，使得数学口诀时有失灵的现象。于是避免数学口诀的失灵，充分发挥数学口诀的作用就成了一个值得数学教学工作者探讨的问题。     

初中数学教学中利用思维导图培养学生的数学表达能力

在课程改革的背景下，初中数学教学应当重视对学生多种能力的培养，尤其是对学生数学表达能力的培养，让学生更加流畅地阐述自身在数学学习中的观点与看法，在严谨的数学交流中，进一步提升自身的数学水平．思维导图作为一种实用的思维工具，对培养学生的数学表达能力具有重要应用作用．文章对教师在初中数学教学中利用思维导图培养学生数学表达能力的形式展开探讨，以期为广大教学工作者提供参考．     

数学解题中的转化策略

数学工作者都离不开解题，解题是教学工作者活动的基本形式和主要内容，是教学工作者的一个存在目的，也是教学工作者的一个兴奋中心。解题策略是解题理论中的一个重要方面。数学解题的策略是为了实现解题目标而采用的方针，它体现了选择的机制和组合的艺术。     

数学与实践浅议

本文首先从数学内容、发展、抽象和证明四个方面议论了数学与实践的关系，然后概括地议论了对数学作为工具、作为科学应持有的看法以及数学与各门科学乃至社会发展的关系。旨在说明：数学工作者若跳出数学问题整天萦绕大脑的圈子，从另一个角度看看数学的“真面目”，也许对工作会有一定的益处。     

特殊化解题思想的功能分析

特殊化思想是一种重要的数学解题思想，其在数学解题中的作用历来受到数学解题研究者及数学教学工作者的高度重视．有许多文章探讨了特殊化思想在数学解题中的重要意义，但目前对特殊化解题思想的功能、类型、实现方式等较细微、深入的研究还比较缺乏．本文仅就特殊化解题思想的功能作一简要分析，并举例加以说明．     

中国心理学界数学教学心理研究的十年进展

数学教学心理是教育心理学工作者的重要研究领域.教育心理学工作者对数学应用题结构、数学能力结构、数学学习发展心理和数学思维策略的训练4个方面进行了大量的研究.对近十年来数学教学心理学的研究进行综述可以促进我国数学教学心理研究的发展.     

高师开设中外数学教育比较选修课的实践与认识

高师开设中外数学教育比较选修课的实践与认识曲阜师范大学数学系陆书环近年来，为了全面贯彻“教育要面向现代化，面向世界，面向未来”的方针，改革中学数学教育，我国许多从事数学教育研究的工作者，对世界上发达国家或地区数学学科教育的具体做法作了大量比较研究，从...     

Mathematical Subject Classification在数学文献信息分类中的应用

美国《数学评论》的分类体系《数学主题分类表》(Mathematical Subject Classification)，是国际数学界影响最大使用最广的数学专业分类表。数学工作者可以使用美国数学会在网站上提供的Mathematical Subject Classification为自己的数学论文标引分类号，也可从该分类途径检索网上的数学信息。     

减负不减质从随堂作业开始

巴班斯基说“教育与个性发展相统一和相互联系是教育过程的规律”因此在中学数学教学中提高作业的效率，发挥作业的功能，平衡作业的容量，创新作业的形式，区别学生的差异，发展学生的个性，都是数学工作者在设计和布置作业时需要认真考虑的问题。作业作为课堂教学的延续，也是实现教学效果的重要环节，有效，科学的随堂检测对减轻学生课外负担有重要作用。如何减轻学生的课业负担，是广大数学工作者乃至社会都极考关注的问题。     

谈数学教学中用"启发法"培养学生素质

实施素质教育对发展和完善现有的基础教育,实现从"应试教育"向素质教育的转化,全面提高教育质量有着重要的意义.而作为具有广泛应用的数学学科,在这一新形势下给广大的数学工作者提出了实施数学素质教育的新课题,而"启发法"为实施素质教育的重要方法,对广大数学工作者有广泛的指导意义和实践意义.     

数学文化在中学数学教学中的渗透

广义的数学文化是指数学本身就是一种文化.狭义上说,数学文化指数学的思想、精神、方法、观点、语言及其形成和发展过程.当前对数学文化认识所存在的误区主要有:不少人认为数学文化就是数学史,有些人认为数学文化就是介绍一些数学趣题,更多的人认为数学文化也就是数学本身.在中学数学教学渗透数学文化的途径有:在各章引言中渗透数学文化;在新课引入时渗透数学文化;在讲述概念时渗透数学文化;在定理公式证明时渗透数学文化;在思想方法中渗透数学文化;在例题教学中渗透数学文化;在数学的实际应用中渗透数学文化.     

数学实验融入高等数学教学的探讨

随着时代发展和科技的进步,迫切要求大学生掌握数学技术,也就是在学习过程中,把数学知识与计算机技术结合起来,使二者的学习相互促进.实现这一目标的最基本方法是把数学实验融入到数学教学中去.笔者在实验融入数学教学实践的基础上,通过对教学对象的实际问卷调查,运用层次分析法对实验融入数学教学模式和传统数学教学模式进行定量比较与评价.结果显示实验融入数学教学模式优于传统教学模式,该教学模式值得进一步研究和加强.     

数学建模思想融入《数学分析》教学的研究与实践

针对传统《数学分析》课程教学的弊端,结合自己多年教学实践,论述了《数学分析》课程教学中融入数学建模思想的重要性,并且就数学建模思想全方位融入到《数学分析》教学的各个环节中的具体方法进行了探讨,为《数学分析》课程的教学改革提供有益的参考.     

Causal Connections Between Mathematical Language and Mathematical Knowledge: A Dialogic Reading Intervention

The acquisition of early mathematical knowledge is critical for successful long-term academic development. Mathematical language is one of the strongest predictors of children's early mathematical success. Findings from previous studies have provided correlational evidence supporting the importance of mathematical language to the development of children's mathematics skills, but there is limited causal evidence supporting this link. To address this research gap, 47 Head Start children were randomly assigned to a mathematical language intervention group or a business-as-usual group. Over the course of eight weeks, interventionists implemented a dialogic reading intervention focused on quantitative and spatial mathematical language. At posttest, students in the intervention group significantly outperformed the students in the comparison group not only on a mathematical language assessment, but on a mathematical knowledge assessment as well. These findings indicate that increasing children's exposure to mathematical language can positively affect their general mathematics skills. This study is an important first step in providing causal evidence of the importance of early mathematical language for children's general mathematical knowledge and the potential for mathematical language interventions to increase children's overall mathematics abilities.     

Mathematical Reasoning Requirements in Swedish National Physics Tests

This paper focuses on one aspect of mathematical competence, namely mathematical reasoning, and how this competency influences students’ knowing of physics. This influence was studied by analysing the mathematical reasoning requirements upper secondary students meet when solving tasks in national physics tests. National tests are constructed to mirror the goals stated in the curricula, and these goals are similar across national borders. The framework used for characterising the mathematical reasoning required to solve the tasks in the national physics tests distinguishes between imitative and creative mathematical reasoning. The analysis process consisted of structured comparisons between representative student solutions and the students’ educational history. Of the 209 analysed tasks, 3/4 required mathematical reasoning in order to be solved. Creative mathematical reasoning, which, in particular, involves reasoning based on intrinsic properties, was required for 1/3 of the tasks. The results in this paper give strong evidence that creative mathematical reasoning is required to achieve higher grades on the tests. It is also confirmed that mathematical reasoning is an important and integral part of the physics curricula; and, it is suggested that the ability to use creative mathematical reasoning is necessary to fully master the curricula.     

关于奥数与小学生数学思维能力发展冲突的思考

近年来,小学“奥数”越来越热。小学生做奥数题是否真的有利于小学生的数学思维能力发展,这一问题成为一些教育界人士与家长关心的重要议题。文章认为,大面积的小学生“奥数”培训热,降低了小学生数学学习的兴趣,不利于提高小学生的数学能力。小学数学教学应该把提升小学生的数学素质作为基本出发点,促进小学生的数学思维能力发展。     

管理领域数学方法的理念与模式管窥

管理领域数学方法的理念是，仅从数量上研究管理对象及其运行规律，从中抽象出相应的数学模型，并用之于管理实践。这种方法的模式是，用数字、符号、算式、图示、函数关系式或其图象等数学语言，来描述管理对象及其运行规律，形成特殊的管理模式——数学模型。常用的数学模型主要有回归分析模型和线性规划模型等。     

解析几何教学中强化数学思想方法刍议

阐述了数学思想方法的涵义,明确了解析几何所蕴涵的数学思想方法,着重探究了解析几何教学中强化数学思想方法的必要性及途径.     

Mathematical language and mathematical abilities in preschool: A systematic literature review

It is well established that early general language during preschool is critical for children's mathematical abilities. In an attempt to further characterize this association between language and mathematics, an increasing number of studies show that one specific type of language, namely mathematical language or the key linguistic concepts that are required for performing mathematical activities, is even more critical to children's mathematical abilities. The purpose of this systematic review is to summarize the evidence on mathematical language and mathematical abilities. We focus on preschool children as nearly all of the existing work has been done at this age. We first explain how mathematical language has been defined across studies, and report how it has been evaluated in studies in preschool. Next, we present the results of our systematic review. Following the PRISMA guidelines and after a critical appraisal, we ended with a set of 18 papers that were all of sufficient methodological quality. In these studies, mathematical language was defined as terms that are about numbers and operations on numbers (e.g., nine), but also included linguistic terms that do not directly refer to numbers, yet are important to understand mathematical concepts (i.e., quantitative and spatial terms such as fewest and middle, respectively). Some of these studies evaluated children's performance on mathematical language tasks, while others evaluated the mathematical language input provided to the child by their (educational) environment (teachers/parents/interventionists). Mathematical language correlated positively with children's mathematical abilities, concurrently and longitudinally. It also directly affected children's mathematical abilities, as was shown by intervention studies. We discuss potential directions for future research and highlight implications for education, arguing for more support for teachers and parents to improve the use of mathematical language in the classroom and in home settings.     

数学建模融入大学数学教学改革的探索

文章分析大学数学教育的现状和数学建模的内涵及意义,强调将数学建模内容融入到大学数学教学中的重要性．并探讨性地提出了将数学建模融人大学数学课程教学的几点改革思路。