关于循环结构的分析与思考

1引言 在新课程中，算法作为新增内容之一，已成为广大教师积极讨论的对象．对于任何一个新事物只有发现其存在的问题，才能更好地把握该事物，算法对于一线的中学数学教师来说是一个新事物，为了更好地把握算法教学，有关算法学前学后的调查研究已有不少，但当前对算法中教学难点进行深入分析的文章并不多．本文通过分析《数学通报》上两篇有关算法调查研究的文章的结果，[第一段]     

算法多样化的优化

算法多样化的教学是这一轮数学课程改革的热点问题之一,目前，尽管各种报刊对算法多样化教学阐述了各种颇有见地的观点，但教师在具体的课堂教学中仍然存在很多问题。有的教师对《数学课程标准》提倡算法多样化存在理解上的偏差，或受有关算法多样化教学文章及专家报告的影响，以致在算法多样化教学中重算法的数量而轻算法的质量；有的教师在新授课中该优化时不敢优化。这再次验证了南京大学哲学系郑毓信教授说的一句话：小学教师真“可爱”，书上或专家怎么说就怎么做。     

有限集合的幂集的生成算法探讨

本文在讨论有限集的幂集的有关结论的基础上，分析了按照幂集的构成用组合生成的算法求解其所含元素的方法和规律，并提出了幂集的分解归纳定义及相应的生成算法，同时阐明了该算法应用于中学教学中相关内容教学时的处理意见。     

放手求异，联系生活，进行有效的数学学习活动——加、减法的一些简便算法教学案例分析

数学在现实生活中有着广泛的应用，教师在教学中要善干挖掘生活中的数学教育素材。进行生动有效的数学学习活动，从中培养学生的创新精神和实践能力。本文就在进行加、减法的一些简便算法的教学时，如何引导学生联系生活来学习数学知识进行了有关的阐述。     

2009年数学高考算法试题研赏与启示

2009年的高考落下了帷幕，产生和留下了一批新的试题，呈现和发出了一些新的信息．算法作为课程标准唯一新增章节，其高考试题值得关注和研究，这既是命题者对课程标准的算法所作的解读，也是教师启示算法教学的依据．2009年的数学高考有10个（自主）命题单位同题异构，交出了19份课程标准数学高考试卷，现对其中有关算法的考题进行研赏，希望能从中挖掘出一些有利于算法教学的启示．     

高中数学新课程中"算法初步"几个问题的探讨

人类已进入了21世纪，这是一个以计算机为代表的高度信息化的时代和社会．算法作为一个全新的课题。已经成为计算科学的重要基础，它在科学技术和社会发展中起着越来越重要的作用．算法的思想和初步知识。也正在成为普通公民的常识．因此，作为信息化社会未来的主人，中学生尤其是高中学生掌握一些基本的算法知识、进而养成用算法的思想意识看待世界及解决问题很有好处．这样，“算法初步”就成为高中数学新课程中模块3的必修内容，算法思想将贯穿高中数学课程的相关部分．但是，算法毕竟是这次高中数学课改新增加的内容。作为即将进行新课程教学的高中数学教师（有些省市已经开始了与《普通高中数学课程标准》（实验）相配套的新教材的教学实验，许多教师在教学时也存在很多问题），就应该对算法的有关知识提前有所理解．基于此，本文试图就“算法”的有关问题和高中数学教师一起作以探讨．     

关于循环结构的分析与思考

1引言在新课程中,算法作为新增内容之一,已成为广大教师积极讨论的对象.对于任何一个新事物只有发现其存在的问题,才能更好地把握该事物,算法对于一线的中学数学教师来说是一个新事物,为了更好地把握算法教学,有关算法学前学后的调查研究已有不少,但当前对算法中教学难点进行深人分析的文章并不多.本文通过分析《数学通报》上两篇有关算法调查研究的文章的结果,并从有意义学习的角度阐述算法教学中存在的问题及对策.     

数据挖掘中关联规则的教学研究

本文探讨了使用影印版教材教学的相关问题，并就影印版教材《数据挖掘－概念与技术》中有关布尔（boolean)型关联规则部分的内容，分析了算法的基础理论，补充了生命FP－tree的详细过程，讨论了用Apriori算法改进冰山问题（iceberg queries)效率的思想。     

尊重个体差异 促进自主优化——引导学生进行算法自主优化的实践和体会

对算法多样化，需要教师有效主导，引导学生进行优化。教学中，本人对如何引导学生进行算法优化进行了摸索实践，主要有以下几点体会：     

新课程中算法教学的几个注意点

在新课程中，算法是数学必修课的重要组成部分，预计于高一下学期进行教学．新增算法内容，既反映时代的要求，也反映我国古代数学重视计算的优良传统．此外，算法教学有利于培养学生的逻辑思维能力、理性精神和实践能力，发展解决问题的程序化能力，有利于学生理解构造性数学，为学生未来的学习特别是信息技术方面的学习提供支持．如何进行算法教学?教学中该注意哪些方面?本文试就这些问题作一些探讨。     

分析小学高段数学教学中学生口算能力的培养策略

口算能力是小学高段数学学习能力的有效体现。在教学过程中,教师要打破传统教学观念的束缚,提高学生对数学口算的兴趣,培养学生良好的口算习惯。本文以小学高段数学教学中培养学生口算能力为出发点,深度探究小学高段数学教学中培养学生口算能力的有效途径,给小学教师提供理论参考。     

Can young students understand the mathematical concept of equality? A whole-year arithmetic teaching experiment in second grade

European Journal of Psychology of Education - Ensuring students correctly understand the notion of equality is a fundamental problem in teaching mathematics. Is it possible to teach arithmetic in...     

Change in mathematics education since the late 1950's — Ideas and realisation Nigeria

Conclusion This chapter has tried to expose the reader to the dynamics of curriculum change in mathematics in Nigeria in the last 20 years. The teaching of arithmetic processes became a part of school curriculum early in the colonal era. Then shortly after Independence Day the years of experimentation with mathematics curriculum materials originally produced by the African Mathematics Programme began. Just when it was thought by professionals that modern mathematics had become entrenched in the system, Government action seems to be pushing for a return to the teaching of arithmetic processes.Yet, we need to introduce system-wide in our educational institutions the type of mathematics curriculum which should ensure that Nigeria be not left behind by other countries as the countries of the world strive in their various ways to maximize the fruits of technology. What Nigeria should do is to use the Nigeria Educational Research Council to plan and implement a teacher education programme that should help teachers to teach the mathematics demanded of the age. Nothing short of this can suffice.     

生活化教学法在培智数学教学中的应用

在培智数学教学中 ,笔者应用生活化教学法进行以下五方面内容的教学 :用生活化教学法进行式题、应用题、图形表象的教学 ;对教材中本来就生活化的内容进行教学 ;用生活化教学方法进行主题教学 ,使数学贴近弱智学生的生活实际 ,从而提高数学教学的效果。     

Development of Arithmetical Thinking: Evaluation of Subject Matter Knowledge of Pre-Service Teachers in Order to Design the Appropriate Course

One of the key courses in the mathematics teacher education program in Israel is arithmetic, which engages in contents which these pre-service mathematics teachers (PMTs) will later teach at school. Teaching arithmetic involves knowledge about the essence of the concept of “number” and the development thereof, calculation methods and strategies. properties of operations on different sets of numbers, as well as the properties of the numbers themselves. Hence, the question arises: how to educate PMTs in order to supplement their mathematical knowledge with the required components? The present study explored the development of arithmetic thinking among pre-service teachers intending to teach mathematics at elementary school. This was done by matching the van Hiele theory of the development of geometric thinking to arithmetic. Analysis of findings obtained both in the present study and in many studies of geometry teaching indicates that this approach to considering the learners’ level of thinking development might lead to meaningful learning in arithmetic course for PMTs.     

从算术到代数

从算术向代数过渡,是学生数学学习过程中极为重要的转变阶段.符号是代数不同于算术的典型特征,学生从算术向代数的过渡,是从对数的思考向对符号的思考的转变,是从算术思维向代数思维的转变,是思维层次从个别到一般、具体到抽象的飞跃.     

Fifteenth and sixteenth century arithmetic texts: What can we learn from them?

Fifteenth and sixteenth century European arithmetic texts set new standards and procedures for the learning and teaching of mathematics. Commercial problem solving situations both directed and reinforced the mathematical concepts presented. A new dynamic, active problem solving, now became the central feature of mathematics learning and teaching. This article surveys the format and contents of fifteenth and sixteenth century arithmetic books. It discusses the types of problems that were most popular in these early texts and briefly analyzes problem contents. The residual educational influence of fifteenth and sixteenth century arithmetical and instructional practices is noted.     

高职高专高等数学中求极限运算所适用的常用方法

高等数学教学中极限的求取是一种重要的、基本的运算方法,但对于高职高专的学生而言,由于知识结构方面相对比较薄弱,数学学习基础不牢固,对于抽象概念的理解与熟练应用也存在一定难度,因而探讨常用的运算方法并总结规律,对于有效教学和提高学习理解程度具有重要意义。     

Mathematical tasks designed to foster a reconceptualized view of early arithmetic

We discuss mathematical tasks used in a first mathematics content course for elementary teachers at our university to foster a deep conceptual understanding of early arithmetic, including basic concepts of number, number relationships and strategies, and coordinating units of different rank. Our approach is to immerse our students in a base 8 world for up to six weeks. A key aspect is that we develop base 8 vocabulary. We use base 8 analogs of instructional sequences developed in classroom teaching experiments in the elementary grades that have been proven successful to promote deep conceptual understandings of basic arithmetic and place-value numeration in young children. As a result, our students have unique opportunities to develop a reconceptualized view of early arithmetic and learn how it can be advanced.