将数学建模的思想融入代数学的驱动式教学方法中

代数学是所有自然学科的基础,学科中的微积分、代数学、复变函数以及概率论与数理统计是研究自然现象、揭示自然规律、探索规模应用的理论研究工具。在高等数学的这些分支中,代数学的重要性尤其突出,特别是随着大规模科学计算与大规模工程应用的发展,越来越多的科学领域都比以往更加迫切地需要代数学的理论与应用支持。如何教好代数学?如何让代数学适应时代的需要?如何让学生们学以致用?都是每个代数学教师必须考虑的问题。本文将从代数学课堂教学的实际出发,阐述数学建模思想在代数学的驱动式教学方法中的实践与应用。     

代数结构思想及其方法论意义

以代数学发展的历史为主线，考察代数结构思想的形成，在此基础上，从数学抽象的层次观念，数学问题的否定解法，数学对象的整体处理以及数学概念的应用四个方面，讨论代数结构思想方法的论意义，进一步指出它对近代数学发展的影响。     

代数学相关课程整合的探讨

从代数学的教学改革入手,结合自身教学实践分析了代数学相关课程的教学现状以及教学中存在的一些问题,探讨了代数学课程体系中高等代数、近世代数与初等数论的整合以及教学方法改革的尝试．     

从代数发展看数学教育

本文通过对代数学发展的几个阶段、特点及相关数学家生平的简介,使读者从宏观上认识代数学的整体结构,形成数学思想观念和科学探索信念的精神,从而使数学融入人的整体素质。     

初中数学教学中的数学思想方法教学

数学思想方法是人们通过教学活动对数学知识所形成的一个总的看法或观点。它对人们学习和应用数学知识解决问题的过程中的思维活动起着指导和调控的作用。突出数学思想方法教学，是当代数学教育的必然要求，也是数学素质教育的重要体现。     

代数学教学团队建设的实践与探索

渭南师范学院代数学教学团队以数学与应用数学特色专业为依托,强化专业建设、课程建设、教材建设和青年教师培养为主要内容的师资队伍建设,推进了人才培养模式的改革与创新.通过几年的探索与实践,进一步优化了团队师资结构、代数学课程体系,基本形成了较为完整的代数学课程群;建立了良好的团队合作机制,实现了教学改革成果的交流与共享,增强了团队竞争力,提升了人才培养的质量.     

关于含有三个量的实际问题的相等关系的确立

方程有悠久的历史，它随着实践需要而产生，并且具有极其广泛的应用．从数学学科本身看，方程是代数学的核心内容，正是对于它的研究推动了整个代数学的发展．从代数中关于方程的分类看，一元一次方程是最简单的代数方程．     

开心角——平分

《时代数学学习》(初中版)伴你度过难忘的初中时代．长年来，本刊的许多读者在升入高中以后，常来信来电询问有无相应的高中版《时代数学学习》，不久，这一遗憾将不复存在．2005年9月，《时代数学学习》高一年级版即将问世!     

复数在数学解题中的应用

复数原本是为了解决代数学中那些在实数范围内不能解决的问题而产生的，但在复数基础知识结构形成以后，其适用范围已远远超出起初的设想，应用越来越广泛。     

关于“代数”起源的两个问题

“Algebra”(代数学)这个术语起源于九世纪中亚地区的数学家、天文学家穆罕默德·伊本·穆萨·花拉子密的一篇论文,题目是“Al-Jabr w'al Mugabala”。公元七世纪到十三世纪,阿拉伯帝国统治营中亚和近东地区,从印度直到西班牙。这一时期历代君主都鼓励科学文化发展,形成经济、文化的繁盛时期。花拉子密在前人和同代人工作的基础上,用阿拉伯文写成了第一篇代数学的论文。论文的主要内容为解一次和二次方程。其解法过程不用任何算式和符号,而全部     

Geometry of spin: Clifford algebraic approach

Spin is a fundamental degree of freedom of matter and radiation. In quantum theory, spin is represented by Pauli matrices. Then the various algebraic properties of Pauli matrices are studied as properties of matrix algebra. What has been shown in this article is that Pauli matrices are a representation of Clifford algebra of spin and hence all the properties of Pauli matrices follow from the underlying algebra. Clifford algebraic approach provides a geometrical and hence intuitive way to understand quantum theory of spin, and is a natural formalism to study spin. Clifford algebraic formalism has lot of applications in every field where spin plays an important role.     

Stages in the History of Algebra with Implications for Teaching

In this article, we take a rapid journey through the history of algebra, noting the important developments and reflecting on the importance of this history in the teaching of algebra in secondary school or university. Frequently, algebra is considered to have three stages in its historical development: the rhetorical stage, the syncopated stage, and the symbolic stage. But besides these three stages of expressing algebraic ideas, there are four more conceptual stages which have happened along side of these changes in expressions. These stages are the geometric stage, where most of the concepts of algebra are geometric ones; the static equation-solving stage, where the goal is to find numbers satisfying certain relationships; the dynamic function stage, where motion seems to be an underlying idea, and finally, the abstract stage, where mathematical structure plays the central role. The stages of algebra are, of course not entirely disjoint from one another; there is always some overlap. We discuss here high points of the development of these stages and reflect on the use of these historical stages in the teaching of algebra. Commentary from a Mathematics Educator Bill Barton. See also the last page. Commentary from a Mathematics Educator     

Using concept maps to assess change in teachers’ understandings of algebra: a respectful approach

The purpose of this study was to explore teachers’ growth in understanding of algebra using concept maps. The study was set in the context of a five-year National Science Foundation funded teacher retention and renewal professional development project. In this project both beginning and experienced teachers are supported as they increase their understanding about mathematics, their ability to implement effective mathematics practices in their classrooms, and their knowledge of working with English Learners. Results indicate that teachers’ algebraic knowledge structures became more complex and connected as a result of their professional development. In addition, they were able to adapt their knowledge networks to incorporate important aspects of algebra into them. Concept maps are recommended to other leaders of mathematics professional development as a means of assessing change.     

Parsing the notion of algebraic thinking within a cognitive perspective

There is a growing consensus that algebra is an important aspect of mathematics teaching and learning and several abilities are required in order students to have successful performance in algebra. The present study uses insights from the domain of psychology to enrich what is currently known in the domain of mathematics education about the relationship of algebraic thinking with abilities involved in fundamental cognitive processes. In total, 190 students between the ages of 13–17 years old were tested through two tests. The first test addressed four types of cognitive systems which are responsible for the representation and processing of different types of relations in the environment: the spatial-imaginal, the causal-experimental, the qualitative-analytic and the verbal-propositional. The second test addressed algebraic thinking. The results support the key role of the four types of cognitive processes in students’ algebraic thinking. The results also suggest that abilities involved in the four types of cognitive processes predict algebraic thinking abilities, irrespective of the age of the students.     

Gauss变换与矩阵的LU分解的教学注记

Gauss变换与矩阵的LU分解是数值线性代数中的基本内容,在中小规模线性方程组的求解中有着不可取代的重要地位.结合在数值线性代数教学过程中的个人体会,论述了Gauss变换和矩阵的LU分解的定义和常用结论,证明了三个在用Gauss变换实现矩阵LU分解中的重要命题.     

平面解析几何

在解析几何中,人们建立了几何与代数之间的对应关系．几何中的基本概念及定理可以代数地描述和证明;代数中的基本概念和过程可以几何地解释．当一个几何问题看起来比较困难时,可考虑相应的代数问题．如果在这个特殊情况下,代数工具更加有效的话,我们就先代数地解决这个问题,而后把结果翻译成几何语言．但常常是沿相反的方向进行的．     

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.     

Providing a computer based framework for algebraic thinking

This paper describes and presents the findings of a study which aimed to trace the development of pupils' use and understanding of algebraic ideas within a Logo programming context relating this to their use and understanding of similar ideas within a non-computational context. The research consisted predominantly of a three year longitudinal case study of four pairs of pupils (aged 11–14) programming in Logo during their normal school mathematics lessons. The data included video recordings of all the case study pulils' Logo sessions, and individually presented Logo and algebra structured interviews. The overall conclusion of this research is that Logo experience does enhance pupils' understanding of algebraic ideas, but the links which pupils make between Logo and algebra depend very much on the nature and extent of their Logo experience.     

Preparing elementary prospective teachers to teach early algebra

Researchers have argued that integrating early algebra into elementary grades will better prepare students for algebra. However, currently little research exists to guide teacher preparation programs on how to prepare prospective elementary teachers to teach early algebra. This study examines the insights and challenges that prospective teachers experience when exploring early algebraic reasoning. Results from this study showed that developing informal representations for variables and unknowns and learning about the two interpretations of the equal sign were meaningful new insights for the prospective teachers. However, the prospective teachers found it a conceptual challenge to identify the relationships contained in algebraic expressions, to distinguish between unknowns and variables, to bracket their knowledge of formal algebra and to represent subtraction from unknowns or variables. These findings suggest that exploring early algebra is non-trivial for elementary prospective teachers and likely necessary to adequately prepare them to teach early algebra.     

正交模格上的代数性质

本文比较系统地控计了正交模格的一些代数性质,得到了拟Heyting代数与弱BL代数等新的几类代数系统。