从数学方法论看高等代数与中学数学的多种联系

高等数学类课程在知识上是中学数学的继续和提高，在思想方法上是中学数学的因袭和扩张，在观念上是中学数学的深化和发展．高等代数与中学数学在思想方法方面的联系主要体现在抽象化思想、分类思想、结构思想、类比推理思想、公理化方法等方面．注意与中学数学的联系对比不但可以降低高等代数课的学习难度，而且增强了高等代数课对培养中学数学教师的指导作用。     

简述提高《高等代数》教学效果的途径

当前高等代数课程在教学方面存在一系列的问题：课时结构不合理、以考试为目的和传统的数学理论知识的教学模式等,这些问题在很大程度上影响了《高等代数》课程的教学效果,特别是在培养未来的中小学数学教师方面。因此,提高该课程的教学效果刻不容缓,建议在如下方面做必要的改革：介绍基本思想与历史、优化教学内容、开展多样化的教学模式、高等代数知识与中小学数学知识应用相结合等。     

建设"高等代数"精品课程的思路与实践

本文从以学科思想理解课程的结构与教学内容,突出学科思想方法的教学活动,建设资源共享的课程网站,开展全省课程研讨活动等方面,介绍了厦门大学"高等代数"国家精品课程建设的思路与实践.     

同构思想在"高等代数"教学中的体现与运用

高等代数是数学专业的专业基础课之一，同构、同态思想则是学习和研究代数的基本思想，也是研究代数结构的灵魂。本文就“高等代数”就中如何体现和运用同构思想进行一些探索。     

《高等代数》的公理化思想方法的认识与研究

通过对《高等代数》课程中蕴含着大理的公理化思想方法的挖掘，阐述它在《高等代数》和其它学科中的重要作用。     

高等代数教学的思考

针对高等代数课程特点,结合高等代数教学实践,从加强基本概念教学、结合现代化教学手段教学、善于总结数学思想、注重习题课教学等方面谈几点教学体会.     

简谈高等代数教学中的辨证唯物主义思想

高等代数是高等教学的一门分支学科 ，这门课程同样蕴含着极其丰富，极其深刻的辨证唯物主义思想内容及观点方法，本简谈一下高等代数中的辨证唯物主义观点及在教学中的应用。     

基于数学建模思想的高等代数课程教学研究

针对二本院校数学专业基础课程高等代数的教学现状和存在的问题,结合数学建模思想和方法,阐述了将数学建模思想融入高等代数课程教学的必要性,通过实例从教材、教学方法、授课对象三方面提出了融合数学建模思想的具体方法和措施。     

高等代数学习与数学建模思想的相互渗透

本文通过叙述高等代数课程学习的重要性．以及数学建模思想对高等代数学习的促进作用,结合实例,探讨了如何把高等代数的学习过程与数学建模相互渗透的途径。     

探析数学思想方法在高等代数教学中的渗透

高等代数是大学课程里的一门基础课程,对其他专业课的学习充当着工具的作用,因此高等代数是解决问题的一种手段.而在高等代数中,问题解决的方式有不同种,但灵魂是主导.数学思想方法则是其精髓与灵魂,对于深刻理解高等代数的原理以及进一步的掌握有重要意义.文章提出几种高等代数中的数学思想方法,为相关教育工作者提供一定参考借鉴.     

Success in Algebra Among Community College Students

College algebra is a required course for most majors, but is viewed by many as a gatekeeper course for degree completion by students. With almost half a million students taking college algebra each year, faculty are experimenting with new course lengths of time that might result in higher success, completion, and retention rates for college algebra students. This article reports on a study of the traditional 16-week versus an 8-week course length in college algebra at a two-year Metropolitan Community College (MCC) in the United States. The study was to determine which course length of time, 8 weeks or 16 weeks, results in a higher proportion of students successfully completing the college algebra course. Also investigated were success rates among ethnicities, genders, and age groups. The study included 231 students in college algebra. Data were analyzed on four sections of the traditional 16-week courses and four sections of 8-week courses. In this study, success was measured as earning a grade of A, B, or C in the course. Understanding more about course lengths of time for college algebra can aid in increased understanding of time as a factor and, ultimately, may determine if students are more successful in 8-week or 16-week courses of instruction.     

Incorporation of Computer Algebra into an Undergraduate Course in Open Channel Hydraulics

Modern computer algebra systems have wide-ranging mathematical capabilities and user-friendly interfaces, which make them ideal tools for research and education. To demonstrate the applications of computer algebra for teaching, this paper reports on its successful incorporation into a senior, undergraduate, civil engineering course in open-channel hydraulics. Computer algebra is particularly useful for this course, since many hydraulics problems are non-linear and have traditionally required laborious solution techniques. The advanced capabilities of computer algebra systems also make them ideal tools for the design of hydraulic structures.     

College Algebra: Past,Present, and Future

Issues within college algebra are well-documented. Over the past two decades, reform has brought about significant modifications in the course, yet to date there has been no synthesis of the efficacy of these efforts. This paper situates college algebra within a historical context, and synthesizes research on reform. I argue that, notwithstanding the successes brought about by change, the course is still not in a position to fulfill quantitative literacy requirements; that is, there exists nontrivial components of quantitative literacy that a college algebra course, by its nature, tends not to provide. I conclude with realistic steps forward for administrators and instructors.     

数学与应用数学专业“高等代数”课程教学之我见

该文主要从注重高等代数与初等数学的结合、一题多解、加深教学内容的深度与难度以及改革学生学习评价四个方面,探讨了数学与应用数学专业高等代数课程教学的有关问题。     

谈谈如何学好高等代数

高等代数是高等院校里数学专业的一门专业基础课程,该课程概念多,抽象,且逻辑性强。不少学生感觉基本概念难以理解,习题难做,基本方法难以掌握。针对这些困难,提出学好该课程的系统的学习方法与建议。     

Situated learning in an abstract algebra classroom

Advisory committees of mathematics consider abstract algebra as an essential component of the mathematical preparation of secondary teachers, yet preservice teachers find it challenging to connect the topics addressed in this advanced course with the high school algebra they must someday teach. This study analyzed the mathematical content knowledge that developed in preservice teachers during a semester course in abstract algebra utilizing Lerman's “person-in-practice-in-person” lens. This unit of analysis provided insights into the situated nature of the algebra learned by illuminating how the goals of the instructor and preservice teachers impacted the community of practice created in the university classroom and how participating in that community impacted the preservice teachers' mathematical identities.     

The Struggle to Pass Algebra: Online vs. Face-to-Face Credit Recovery for At-Risk Urban Students

Students who fail algebra are significantly less likely to graduate on time, and algebra failure rates are consistently high in urban districts. Identifying effective credit recovery strategies is critical for getting students back on track. Online courses are now widely used for credit recovery, yet there is no rigorous evidence about the relative efficacy of online versus face-to-face credit recovery courses. To address this gap, this study randomly assigned 1,224 ninth graders who failed algebra in 17 Chicago public high schools to take an online or face-to-face algebra credit recovery course. Compared to students in face-to-face credit recovery, students in online credit recovery reported that the course was more difficult, were less likely to recover credit, and scored lower on an algebra posttest. There were no statistically significant differences by condition on any outcomes measured during the second year of high school (standardized mathematics test and algebra subtest scores, likelihood of passing subsequent math classes, cumulative math credits, or on-track rates). The benefits and challenges of online learning for credit recovery are discussed in light of the findings to date.     

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.     

An engineering-oriented linear algebra course with elements of functional analysis

The paper presents a new linear algebra course specifically tailored by the author to cater for the exigencies of engineering-oriented students, in general, and for the conditions at his institution, in particular. After a brief analysis of existing linear algebra courses, the clear advantages, structure and main features of this new course together with first experiences of teaching it, are presented.     

提高自考线性代数教学效果的几点突破

《线性代数》是高等院校一门重要的公共基础课,内容具有很强的抽象性,逻辑性,内在联系性。本文研究了自考课程《线性代数（经管类）》助学中要注意的教学重难点以及教学内容的内在联系,旨在帮助自考学生掌握线性代数课程,提高学习效率和自考考试成绩。