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1.
从当下大学线性代数教学现状出发,以数学方法论和认识论为指导,探究线性代数与中学数学在数学知识、数学思想方法、数学观念等方面的联系,以期帮助大学生顺利地从中学过渡到大学线性代数的学习。 相似文献
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An Integrative Analysis of Reputation and Relational Quality: A Study of University-Student Relationships 总被引：1，自引：1，他引：0
The purpose of this research is to explore the link between reputation and relational quality in the context of student-university relationships, based on a perceptual analysis of the participants' subjective views (i.e., factor analysis with Q methodology). To this end, the researchers selected a private university located in the Northeast region of the United States as the research setting, with students of the university serving as research participants. The researchers proposed three research questions regarding the link between student-university relational quality and university reputation. The findings of this research indicate that the concepts of relational quality and reputation can be “variantly” intertwined on the basis of individual stakeholders' subjective views of their experience, interactions, and information, rather than intertwined in a linear way. 相似文献
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现在大学线性代数教学的现状是学时紧、学生学习投入不足,针对这种情况本文探讨了怎样进行线性代数课程教学改革和如何提高教学质量的问题。作者认为教师应采取如下措施：在教学中要选择学生容易理解的教材体系进行教学,重视线性代数中概念教学,并在教学中以问题为先导,根据新课中概念的疑点、重点和难点,设计一系列问题即“问题链”,以吸引学生的学习兴趣。还应让学生学会使用Matlab等数学软件,加强数学实验教学。 相似文献
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How do students think about algebra? Here we consider a theoretical framework which builds from natural human functioning in terms of embodiment – perceiving the world, acting on it and reflecting on the effect of the actions – to shift to the use of symbolism to solve linear equations. In the main, the students involved in this study do not encapsulate algebraic expressions from process to object, they do not solve ‘evaluation equations’ such as \( 3x + 2 = 8 \) by ‘undoing’ the operations on the left, they do not find such equations easier to solve than \( 3x - 1 = 3 + x \) , and they do not use general principles of ‘do the same thing to both sides.’ Instead they build their own ways of working based on the embodied actions they perform on the symbols, mentally picking them up and moving them around, with the added ‘magic’ of rules such as ‘change sides, change signs.’ We consider the need for a theoretical framework that includes both embodiment and process-object encapsulation of symbolism and the need for communication of theoretical insights to address the practical problems of teachers and students. 相似文献
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The purpose of this paper is to present an analysis of the difficulties faced by students when working with different representations of vectors, planes and their intersections in \(\mathbb {R}^{3}\). Duval’s theoretical framework on semiotic representations is used to design a set of evaluating activities, and later to analyze student work. The analysis covers three groups of undergraduate students taking introductory courses in linear algebra. Different types of treatments and conversions are required to solve the activities. One important result shows that, once students choose a register to solve a task, they seldom make transformations between different registers, even though this facilitates solving the task at hand. Identifying these difficulties for particular transformations may help teachers design specific activities to promote students cognitive flexibility between representation registers. 相似文献
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This study investigated the effect of instruction with a cognitive tutoring software system in a remedial algebra course. The performance on algebra tasks of students who attended the experimental (cognitive tutor) and a control class was compared. The results indicated that the two groups of students were equally proficient with respect to algebraic manipulation skills. However, students who attended the experimental algebra section performed significantly better in problem solving than students in the control section. This finding suggested that the use of the cognitive tutor (a) improved students' problem‐solving abilities; (b) fostered student development of richer concepts of variable and function; and (c) improved students' procedural abilities in approaching and carrying through mathematical analyses of relatively complex situations. 相似文献
8.
《Journal of Further & Higher Education》2012,36(1):73-84
The present paper discusses the decontextualization of learning in a case of compulsory Swedish language studies for university degrees. In this case learning Swedish is mostly disconnected, not only from the everyday lives of the students in a way typical of formal learning in general, but also from the study activities and contexts that students engage in for their major subject. Learning has been transferred to a specific context, the University Language Centre Swedish courses, where the main purpose is to learn Swedish for possible future needs. The study explored the correspondence between Finnish speaking students' own learning goals and the formal objectives set for these compulsory studies (i.e. learning Swedish for educational and occupational purposes). The sample consisted of 10 student groups from different subject majors. The results suggest that all students do not necessarily share the prescribed formal objectives. First of all, students expressed goals which contradicted the formal objectives, namely learning only discrete words or grammar rules. In addition, only four of the 10 groups mentioned learning goals related to their present studies (educational domain) and only five groups discussed learning goals from the point of view of their future professions (occupational domain). The paper discusses ways to overcome the problems of decontextualization in compulsory language studies for university degrees. 相似文献
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The organization of conceptual materials: A methodology for measuring ideal and actual cognitive structures 总被引：1，自引：0，他引：1
Richard M. Fenker 《Instructional Science》1975,4(1):33-57
The teaching-learning process is described in terms of a simple communication model with four components: the sender, the encoding structure, the decoding structure, and the destination. Within this context a method is proposed and illustrated for evaluating a student's understanding of the system of concepts underlying the topic areas in an elementary statistics and measurement course. The method, multidimensional scaling, involves determining the students' and instructor's cognitive maps for the various topics. A cognitive map represents a hypothetical cognitive structure of a student or instructor which characterizes his perceived organization of the concepts in a topic area. These individual cognitive maps were compared to the optimal organization or formal structure, as a basis for assessing the students' under-standing of the material. The present research was exploratory but demonstrated that:
- With the help of experts it is possible to define the formal structure for the concepts in a topic area.
- It is possible to measure, in a classroom setting, the cognitive maps that both the students and instructors have for a topic area.
- By comparing individual students' cognitive maps to the instructor's cognitive map or to the formal structure, the student's understanding of the system of concepts defining the topic area can be evaluated.
10.
Wallace Feurzeig 《Instructional Science》1986,14(3-4):229-254
For many students the ideas and methods of algebra appear obscure and mysterious, their sense and purpose unclear, and their applicability to anything genuinely real or interesting very remote. Students often fail to acquire an understanding of the key concepts, despite their inherent simplicity. Even when they gain the notion of variables, expressions and equations, students often lack the strategic knowledge required to motivate and direct the global planning and detailed execution of an attack on a problem. These conceptual and strategic difficulties are compounded by the needs for precise performance of the arithmetic and symbolic operations required in manipulating expressions. Extended operations like subtracting an expression from both sides of an equation or expanding a product of three terms, are very difficult for beginning students. Their buggy performance in carrying out the detailed manipulative work greatly confounds and frustrates their acquisition and assimilation of the most important and central ideas.In an effort to confront these difficulties and show how they can be overcome, we are developing a Logo-based introductory algebra course for sixth graders. Our approach has three major components: work on Logo programming projects in algebraically rich contexts whose content is meaning ful and compelling to students, the use of algebra microworlds with concrete iconic representations of formal objects and operations, and the introduction of the algebra workbench, an expert instructional system to aid students in performing extended algebraic operations.The algebra workbench will employ a set of powerful symbolic manipulation tools for performing the standard manipulations of high school algebra. It will have two main modes of use: demonstration mode, which uses an expert tutor program to solve algebra problems incrementally, explaining its strategy and its step by step operations in straightforward terms along the way; and practice mode, in which the student tries to solve a problem with the assistance of the tutor, which performs the operations requested by the student at each step and which can be called at any point to advise the student of the correctness of a step, to perform or explain any step, to evaluate the student's solution, or to perform a problem that she poses.These powerful aids make it possible to effectively separate out the difficulties in performing the formal and manipulative aspects of algebra work from those encountered in learning the central conceptual and strategic content. Distinctly different kinds of instructional tools and activities-Logo programming, expert tutors, or algebra microworlds-can thus be brought to bear where each is most appropriate and effective. 相似文献
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要教好线性代数课程,其核心问题就是要通过课堂教学,使学生理解相关的数学知识;训练和培养学生的思维能力以及数学交流能力;帮助学生寻找新旧知识之间的内在联系,使知识系统化;在巩固已有知识的基础上,让学生自己去发现新知识.要实现这一教学目标,训练学生掌握"数学证明"的概念和在实践中的应用至关重要.传统的做法往往是通过"定义一引理一证明一定理一证明一推论"这种复杂的、程序化方法来进行训练的.由于在初等代数课程中,学生很少接受严格数学证明的训练,所以这种俗套的做法成效甚微.相反,如果把线性代数的主题和概念用一种完全合理的探究式方法来引入,那么数学证明的概念和架构将牢固植根于学生的头脑,并且这种思维习惯将对他们后续课程的学习和掌握公理化推理方法都会有很大帮助. 相似文献
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现代数学基础理论中的一个不可解危机 总被引：2，自引：6，他引：2
欧阳耿 《喀什师范学院学报》2005,26(3):84-87
从新构建的基础理论学的角度,讨论同时存在于现有集合论中两种性质上截然不同的“无穷集合”概念——潜无穷式的与实无穷式的无穷集合．指出现有数学中通常所使用的“无穷”概念极端的模糊不清,一方面混淆了原来的“有穷”概念,另一方面使人们无法理解与解析数学中与“无穷”相关的许多数量形式的性质,因此导致许多错误的数学行为．数学基础理论中这个致命缺陷是导致第二次与第三次数学危机的最根本原因．因此,只有对传统的“无穷”概念进行修正,构建新的“有穷-无穷”理论体系及相关的数量体系才是彻底解决第二次与第三次数学危机的惟一途径． 相似文献
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Heinz Steinbring 《Educational Studies in Mathematics》1991,22(6):503-522
The paper analyzes the relationship between the epistemological nature of mathematical knowledge and its socially constituted meaning in classroom interaction. Epistemological investigation of basic concepts of elementary probability reveals the theoretical nature of mathematical concepts: The meaning of concepts cannot be deduced from more basic concepts; meaning depends in a self-referent manner on the concept itself. The self-referent nature of mathematical knowledge is in conflict with the linear procedures of teaching. The micro-analysis of a short teaching episode on the concept of chance illustrates this conflict. The interaction between teacher and students in everyday teaching produces a school-specific understanding of the epistemological status of mathematical concepts: the concept of chance is conceived of as a concrete generalization, which takes chance as a fixed and universalised pattern of explanation instead of unfolding potential and variable conceptual relations of chance or randomness and developing the theoretical nature of this concept in an appropriate way for students' comprehension. 相似文献
16.
Caroline Bardini Robyn U. Pierce Kaye Stacey 《International Journal of Science and Mathematics Education》2004,2(3):353-376
This study analyses some of the consequences of adopting a functional/modelling approach to the teaching of algebra. The teaching of one class of 17 students was observed over five weeks, with 15 students undertaking both pre- and post-tests and 6 students and the teacher being interviewed individually. Use of graphics calculators made the predominantly graphical approach feasible. Students made considerable progress in describing linear relationships algebraically. They commented favourably on several aspects of learning concepts through problems in real contexts and were able to set up equations to solve contextualised problems. Three features of the program exerted a triple influence on students use and understanding of algebraic symbols. Students concern to express features of the context was evident in some responses, as was the influence of particular contexts selected. Use of graphics calculators affected some students choice of letters. The functional approach was evident in the meanings ascribed to letters and rules. Students were very positively disposed to the calculators, and interesting differences were observed between the confidence with which they asked questions about the technology and the diffidence with which they asked mathematical questions.
Kaye Stacey: Author for correspondence. 相似文献
17.
刘玉萍 《新疆教育学院学报》2004,20(4):110-112
本文根据学生的实际情况以及本人的教学实践,针对普通物理教学中困扰学生的极值问题,利用数学、物理的概念、公式等,尝试对物理极值问题的求解规律进行归纳与探析. 相似文献
18.
童少飞 《湖州师范学院学报》2000,(Z1)
高中数学教材中的向量内容,为高中学生学习几何的代数化方法提供了一个有效能算的工具．学生掌握了向量运算体系后,就可以运用他们熟悉的代数方法进行推理,以此来掌握几何图形的性质,并能丰富思维结构和运用数学解决问题的能力． 相似文献
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《数学分析》、《高等代数》等是非常重要的基础课程,这些课程的学习对学生数学素质的培养、学生思维能力的训练、学生后续课程的学习及其它方面能力的发展与提高都起着至关重要的作用.本文从教学方法、教学手段、考核方法及实践教学等方面对数学基础课程教学进行探索,以期提高学生对数学的兴趣、激发学生的学习动力,最终达到提高课堂教学质量目的.我们也注重加强与学生的联系,及时解决学生中的疑惑.通过组织学生申报湖南省及学院大学生研究性学习和创新性实验计划项目,来培养学生的科学研究能力及创新精神. 相似文献
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University students' situational reaction tendencies: Reflections on general study orientations,learning strategies,and study success 总被引：1，自引：1，他引：0
The purpose of the study was to bridge the gap between situational and more general measures in investigating university students' studying. More precisely, the aim was to establish a connection between students' situational reaction tendencies and their general study orientations. Furthermore, situational reaction tendencies were related to the applied learning strategies and actual study success. The participants in the study were 578 second year students in a multi-disciplinary Finnish university. A questionnaire was used including the Inventory of General Study Orientations (IGSO) and measures concerning situational reaction tendencies, learning strategies, self-efficacy and self-evaluated expertise. Archive data from the university's student register were utilized to objectively examine study success. The following four groups of students with differing situational reaction tendencies were distinguished: performance-oriented students, task-oriented students, socially oriented students and avoiders. It was found that the groups differed from each other regarding general study orientations, applied learning strategies and study success. 相似文献