《复变函数》教学基本要求

<正> 复变函数是高等工科学校有关专业的基础课,通过本课程的学习,使学生初步掌握复变函数的基本理论和方法,为学习有关专业课和扩大数学知识面提供必要的数学基础。一、复数与复变函数     

工科复变函数的几个问题讨论

<正> 为了把学生培养为生产科研中的高级人材,使学生能够适应科学技术的迅速发展,就必须加强对学生的工程数学教学。工科复变函数课不同于数学专业的复变函数课,其最主要的不同点就是教学内容的要求与安排。我的体会是:在考虑内容取舍时,应该注意保持逻辑完整,以免给学生模糊的信息,使学生感到难以理解,甚至造成错误的理解。下面的例,主要来源于学生的反馈问题。使用教材为西安交通大学高等数学教研室编《工科数学·复变函数》。     

关于复变函数几个问题的师生讨论

<正> 为了把学生培养为生产科研中的高级人材,使学生能够适应科学技术的迅速发展,就必须加强对学生的工程数学教学.工科复变函数课不同于数学专业的复变函数课,其最主要的不同点就是教学内容的要求与安排.我的体会是:在考虑内容取舍时,应该注意保持逻辑完整,以免给学生模糊的信息,使学生感到难以理解,甚至造成错误的理解.下面的例子主要     

复变函数教学法探讨

复变函数是高等院校工科专业一门重要的基础理论课,它是高等数学的扩展.本文主要探讨在复变函数的教学过程中,教师可以利用"类比"、"转化"和"反例"等教学方法,使学生达到巩固旧知识、探索新课程的目的.     

以问题为导向的复变函数教学与实践

复分析在数学的众多分支、物理学、工程领域有着重要应用,因此它是众多工程类专业的必修课程.传统的复变函数教学方式存在着一些不足,并不完全适合当下的学生.这导致相当数量的学生觉得复变函数枯燥而不易学习.为解决这一问题,教师可以通过有效的启发,并以讨论问题的方式开展复变函数的教学.这种方式不仅有益于提高学习效率并且可以增加学生的学习兴趣.     

类比迁移优化数学认知结构

类比是根据两个对象或两类事物的一些属性相同或相似，猜测另一些属性也可能相同或相似的方法．迁移是一种学习对另一种学习的影响．凡是一种学习对另一种学习起到促进作用的就称为正迁移；反之起干扰或抑制作用的称为负迁移．从教学目的上看，数学教学应该努力促进一种学习对另一种学习的正迁移，正迁移量越大，说明学生通过学习产生的适应新学习情境或解决新问题的能力越强，在学习中，经常会出现负迁移的情况，关注负迁移发生的可能，防止其负面影响非常重要．数学学习既有知识技能和思维方法的迁移，又有学习态度的迁移，而类比可以成为其相互迁移的桥梁和纽带．     

工科复变函数中一道作业题不同解法的讨论

分析了学生对工科复变函数课程中一道作业练习题的4种解法,并对幂函数单叶解析区域的特征进行了讨论.通过在教学中进行这些分析和讨论,使学生能够更深入理解和掌握相关知识,分析和解决问题的能力以及发散思维能力能够得到培养和提高.     

谈知识迁移应注意的几个问题

知识迁移也称学习迁移,是一种学习对另一种学习的影响,现代认知心理学认为,学习者在进行迁移前所掌握的知识叫做源知识,学习者将要学习的新知识叫做目标知识,如果学习者将源知识运用到了目标知识的学习,或阻碍或促进了学习,我们就说发生了迁移.     

思维定势引发的解题缺陷问题

<正>一、思维定势的概念思维定势是指由定向思维所造成的思维趋向性或专注性状态.在数学学习中,学生的思维定势是客观存在的,它是一种思维的定向预备状态,既能产生积极影响,同时也会产生明显的消极影响.当它发生正迁移作用时,学生就能够迅速联想和使用已有的数学知识与思想方法来分析和解决问题;当它发生负迁移作用时,学生就会表现出思维僵化、呆板等封闭性状态,不能多角度、整体地、全面地看待数学问题,陷入思维误区,阻碍问题的解决.因此,在高中数学教学中,要根据学生的心理特     

学习迁移理论在珠心算教学中的应用研究

迁移是学习中的普遍现象,同时也在珠心算教学中起着至关重要的作用。本文以学习迁移理论为基础,梳理了珠心算学习中的迁移规律,探讨了影响珠心算学习迁移的重要因素,并结合珠心算教学实际,提出培养和提高学生学习迁移能力的策略,为广大珠心算教师教学工作提供理论支持。     

数理方程教学方法探讨

旨在通过教学实践体会来探讨数理方程课的教学方法.主要在分析课程特点、挖掘学生学习难点的基础上,从授课内容和思路、理论结合实际、培养学生学习思想、教学手段等多方面论述了提高数理方程课程教学质量的教学方法,同时结合教学实践列举多个数理方程的教学实例来说明锻炼学生能力的途径.     

Supporting Preservice Teachers' Understanding of Place Value and Multidigit Arithmetic

This article provides an analysis of a teaching experiment conducted in the context of teacher education designed to support preservice teachers' understandings of place value and multidigit addition and subtraction. The experiment addresses the following research question: Can the results from research conducted in elementary mathematics classrooms guide preservice elementary teachers' development of conceptual understanding of the same concepts? In both cases, the students (e.g., elementary students and preservice teachers) participated in activities from an instructional sequence designed to support conceptual understanding of both place value and multidigit addition and subtraction. Analyses of the episodes from the teaching experiment document the learning of the preservice teachers and how that learning was supported by initial conjectures grounded in the research on elementary students' ways of reasoning.     

Using Student Reasoning to Inform the Development of Conceptual Learning Goals: The Case of Quadratic Functions

Despite the proliferation of mathematics standards internationally and despite general agreement on the importance of teaching for conceptual understanding, conceptual learning goals for many K-12 mathematics topics have not been well-articulated. This article presents a coherent set of five conceptual learning goals for a complex mathematical domain, generated via a method of systematic empirical analysis of students' reasoning. Specifically, we compared the reasoning of pairs of students who performed differentially on the same task and inferred the pivotal intermediate conceptions that afforded one student deeper engagement with the task than another student. In turn, each pivotal intermediate conception framed an associated conceptual learning goal. While the empirical analysis of student reasoning is typically used to understand how students learn, we argue that such analysis should also play an important role in determining what concepts students should learn.     

MATLAB in first-year engineering mathematics

The paper details the integration of the mathematical software MATLAB into the teaching of core mathematics to first-year university engineering students. The engineering faculty requested that the mathematics staff allocate one hour per week for students to learn and use MATLAB in a computer pool and that group projects involving the use of MATLAB and other similar tasks be included in the overall assessment of the subject. The central concept in achieving this integration was the production of a guide A Focused Introduction to MATLAB which provides a bridge between the software and the core subject material covered in the textbooks and lectures. Recent extensions involve the construction of a Web site dedicated to this subject where students can obtain all information concerning the subject, including a copy of all MATLAB code and corresponding graphical demonstrations used in the lectures. Feedback has been very positive.     

Backward transfer influences from quadratic functions instruction on students’ prior ways of covariational reasoning about linear functions

The study reported in this article examined the ways in which new mathematics learning influences students’ prior ways of reasoning. We conceptualize this kind of influence as a form of transfer of learning called backward transfer. The focus of our study was on students’ covariational reasoning about linear functions before and after they participated in a multi-lesson instructional unit on quadratic functions. The subjects were 57 students from two authentic algebra classrooms at two local high schools. Qualitative analysis suggested that quadratic functions instruction did influence students’ covariational reasoning in terms of the number of quantities and the level of covariational reasoning they reasoned with. These results further the field’s understanding of backward transfer and could inform how to better support students’ abilities to engage in covariational reasoning.     

Supporting Preservice Teachers' Understanding of Place Value and Multidigit Arithmetic

This article provides an analysis of a teaching experiment conducted in the context of teacher education designed to support preservice teachers' understandings of place value and multidigit addition and subtraction. The experiment addresses the following research question: Can the results from research conducted in elementary mathematics classrooms guide preservice elementary teachers' development of conceptual understanding of the same concepts? In both cases, the students (e.g., elementary students and preservice teachers) participated in activities from an instructional sequence designed to support conceptual understanding of both place value and multidigit addition and subtraction. Analyses of the episodes from the teaching experiment document the learning of the preservice teachers and how that learning was supported by initial conjectures grounded in the research on elementary students' ways of reasoning.     

A framework for using learning theories to inform ‘growth mindset’ activities

ABSTRACT

The social psychology theory of fixed and growth mindsets offers one reason for observed underachievement in science, technology, engineering and mathematics (STEM), particularly for students who have previously excelled in these disciplines. Fixed mindset beliefs are linked to behaviours that can lead to avoiding challenges and reduced learning, such as concealing a lack of understanding to retain an image of being ‘smart’. The potential impact of a growth mindset on STEM achievement, particularly for minority and low-household-income students, resulted in calls to develop interventions that encourage growth mindsets and discourage fixed mindsets. However, education interventions are influenced by the educator's understanding of how learning occurs. A framework to show how activities based on different learning theories may encourage growth mindsets or (unintentionally) encourage fixed mindsets can guide the developers of growth mindset interventions. We present such a framework in six tables relating to key areas associated with growth and fixed mindsets: dealing with challenges, persistence, effort, praise, the success of others and learning goals. Each table gives examples of learning activities that may encourage growth or fixed mindsets, fitting with each of four key learning theories: behaviourism, constructivism, communities of practice and connectivism.     

Designing an intelligent teaching simulator for learning to teach by practicing

Learning to teach is difficult for prospective teachers because of the complex nature of the work of teaching. Practicing (Lampert in J Teach Educ 61(1–2):21–34, 2010), interacting with the practice of teaching from a first-person perspective, may give them a unique experience in learning to teach. Computer-based simulators in which the apprentice teacher can interact with virtual students may be used to create that kind of experience. In this paper, we show how to apply techniques in artificial intelligence to design an intelligent learning environment. We show how to model the apprentice’s decision making and resources that can help him or her improve the practice of teaching.     

思维定势在大学数学课堂创新教育中的迁移作用

从当今教育教学改革研究和创新人才培养的要求出发,结合大学数学课堂教学实践,阐述了思维定势在创新教育过程中的重要性,论述了思维定势在大学数学课堂教学中的正、负迁移作用,最后指出了消除思维定势的负迁移作用、培养学生的创新能力的方法.