基于问题驱动的高中复数教学研究与教学内容的重构

发布时间：2018-01-22 19:46

本文关键词： 问题驱动复数概念复数运算教学内容重构　出处：《广州大学》2016年博士论文　论文类型：学位论文

【摘要】：复数不仅在数学发展史上有着重大的历史意义,而且对科学的认识论和方法论产生了深远的影响,同时它在现代科技中也有着广泛的应用.在高中数学课堂教学中,复数章节的教学是“容易教”的难点课.一方面教材内容代数形式化的叙述,使学生对复数概念及其运算可以较轻松地获得机械的识记和应用,这就是复数内容表面上相对易教的原因;另一方面,正是教科书以复数产生的历史结果为出发点,以代数形式表示复数及形式化定义复数运算,它们掩盖了复数概念及复数运算产生的本原性问题,不利于复数及其运算的数学本质和思想方法的揭示.本研究基于问题驱动的数学教学理念,审视了高中复数教学的基本现状:首先,剖析了现行中学数学教科书中有关虚数引入、数系扩充和复数运算等知识点的叙述脉络,分析了教材编写中的存在问题;比较了主要发达国家及地区和我国有关中学复数知识的教学要求和教学内容的差异,指出我国高中复数教学要求的差距.其次,为了掌握中学复数教学的实际现状,通过听课观摩、教学研讨,对复数章节的教学进行调查研究,分析和寻找高中复数教学存在的问题及其根源;研究了中学一线教师有关复数教学方面的研究文献,考察数学教师对复数教学问题的相关认识.论文进一步介绍了复数产生和发展的脉络,阐述推动复数理论发展的深刻的物理背景,探讨了复数及其运算的重要思想和方法,并从数学思想性角度审视了高中复数内容的教学问题,提出高中复数教学内容重构的建议.最后,本研究在调查和分析的基础上,重构和编写了基于问题驱动的高中复数教学内容,希望能够准确把握复数产生与发展的本原性问题,希望能够深度挖掘在复数认识中起统帅作用的、触及与揭示复数本质的问题,并贯穿于问题驱动的复数教学内容的设计与重构.重构方案进行了教学试验和评价.新教学内容摒弃了代数视角,确立了几何与物理视角介绍复数,它能够很好地回答:为什么要提出和引入虚数概念?如何适当地定义复数概念和复数运算?这些概念和运算给我们带来了什么?复数的重大意义和科学价值体现在哪里?
[Abstract]:Plural is not only of great historical significance in the history of mathematics development, but also has a profound influence on the epistemology and methodology of science. At the same time, it is also widely used in modern science and technology. In the teaching of mathematics in senior high school, the teaching of plural chapters is a difficult course which is easy to teach. On the one hand, the formal description of the content algebra of the teaching material. It is easy for students to obtain mechanical memorization and application of complex number concept and its operation, which is the reason why the complex number content is relatively easy to teach on the surface; On the other hand, the textbook takes the historical result of the complex number as the starting point, expresses the complex number and formally defines the complex number operation in the algebraic form, which cover up the original problem of the complex number concept and complex number operation. This research is based on the problem-driven mathematics teaching concept, examines the basic situation of the complex number teaching in senior high school: first of all. This paper analyzes the narrative context of the knowledge points in the current middle school mathematics textbooks, such as the introduction of imaginary numbers, the expansion of the number system and the complex number operation, and analyzes the problems existing in the compilation of the textbooks. This paper compares the differences of teaching requirements and contents of plural knowledge in middle schools between the main developed countries and regions and our country, and points out the differences in the requirements of plural teaching in senior high schools in our country. In order to grasp the actual situation of plural teaching in middle schools, through the observation of lectures, teaching discussion, the teaching of plural chapters of the investigation and research, analysis and search for the problems and root causes of plural teaching in senior high school; This paper studies the literature on the plural teaching of the first-line teachers in middle schools, and investigates the mathematics teachers' understanding of the plural teaching. The paper further introduces the context of the emergence and development of the plural. This paper expounds the profound physical background of promoting the development of plural theory, probes into the important ideas and methods of plural number and its operation, and examines the teaching problems of plural content in senior high school from the angle of mathematical thought. Finally, on the basis of investigation and analysis, this study reconstructs and compiles the plural teaching content based on problem driven. Hope to accurately grasp the origin of the emergence and development of the plural, hope to be able to dig in depth in the plural understanding of the role, touch and reveal the essence of plural problems. And the design and reconstruction of the complex teaching content which is driven by the problem. The reconstruction scheme has carried on the teaching experiment and the appraisal. The new teaching content has abandoned the algebra angle, established the geometry and the physics angle to introduce the complex number. It can answer well: why put forward and introduce the concept of imaginary number? How to define plural concepts and complex operations properly? What do these concepts and operations bring us? Where is the significance and scientific value of the plural?
【学位授予单位】：广州大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：G633.6

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