高中圆锥曲线的概念教学探究
发布时间：2018-09-04 15:49
【摘要】：圆锥曲线是高中平面解析几何的核心内容,它借助平面直角坐标系用坐标法研究平面几何图形的方程,并从方程出发,研究平面几何图形的性质,把数和形紧密结合在一起,充分展示了数形结合的思想方法。本文从圆锥曲线的历史出发,基于阿波罗尼奥斯(Apollonius,约公元前262～190年)的《圆锥曲线论》,从数学史的角度考察圆锥曲线的产生和发展过程。结合笔者多年的教学实践和领会,就大纲版高中数学教科书和新课标高中数学教科书(人教版)中各知识点的具体要求和变化进行探析,同时对现行人教版教科书(A版、B版)、苏教版、北师大版教科书进行简单比较,发现在由应试教育向素质教育转变的今天,不应“重解题,轻概念”,造成数学概念与解题相脱节,概念含糊不清则知识体系将不完整,这不符合素质教育的要求,也影响学生的思维品质。数学概念是学生学习数学知识的起点,是导出数学定理和数学相关知识的逻辑前提,是基础知识、基本能力教学的核心,是数学教学的重要组成部分,深刻理解概念的内涵与外延是掌握这些重要圆锥曲线的前提,因此要让学生动手、动脑、动口,对知识进行主动探索、主动发现、自主学习。通过比较分析,提出了圆锥曲线概念教学的处理方法：通过实例激发学生的学习兴趣；借助多媒体和数学教室展示圆锥曲线形成过程；用准确的语言文字描述圆锥曲线的概念并将其符号化；将概念运用到问题解决中,在概念教学中渗透数学思想方法；归纳典型题及教师如何合理地使用数学教科书中的内容等。在理解概念和应用概念上,采取活动式教学为主让学生主动参与其中,并结合从形到数、再从数到形的例题,充分地理解概念并进行相关的问题解决。教学中合理使用数学教科书中提供的例题和习题,通过深入挖掘进行变式训练、一题多解等培养学生的解题能力。
[Abstract]:Conic curve is the core content of plane analytic geometry in high school. It studies the equation of plane geometry by using coordinate method with the aid of plane rectangular coordinate system, and studies the properties of plane geometry from the point of view of equation, which combines the number and shape closely together. The thought method of the combination of number and form is fully demonstrated. Starting from the history of conic, based on the theory of conic by Apollonius, (about 262 ~ 190 BC), this paper investigates the generation and development of conic from the point of view of the history of mathematics. Combined with the author's teaching practice and understanding for many years, this paper probes into the specific requirements and changes of the knowledge points in the syllabus edition of senior high school mathematics textbooks and the mathematics textbooks in the new curriculum marking (people's Education Edition). At the same time, a simple comparison is made among the current textbooks for the education of people (A edition, edition B), the Soviet edition, and the edition of Peking normal University, and it is found that in today's transition from examination-oriented education to quality-oriented education, we should not "pay more attention to solving problems than to concepts." This will lead to the disconnection between mathematical concept and problem solving, and the ambiguity of concept will result in incomplete knowledge system, which does not meet the requirements of quality education and affect the thinking quality of students. The concept of mathematics is the starting point for students to learn mathematical knowledge, the logical premise for deriving mathematical theorems and related knowledge, the core of basic knowledge and basic ability teaching, and the important part of mathematics teaching. A deep understanding of the connotation and extension of the concept is the premise of mastering these important conic curves, so students should be allowed to start, use their brains, move their mouth, actively explore knowledge, discover actively, and learn independently. Through comparison and analysis, the paper puts forward the teaching methods of conic curve: arousing students' interest in learning through examples, displaying the forming process of conic curve by means of multimedia and mathematics classroom; The concept of conic curve is described and symbolized with accurate language and characters; the concept is applied to the problem solving, and the mathematical thinking method is infiltrated in the concept teaching; the typical problems and how to use the contents of the mathematics textbook reasonably are summarized. In terms of understanding concepts and applying concepts, active teaching is adopted to let students take part in them actively, and combined with examples from form to number, then from number to form, the concept is fully understood and the relevant problems are solved. In teaching, the examples and exercises provided in mathematics textbooks are used reasonably, and the students' ability to solve problems is trained by digging deeply and solving many problems.
【学位授予单位】：内蒙古师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6
本文编号：2222631
[Abstract]:Conic curve is the core content of plane analytic geometry in high school. It studies the equation of plane geometry by using coordinate method with the aid of plane rectangular coordinate system, and studies the properties of plane geometry from the point of view of equation, which combines the number and shape closely together. The thought method of the combination of number and form is fully demonstrated. Starting from the history of conic, based on the theory of conic by Apollonius, (about 262 ~ 190 BC), this paper investigates the generation and development of conic from the point of view of the history of mathematics. Combined with the author's teaching practice and understanding for many years, this paper probes into the specific requirements and changes of the knowledge points in the syllabus edition of senior high school mathematics textbooks and the mathematics textbooks in the new curriculum marking (people's Education Edition). At the same time, a simple comparison is made among the current textbooks for the education of people (A edition, edition B), the Soviet edition, and the edition of Peking normal University, and it is found that in today's transition from examination-oriented education to quality-oriented education, we should not "pay more attention to solving problems than to concepts." This will lead to the disconnection between mathematical concept and problem solving, and the ambiguity of concept will result in incomplete knowledge system, which does not meet the requirements of quality education and affect the thinking quality of students. The concept of mathematics is the starting point for students to learn mathematical knowledge, the logical premise for deriving mathematical theorems and related knowledge, the core of basic knowledge and basic ability teaching, and the important part of mathematics teaching. A deep understanding of the connotation and extension of the concept is the premise of mastering these important conic curves, so students should be allowed to start, use their brains, move their mouth, actively explore knowledge, discover actively, and learn independently. Through comparison and analysis, the paper puts forward the teaching methods of conic curve: arousing students' interest in learning through examples, displaying the forming process of conic curve by means of multimedia and mathematics classroom; The concept of conic curve is described and symbolized with accurate language and characters; the concept is applied to the problem solving, and the mathematical thinking method is infiltrated in the concept teaching; the typical problems and how to use the contents of the mathematics textbook reasonably are summarized. In terms of understanding concepts and applying concepts, active teaching is adopted to let students take part in them actively, and combined with examples from form to number, then from number to form, the concept is fully understood and the relevant problems are solved. In teaching, the examples and exercises provided in mathematics textbooks are used reasonably, and the students' ability to solve problems is trained by digging deeply and solving many problems.
【学位授予单位】：内蒙古师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6
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