数形结合思想在高中数学教学中的应用与分析
发布时间：2018-10-13 11:19
【摘要】：2003年4月,我国教育部制定并颁布了《普通高中数学课程标准(实验稿)》,其中提到“了解概念、结论等产生的背景,体会其中所蕴含的数学思想方法,以及它们在后续学习中的作用[1].”数形结合思想源于数学,是数学四大思想方法之一,也是高中数学学习的精髓,贯穿整个高中数学的学习.数形结合思想改变了数学中代数和几何相分离的趋势,把相对独立的“数”与“形”统一了起来.使抽象的代数方程和几何曲线有了完美的结合,推动了数学的发展.在高中数学中,分析数形结合思想具有重要的理论及现实意义,其作用主要体现在：丰富及完善高中数学解题理论,大力促进学生对数学知识的掌握,积极落实教育部颁布的高中数学新课标要求.利用数形结合思想可以引进新知识、构建新概念、解决新问题.利用数和形的互补激发学生的学习兴趣,进而为学生以后的学习和工作打下夯实的基础. 该论文结合自己的教学经验,研究了数形结合思想在高中数学教学中的现状.在教学中发现：学生基本上都可以运用数形结合思想解题,但是学生的数形结合思想的理解并不深刻,对它的历史发展认识不足,运用数形结合解题时解题思路及解题技巧并未达到预期的效果.在解题过程中还存在不少误区：(1)数形互化不等价、不简洁；(2)思维混乱,以偏概全；(3)互化过程陷入逻辑循坏；(4)画图潦草,引起错觉；(5)主观臆断,无中生有.造成这种结果的原因是多方面的：第一,教材上并没有给出数形结合思想的严格定义；第二,教师在平时教学中,重方法解题,轻思想培养；第三,学生逻辑思维、抽象思维有待提高. 通过对原因的分析,提出了培养学生数形结合思想的方法：实例法；数学现象的分析、整理与归纳法；概念、定理、推论的几何性质解释法.运用数形结合提高解题能力的教学方法有：教师运用新的教学观念,学生改变旧的学习方式；注重典型例题教学及对典型错误的分析；加强学生的数形互化能力.
[Abstract]:In April 2003, the Ministry of Education formulated and promulgated the Mathematics Curriculum Standard of General Senior High School (Experimental draft), which mentioned "understanding the background of concepts and conclusions, and experiencing the mathematical thinking methods contained therein." And their role in further learning [1]. " The thought of the combination of number and form originates from mathematics and is one of the four thought methods of mathematics. It is also the quintessence of mathematics study in senior high school and runs through the study of mathematics in the whole senior high school. The combination of numbers and shapes has changed the trend of separating algebra from geometry in mathematics and unified the relatively independent numbers and shapes. The abstract algebraic equation and geometric curve are combined perfectly and the development of mathematics is promoted. In senior high school mathematics, it is of great theoretical and practical significance to analyze the thought of combination of numbers and shapes. Its function is to enrich and perfect the theory of solving problems in high school mathematics, and to promote the students' mastery of mathematical knowledge. Actively implement the Ministry of Education issued the new high school mathematics curriculum requirements. New knowledge can be introduced, new concepts can be constructed and new problems can be solved by using the combination of numbers and shapes. Using the complement of number and form to stimulate students' interest in learning, and then lay a solid foundation for students' future study and work. This paper studies the present situation of the combination of numbers and shapes in mathematics teaching in senior high school. It is found in the teaching that students can basically solve problems by using the idea of combination of numbers and shapes, but their understanding of the idea of combination of numbers and forms is not profound, and they do not have enough understanding of its historical development. The thinking and skill of solving problems by combining numeral-form with problem-solving have not achieved the desired results. There are still many misunderstandings in the process of solving the problem: (1) the number and form are not equivalent and not simple; (2) the thinking is confused, which is partial and complete; (3) the mutual process falls into the bad logic; (4) the drawing is scribbled, causing the illusion; (5) the subjective assumption is made out of nothing. The reasons for this result are various: first, the textbook does not give a strict definition of the idea of combining numerals and shapes; second, teachers pay more attention to solving problems with methods rather than cultivating ideas in normal teaching; and third, students think logically. Abstract thinking needs to be improved. Based on the analysis of the reasons, this paper puts forward the methods of cultivating the students' thought of the combination of number and form: case method; the analysis, arrangement and induction of mathematical phenomena; the method of explaining the geometric properties of concepts, theorems and corollaries. The teaching methods of improving the ability of solving problems by using the combination of number and form are as follows: teachers use new teaching concepts, students change their old learning methods, pay attention to the teaching of typical examples and the analysis of typical mistakes, and strengthen the students' ability to transform each other into figures.
【学位授予单位】：信阳师范学院
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6
本文编号：2268425
[Abstract]:In April 2003, the Ministry of Education formulated and promulgated the Mathematics Curriculum Standard of General Senior High School (Experimental draft), which mentioned "understanding the background of concepts and conclusions, and experiencing the mathematical thinking methods contained therein." And their role in further learning [1]. " The thought of the combination of number and form originates from mathematics and is one of the four thought methods of mathematics. It is also the quintessence of mathematics study in senior high school and runs through the study of mathematics in the whole senior high school. The combination of numbers and shapes has changed the trend of separating algebra from geometry in mathematics and unified the relatively independent numbers and shapes. The abstract algebraic equation and geometric curve are combined perfectly and the development of mathematics is promoted. In senior high school mathematics, it is of great theoretical and practical significance to analyze the thought of combination of numbers and shapes. Its function is to enrich and perfect the theory of solving problems in high school mathematics, and to promote the students' mastery of mathematical knowledge. Actively implement the Ministry of Education issued the new high school mathematics curriculum requirements. New knowledge can be introduced, new concepts can be constructed and new problems can be solved by using the combination of numbers and shapes. Using the complement of number and form to stimulate students' interest in learning, and then lay a solid foundation for students' future study and work. This paper studies the present situation of the combination of numbers and shapes in mathematics teaching in senior high school. It is found in the teaching that students can basically solve problems by using the idea of combination of numbers and shapes, but their understanding of the idea of combination of numbers and forms is not profound, and they do not have enough understanding of its historical development. The thinking and skill of solving problems by combining numeral-form with problem-solving have not achieved the desired results. There are still many misunderstandings in the process of solving the problem: (1) the number and form are not equivalent and not simple; (2) the thinking is confused, which is partial and complete; (3) the mutual process falls into the bad logic; (4) the drawing is scribbled, causing the illusion; (5) the subjective assumption is made out of nothing. The reasons for this result are various: first, the textbook does not give a strict definition of the idea of combining numerals and shapes; second, teachers pay more attention to solving problems with methods rather than cultivating ideas in normal teaching; and third, students think logically. Abstract thinking needs to be improved. Based on the analysis of the reasons, this paper puts forward the methods of cultivating the students' thought of the combination of number and form: case method; the analysis, arrangement and induction of mathematical phenomena; the method of explaining the geometric properties of concepts, theorems and corollaries. The teaching methods of improving the ability of solving problems by using the combination of number and form are as follows: teachers use new teaching concepts, students change their old learning methods, pay attention to the teaching of typical examples and the analysis of typical mistakes, and strengthen the students' ability to transform each other into figures.
【学位授予单位】：信阳师范学院
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6
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