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摘要数形结合是数学中特有的一种基本方法，其思想主要产生于数学。数形结合思想有利于学生对所学知识的掌握与记忆，能培养学生的数学直觉思维能力，有利于培养学生的发散思维能力，有益于培养学生的创造性思维能力。在数学解题中运用数形结合思想可以使某些抽象的数学问题变得更加直观和生动，有助于抓住数学问题的本质，更好帮助学生对数学知识进行识记和掌握，发展数学思维。本文从以数解形和以形助数两个方面，分别分析了利用代数法、面积法解决几何，利用图形解决函数问题、利用图形解决方程和不等式问题以及构造几何图形解决代数问题几种情况，从这几方面讲述数形结合在中学数学解题中的应用为数学解题带来的便利，以开拓学生的创造性思维，促进其学习数学知识。同时，在了解数形结合给数学解题带来的简便后，分析了应用该思想方法的注意点，以及数形结合方法存在的局限性。作为教师，应发挥数形结合方法的优势，同时注意培养学生的思维，使其有更大的进步。48395
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Symbolic-graphic combination is a basic method in Mathematics. It mainly produces in Mathematics. Symbolic-graphic combination is conducive to the students to learn the knowledge and memory, can cultivate students' mathematical intuitive thinking ability, is conducive to the cultivation of students' pergent thinking ability, beneficial to the training of students' creative thinking ability. Symbolic-graphic combination is a common method in solving mathematical problems, number shape union thinking can make some abstract mathematics problems intuitive, vivid, can change the abstract thinking is the thinking in images helps to grasp the essence of mathematical problems, can help students to learn the knowledge and memory. This article from to the number of solutions and help to form the two aspects were analyzed using algebraic method, the area method solve geometry, using graphics to solve function problems, using graphics to solve equations and inequalities and structural geometry to solve the algebraic problem, from the about number shape combined with the application in the middle school mathematics for solving mathematical problems bring convenience, to develop students' creative thinking, promote the learning of mathematics knowledge. Meanwhile, after understanding the advantage of symbolic-graphic combination to solve mathematical problem, analyzing the attention of the application of this method, also the limitations of the method of number shape combination. As a teacher, we should give full play to the advantages of the combination of number and shape, at the same time, pay attention to the cultivation of students' thinking, and make it have greater progress.
毕业论文关键词：数学方法； 数形结合思想； 中学数学教学； 数学解题；
Keyword: Mathematical method；symbolic-graphic combination； Middle school mathematics teaching；mathematics problem solving
目录
一、数形结合的起源及发展史 1
二、数形结合在中学数学教学中的地位 1
三、数形结合思想在中学数学教学中的研究意义 2
四、数形结合方法在中学数学问题解决中的应用 4
4.1 以数解形 4
4.1.1利用函数解决几何的问题 4
4.1.2 利用面积法解决几何问题 5
4.2 以形助数 5
4.2.1 利用几何图形解决函数问题 5
4.2.2 利用图形解决方程和不等式问题 8
4.2.3 利用几何图形解决代数问题 8
4.2.4 利用数形结合求方程中未知常数的取值范围 9
五、在数形结合思想方法的教学过程中要注意的几个问题 10