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摘要“数”与“形”是数学里两个最基本的概念，它们既是统一的，又是对立的。每一个的几何图形都含有与之大小、形状、位置等密切相关的数量关系；相反的，数量关系也常常可以通过几何图形来做出直观的描述与反映。数形结合的本质就是把直观的图形和抽象的数学语言相互结合起来，使抽象思维和形象思维这两种思维结合起来。 在解决相应的代数问题是，能够想到它的图形，从而启发自己的思维并以此找到解题的思路；或者在研究数学图形的时候，利用代数的性质，来解决几何中的问题。数形结合其最终的目的就是为了让一切难以理解的题目变得简洁明了，把复杂的题目变得简单，并且实现数与形的相互结合。我将从以下的几个方面来讲述数形结合的思想在中学数学中的应用：（1）在集合中的应用；（2）在解方程中的应用；（3）在解不等式中的应用；（4）在解析几何中的应用；（5）在解决最值、值域问题上的应用。通过文章中使用的分析、归纳和比较等几种方法充分地表现出数形结合在帮助学生处理实际问题时的优越性和特点，借此将数形结合的思想结合到课堂上然后传输给学生，并且还培养学生数形结合思想的意识。48387
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Abstract"Number" and "form" are the two most basic concepts in mathematics, they are unified but also opposite. Each geometric shape is closely related to the size, shape, position and so on. In contrast, the quantitative relation can also be used to make the intuitive description and reflection. The essence of the number line combination is to combine the visual graphics and the abstract mathematical language together, to combine the two kinds of thinking of abstract thinking and image thinking. In solving the corresponding algebraic problem is to think of its graphics, so as to inspire their thinking and tries to find the solution of ideas, or in mathematical research pattern when using the algebraic properties to solve geometry problems. The final purpose of the number shape combination is to make all the difficult problems become simple and clear, to make the complicated problems simple, and to achieve the combination of numbers and shapes. I will from the several aspects to tell application of number shape union thinking in middle school mathematics: (1) in the collection of application; (2) in the solution of equations in the application; (3) application of inequality in the solution; (4) in the analytic geometry application; (5) in solving the most value and range of application. Through the analysis, the induction and the comparison of several methods fully showed combination of number and shape in helping students to deal with practical problems of superiority and characteristics, to take the number shape union thinking binding to class although rear lost to students, and cultivate students' ideological consciousness of number and shape node.
毕业论文关键词：中学数学； 数形结合； 应用； 思想方法
Keyword: Middle school mathematics; Several form combined with; An application example; Thought method
目 录
1.引言5
2.数形结合思想概述5
3.数形结合的作用与地位5
4.数形结合的原则6
5.数形结合在中学数学中的应用6
5.1解决集合问题6
5.2解决解方程问题8
5.3解决不等式问题9
5.4数形结合在数列问题中的应用10
5.5数形结合思想解决最值、值域问题11
5.6数形结合思想在解析几何中的应用12
6.培养学生数形结合思想的一些教学措施12