摘要数形结合是解决数学题目中常用的一种数学方法思想，使用数形结合的方法能够使很多问题迎刃而解，且解法简洁。所谓的数形结合就是根据数与形的对应关系，通过数与形的各种转化来解决数学问题的一种思想方法。数形结合通过“以数助形、以形助数”，使复杂的问题简单化、抽象问题具体化，有助于把握数学问题的本质。46732

本文以高中教材为基础，阐述了数形结合思想在高中实践的应用。数形结合贯穿整个高中数学的学习，在线性规划问题、函数问题等问题中起到很大的作用。本文将对这类问题进行详细地介绍，同时本文选取的例题中有历年真题和高考模拟题，具有一定代表性，并且通过题目的改编使得该例题中数形结合思想能够更加充分的体现出来。

The Combination of Number and shapes is one of the mathematic methodology in the mathematics, which is commonly used to solve mathematical problems and the solution is simpler. The Combination of Number and shapes is the way that based on finding correspondence between the number and shape to solve mathematical problems, through various transformation between number and shape. Using “the number help shape “or “the shape help the number”, the Combination of Number and shapes can make the complex issues simpler, and the abstract issues more concrete. It is a great way to help people grasp the nature of mathematics problems.

This paper is based on high school mathematics textbook, introduce the Combination of Number and shapes and its complication, as a carrier to enhance the ability of students to study mathematics. The Combination of Number and shapes can be said throughout whole high school in mathematics learning process, both in complication. It plays a very significant role in the linear programing problems, the function problems and more. The author will introduce the Combination of Number and shapes, its complication and problems will meet in the paper. At the same time, there are examples in this article selected from the university entrance exam, providing good representative.by making adaptation of the examples, the characteristics of the combination of number and shapes will be more obvious.

毕业论文关键词：数形结合； 应用；高中数学；注意问题

Keyword: The Combination of Number and shapes； complication；high school in mathematics teaching； 

目    录

摘    要 2

1 数形结合的含义和研究背景、意义 4

1.1 数形结合的含义 4

1.2 数形结合思想应用大致又可分为两种情形: 4

1.3 利用数形结合思想能够主要解决的几种问题： 4

2 数形结合研究的意义 4

2.1 从历史角度理解数形结合研究的意义 4

2.2 从现代教育角度理解数形结合研究的意义 5

2.2.1  从课标角度理解数形结合研究的意义 5

2.2.2  从高考角度理解数形结合研究的意义 5

2.2.3  从教学角度理解数形结合研究的意义 5

3 数形结合在高中教学实践中的应用