摘要：数量关系和空间形式是初等数学所研究的两个重要对象，“数”与“形”在现代数学中一直是密不可分的，两者之间可以互相转化，在高中阶段的学习中数形结合的思想尤为重要。通过代数分析来反映几何关系，同时又用几何直观反映数量关系。使形象思维和抽象思维相结合，从而起到简化问题的作用，本文旨在通过对近几年高考平面向量解法分析的来阐述数形结合思想在高中数学解题的应用。
笔者首先对平面向量的基本知识和数形结合思想做大致的阐述，后对近几年浙江高考的试题分析其解法，给出相应的教学策略：重视基底化和坐标化两大基础；结合向量的几何背景教学，补充必要的结论；进行开放式教学，以发现、探索的方式鼓励学生自行推导结论，培养发散性思维。
Quantitative relation and spatial form are two important research objects in elementary mathematics. "Number" and "form" have always been inseparable in the modern mathematics, which can be converted into each other.In the study of high school, the concept of combination of number and form is particularly important. Algebraic analysis reflects geometrical relation , and at the same time,geometry can clearly reflect quantity relation,combining image and abstract thinking to simplify problems. This paper aims to expound the application of the idea of combination of number and form in solving mathematical problems in high school through the analysis of plane vector solutions of college entrance examination in recent years.
First of all,the author roughly explains the basic knowledge of plane vector and the concept of combination of number and form, then analyzes the solutions in mathematics problems in Zhejiang college entrance examination in recent years and provides the corresponding teaching methods: attaching great importance to the two basis of basement and coordinate ,combining the geometry background of vector to teach,adding necessary conclusions, conducting open type teaching and using the teaching methods ‘find and explore’ to encourage students to derive conclusions so as to cultivate pergent thinking of students.
关键词：数形结合；平面向量；方法
Keyword: combine numbers with shapes；plain vector；method
目录
引言 4
1 数形结合与平面向量概述 4
1.1 数形结合概述 4
1.2 向量概述 5
2 平面向量的重要概念及其性质 6
2.1 向量 6
2.2 零向量 6
2.3 单位向量 6
2.4 平行向量（共线向量） 6
2.5 相等向量 6
2.6 向量的加法 7
2.7 相反向量 7
2.8 向量减法 7
2.9 向量的数乘 7
2.10 两个向量共线定理 8
2.11 平面向量基本定理 8
2.12 平面向量的坐标表示 8
2.13 平面向量的坐标运算 8
2.14 向量的数量积 9
2.15 向量的投影 9
2.16 两个向量的数量积的坐标运算 近五年来浙江高考的数形结合问题探究以平面向量为例:http://www.chuibin.com/shuxue/lunwen_206571.html