教材是课程改革与发展的先导，也是落实课程标准的载体．在高中数学教材中，几何和代数主线具有重要地位，向量作为沟通几何与代数的桥梁是其重要组成部分．因此，在新的课程标准的背景下，教材中的向量内容是一个非常值得研究的问题．

本学位论文从高观点下教材的内容、教材的结构以及学生在向量几何代数属性测试题的学业成绩表现三个维度出发，采用比较研究、测量研究、相关性分析等方法对教材进行综合研究，并给出了具体的教材编写建议和实例．

在高观点下教材内容方面，本文保持了向量历史发展的原始内容，并与高中教材进行紧密结合. 结果显示：目前教材内容主要以古典数学时期的向量内容为主，没有与现代数学中向量空间定义下的向量内容进行融合，忽视向量内容中公理化和结构化的数学思想.

在教材结构方面，北师大版与人教版教材的核心知识的解释结构模型显示：两个版本的教材的基础层级结构相同，核心知识层级都是向量的运算，向量投影知识均出现在数量积知识之后，并且重视利用数量积计算投影．从总体上看，北师大版重视向量代数与几何之间的联系，而人教版重视向量的代数运算. 

在相关性分析方面，除了采用皮尔逊相关性分析研究学生在向量几何和代数属性上学业成绩表现的相关性外，本文还创造性地使用了广义相关测量．结果显示：学生在几何和代数属性上的学业成绩表现具有很强的正相关关系，学生在代数属性上的学业成绩表现对其在几何属性上的学业成绩表现影响更大．这表明，在教材编写过程中，应该适当地重视向量知识代数思想的传递．

基于以上研究结果，本文主要从向量的定义、有向线段与有序实数组关系的建立、向量投影与向量数量积的定义三方面给出了教材编写的意见以及相应的教材实例．

Textbooks are the forerunners of curriculum reform and development, as well as the carrier of the implementation of curriculum standards. Geometry and algebraic mainlines play an important role in high school mathematics textbooks, and vector are an important part of communicating geometry and algebra. Therefore, in the context of the new curriculum standards, vector content in the textbook is a very worthy of study.

Starting from the content of the teaching material from an advanced standpoint, the structure of the textbook and the academic performance of the students in the vector geometric algebraic attribute test question, this degree thesis makes a comprehensive study of the textbook by means of comparative research, measurement research, correlation analysis, etc., and gives some specific suggestions and examples for the preparation of the textbook.

In terms of textbook content from an advanced standpoint, this study maintains the original content of vector historical development and closely integrates with high school textbooks. The results show that the content of textbook is mainly vector content in classical mathematics period, which is not integrated with vector content under the definition of vector space in modern mathematics, and neglects the mathematical thought of axiom and structure in vector content.

In terms of the structure of textbooks, the interpretation structure model of the core knowledge of textbooks of Beijing Normal University’s edition and PEP’s edition shows that the basic hierarchy of the two versions of the textbook is the same, the core knowledge hierarchy is the operation of vector. The knowledge of vector projection appears after the knowledge of scalar product, and attaches great important to calculating the projection by scalar product. Generally speaking, the BNU’s Edition attaches great importance to the connection between vector algebra and geometry, while the PEP’s attaches great importance to the algebraic operation of vector.

In terms of correlation analysis, in addition to using Pearson correlation analysis to study the correlation between students' academic performance in vector geometry and algebraic properties, the study also creatively uses generalized correlation measurement. The results show that there is a strong positive correlation between students' academic performance in geometry and algebra, and students' academic performance in algebra has a greater impact on their academic performance in geometry. This shows that in the course of textbook compilation, we should pay proper attention to the transmission of vector knowledge algebraic thought.

Based on the above research results, this study mainly gives the opinions of textbook writing and the corresponding examples from three aspects, those are the definition of vector, the establishment of the relationship between directed segment and ordered real numbers set, vector projection and the definition of scalar product.