解析几何是高中数学课程的重难点内容，在《普通高中数学课程标准》中占据着重要的地位。但由于受应试教育的影响，很多学校和老师片面追求升学率，忽视了知识螺旋式上升的规律和学生主体性的培养。概念的讲解轻过程、重结论，学生容易死记硬背，不利于知识的有效迁移，亦或搞题海战术，加之解析几何繁杂的运算，使得高中生对解析几何的学习产生畏难情绪，学习兴趣不高，缺乏毅力。可见，高中生在解析几何学习中存在诸多障碍。在新课改背景下，针对高中生在解析几何学习过程中的障碍，本文为提高解析几何的教学质量提出了切实可行的教学对策，为一线教师的解析几何教学实践提供参考。

       本文以广东省广州市荔湾区某一中学2019届高三理科学生为研究对象，设计了解析几何测试卷和调查问卷，运用EXCEL软件和SOLO分类评价理论对调查结果进行统计分析，得到了高三学生在解析几何学习过程中存在许多障碍。在非认知障碍方面，学生学习解析几何的动机不强、兴趣不高、习惯不好，意志不坚定；在理解障碍方面，学生对解析几何基础知识特别是概念的理解能力不够、偏重于记忆、容易混淆；在数学思想方法运用障碍方面，学生对解析几何蕴含的数学思想方法的运用能力不足，不能灵活运用数学思想方法解决解析几何的综合问题；在运算障碍方面，学生存在运算过程不规范、运算马虎和运算困难等问题。

       根据以上对解析几何学习障碍的研究，本文提出了以下的教学对策：激发学生的学习动机，培养其学习兴趣；培养学生良好的学习习惯，坚定其学习意志；重视基础，循序渐进；加强解析几何数学思想方法的渗透；提高学生的运算能力。

        analytic geometry is an important and difficult part of high school mathematics curriculum，and it plays an important role in the "standards of mathematics curriculum for general senior high schools". however, due to the influence of the examination-oriented education, many schools and teachers unilaterally pursue the rate of enrollment, ignoring the law of the spiraling of knowledge and the cultivation of students' subjectivity. the explanation of the concept does not pay attention to the process and attaches importance to the conclusion. students are easy to memorize, which is not conducive to the effective transfer of knowledge, or engage in sea tactics. coupled with the complicated calculations of analytic geometry, high school students have a fear of analytic geometry learning, low interest in analytic geometry learning, and lack of perseverance. it can be seen that there are many obstacles in high school students' analytic geometry learning. in the context of the new curriculum reform, aiming at the obstacles of high school students in the process of analytic geometry learning, this paper puts forward practical teaching strategies for improving the teaching quality of analytic geometry, and provides reference for the analytic geometry teaching practice of frontline teachers.

        this paper takes 2019 high school science students from a high school in liwan district, guangzhou city, guangdong province as the research , designs analytic geometry test papers and questionnaires, uses excel software and solo classification evaluation theory to analyze the survey results, and obtains that there are many obstacles in the process of analytic geometry learning of the high school students. in terms of non-cognitive obstacles, students' motivation to learn to analyze geometry is not strong, their interests are not high, their habits are not good, and their will is not firm; in terms of understanding obstacles, students have insufficient ability to understand the basic knowledge of analytic geometry, especially concepts, focus on memory and easy to confuse; in terms of the obstacles of the use of mathematical thinking methods, students have insufficient ability to apply mathematical thinking methods in analytic geometry, and cannot use mathematical thinking methods to solve the comprehensive problem of analytical geometry; in terms of calculation obstacles, students have problems with the calculation process being irregular, calculating sloppy and difficult to calculate.

        based on the above research on analytical geometry learning obstacles, this paper proposes the following teaching strategies: stimulate students' motivation and develop their interest in learning; develop students' good study habits and strengthen their will to learn; pay attention to the foundation and proceed step by step; strengthen the penetration of analytic geometry thoughts. improve students' calculating ability.

摘 要 I
ABSTRACT III
1绪论 1
1.1研究背景 1
1.1.1解析几何的创立与发展 1
1.1.2解析几何的教育价值 2
1.1.3解析几何在高考中的地位 3
1.2研究问题 4
1.3研究过程与方法 5
1.3.1研究过程 5
1.3.2研究方法 6
1.4研究意义 7
2解析几何学习障碍的文献综述 9
2.1学习障碍和数学学习障碍的相关综述 9
2.1.1学习障碍的相关综述 9
2.1.2数学学习障碍的相关综述 10
2.2关于解析几何教与学的相关综述 11
3解析几何教学对策的理论基础 13
3.1维果茨基“最近发展区”理论 13
3.2建构主义学习理论 13
3.3SOLO分类评价理论 14
3.4非认知因素 15
4高三学生解析几何学习障碍的调查及分析 16
4.1调查研究的设计与实施 16
4.1.1调查研究的目的 16
4.1.2调查研究的对象 16
4.1.3调查研究的工具 16
4.1.4试卷的分发和回收 17
4.2测试卷的结果与分析 17
4.2.1测试卷的数据统计与分析 17
4.2.2测试卷的结论分析 39
4.3调查问卷的结果与分析 41
4.3.1调查问卷的数据统计与分析 41
4.3.2调查问卷的结论分析 49
4.4解析几何学习障碍的研究结论 50
5应对高中解析几何学习的教学对策 51
5.1应对高中解析几何学习中非认知障碍的教学对策 51
5.1.1激发学生的学习动机，培养其学习兴趣 51
5.1.3培养学生良好的学习习惯，坚定其学习意志 53
5.2重视基础，循序渐进 55
5.2.1重视概念教学，提高理解能力 55
5.2.2运用类比教学，培养迁移能力 56
5.3加强解析几何数学思想方法的渗透 58
5.3.1数形结合思想方法 58
5.3.2函数与方程思想方法 59
5.3.3转化与划归思想方法 61
5.3.4分类讨论思想方法 61
5.4提高学生的运算能力 62
5.4.1加强限时训练，提高运算速度 62
5.4.2选择适当的运算方法，简化运算过程 63
6研究结论、亮点、不足与展望 68
6.1研究结论 68
6.2研究的亮点 69
6.3研究的不足之处 69
6.4研究展望 70
致谢 71
参考文献 73
附录一 解析几何测试卷 76
附录二 解析几何调查问卷 78