数学教育活动中，解题是最基本的活动形式。无论是学生数学概念的形成、数学命题的掌握、数学方法和技能技巧的获得，还是学生智力的培养和发展，都必须通过解题。同时，解题也是评价学生的知识和发展水平的主要手段。虽然我们都希望学生能够顺利地解题，但是学生在解题过程中出现错误是不可避免的。事实上，学生在学习过程中所产生的错误是更为鲜活的教学资源，教师只有充分利用这一错误资源，深入了解学生的解题错误，才能进行更加有效的学习指导，从容把控课堂教学的进程，从而提高学生的学习效率和课堂的教学质量。圆锥曲线作为平面解析几何的核心内容，是高中生数学学习一大难点，学生往往会暴露出许多解题错误。综上所述，有必要对圆锥曲线的解题错误进行深入剖析。

本文通过文献研究，确立了以戴再平、罗增儒和马文杰对于数学解题错误的分析理论为基本研究框架。以广东省某示范性高中226名学生解决8道圆锥曲线解答题时所呈现的全部解题过程作为研究对象，通过文本分析法、描述性统计法等方法研究并总结了高中生在解决圆锥曲线问题时主要出现的错误类型以及出现错误的主要原因。结合对一线数学教师的访谈，形成了减少高中生圆锥曲线解题错误的教学建议。

通过研究，得到以下研究结论：

首先，高中生在解决圆锥曲线问题时出现的解题错误主要是心理性错误和逻辑性错误，其次为知识性错误和策略性错误。从三类学生的角度分析，学优生在解答圆锥曲线题目时主要会出现心理性错误，中等生在解题过程中主要会出现逻辑性错误，学困生在解题过程中主要会出现知识性错误。（1）心理性错误主要表现为计算错误、书写错误以及存在“潜在假设”心理；（2）逻辑性错误主要表现为不能推出和分类不当；（3）知识性错误主要表现为圆锥曲线几何性质记忆混淆；（4）策略性错误主要表现为不能选择最佳解题方案，将解题过程复杂化。

其次，高中生出现圆锥曲线解题错误的主要原因最终可以归结为以下5个方面：（1）学生的运算能力较差；（2）存在“潜在假设”心理；（3）缺乏运用数学思想方法的意识；（4）基础知识掌握不牢固；（5）数学思维能力不足。

最后，基于上述研究结论，得到了减少高中生圆锥曲线解题错误的几点教学建议：（1）区别对待学生不同类型的错误；（2）克服“潜在假设”的负面影响；（3）充分利用学生自然生成的错误资源。

In mathematics education activities, problem solving is the most basic form of activity. Both the formation of mathematical concepts, the mastery of mathematical propositions, the acquisition of mathematical methods and skills and techniques, and the cultivation and development of students' intelligence must be achieved through problem solving. At the same time, problem solving is the primary means of assessing students' knowledge and developmental level. Although we all want students to be able to solve problems successfully, it is inevitable that students will make mistakes in the process of problem solving. In fact, students' errors in the learning process are more vivid teaching resources. Teachers can only make full use of this error resource to understand students' problem solving errors in depth, so that they can provide more effective learning guidance and control the classroom teaching process comfortably, thus improving students' learning efficiency and classroom teaching quality. As the core content of plane analytic geometry, conic curves are the key point and a major difficulty in mathematics learning for high school students, and students often expose many problem solving errors. In view of the above, it is necessary to make an in-depth analysis of the solution errors of conic curves.

In this paper, through literature research, the basic research framework was established with the analysis theories of Dai Zaiping, Luo Zenru and Ma Wenjie for mathematical problem solving errors. Using the solution process of eight conic curve problems already done by 226 students in a model high school in Guangdong Province as the research object, the main types of errors made by high school students in solving conic curve problems and the main reasons for the errors were studied and summarized through the textual analysis method. Combined with the interviews with front-line mathematics teachers, teaching suggestions for reducing conic curve solving errors of high school students were formed.

The following findings were obtained from the study.

First, the solution errors made by high school students in solving conic curve problems were mainly mental and logical errors, followed by intellectual and strategic errors. In addition, analyzed from the perspective of three types of students, the superior students mainly make psychological errors in solving conic curve problems, the intermediate students mainly make logical errors in the process of solving problems, and the poor students mainly make intellectual errors in the process of solving problems. (1) Psychological errors are mainly manifested by calculation errors, writing errors and the existence of "potential assumptions"; (2) Logical errors are mainly manifested by the inability to launch and misclassification; (3) Intellectual errors are mainly manifested by memory confusion of geometric properties of conic curves; (4) Strategic errors are mainly manifested by the inability to choose the best solution to the problem, complicating the solution process. (4) Strategic errors are mainly manifested by the inability to choose the best solution and complicate the process of problem solving.

Secondly, the main reasons for the conic curves' errors in high school students can be attributed to the following five aspects: (1) students' poor arithmetic ability; (2) the existence of "potential assumptions" mentality; (3) lack of awareness of using mathematical thinking methods; (4) poor mastery of basic knowledge; (5) insufficient mathematical thinking ability.

Based on the above findings, the following teaching suggestions were finally formulated to reduce the errors of high school students in solving conic curves: (1) treating students' different types of errors differently; (2) overcoming the negative effects of "potential assumptions"; (3) making full use of students' naturally generated error resources.