勤于反思是中国学生核心素养“学会学习＂的要点之一，在学习数学的过程中，错 题反映学生的知识薄弱之处，是进行反思的良好材料。为了发挥错题的价值，发展学生 “学会学习＂的核 心素养，笔者计划进行在错题管理中培养高一学生数学解题反思的实 践研究。研究的问题包括 ： 学生在错题管理和解题反思方面存在的问题是什么 ？ 在错题 管理中培养高一学生数学解题反思 的教学策略是什么？

通过对现有文献进行梳理分析，发现现有研究大多数是关于解题反思或者错题管理 的研究，将二者结合起来的研究相对较少，从学生解题认知维度进行分析的更少。笔者 在相关研究的基础上设计相应问卷和访谈，从对错题反思的态度、错题笔记的订正策略、 解题反思技能三个方面进行设计。使用问卷对合肥某学校高一年级共计 498 名学生进行问 卷调查，并选取学生进行访谈，分析学生的错题笔记，发现学生存在以下问题 ：

第一，学生普遍不能认识到解题反思的重要性，将错题订正看作是再抄一遍，以大 量做题来代替反思。第二 ，学生错题笔记整理缺乏整体的设计和科学的笔记方法，不利 于学生把握知识间的联系。第三 ，解题反思的过程不够深入，反思的重点内容不明确， 学生反思错题的技能亟待提高。

笔者希望通过教学实践来解决上述调查中发现的问题，实践研究围绕必修第一册第 五章三角函数的内容展开。在分析三角函数一章的教学内容、教学重难点和学生常见错 误类型的基础上，结合调查发现的问题，笔者提出以下教学策略：

第一 ，设计每周一次的学法指导课，将其作为渗透重视反思错题的观念，交流错题 反思体验，提高错题反思技能的平台。第二 ，在错题笔记整理时使用思维导图、康奈尔 笔记法等科学系统的笔记方法。第三 ，基于喻平关于问题解决认知模式理论，笔者针对 反思的重点内容提出以下四条策略 ： （ 1) 反思数学知识间联系，搭建数学知识网络； ( 2) 反思数学问题题意，将数学问题具象化； （ 3) 反思数学问题解决过程，总结问题解决模 式； （ 4) 反思错题解题方法，注重改编变式。

笔者运用上述策略在三角函数一 章实行了为期一个半月左右的的实践研究，实验班 级共计 50 人。研究得到以下结论：自然状态下学生对错题进行解题反思的态度不够重视， 错题笔记管理策略不够系统科学，反思错题的重点内容不明确。在教学实践中笔者对提 出的教学策略进行了应用，发现学生对于解题反思的重视程度得到了提高，错题笔记更 加系统规范，学习成绩相较对照班级进步较大。

Diligent reflection is one of the key points of Chinese students' core literacy of 'learning to learn', in the process of learning mathematics, students' mistakes reflect their weak knowledge, it is a good material for reflection. In order to realize the value of incorrect questions and develop students' core literacy of "learning how to learn", The author plans to conduct practical research on cultivating mathematical problem-solving reflection among first year high school students through error management. The research questions include: What are the problems that students face in managing mistakes and reflecting on problem-solving? What is the teaching strategy for cultivating reflective thinking in math problem-solving among first year high school students in error management?

By reviewing and analyzing existing literature on problem-solving reflection and error management, the author believes that most of the existing research focuses on a certain aspect of problem-solving reflection or error management, there are relatively few studies that combine the two, especially those that analyze students' cognitive dimensions of problem-solving. Based on relevant research, the author designed corresponding questionnaires and interviews, the questionnaire and interview are designed from three aspects: attitude towards problem-solving reflection on incorrect questions, correction strategies for incorrect note taking, and problem solving reflection skills. A questionnaire survey was conducted on a total of 498 students in the first grade of a school in Hefei, and selected students were interviewed, analyzing students' error notes, it was found that they have the following problems:

Firstly, students generally do not recognize the importance of problem-solving reflection, and consider correcting incorrect questions as copying them again, replacing reflection with a large amount of problem-solving.

Secondly, the organization of students' wrong question notes is not scientific and systematic, lacking overall design and scientific note taking methods, which is not conducive to students grasping the connections between knowledge.

Thirdly, students' skills in reflecting on mistakes urgently need to be improved. The process of problem-solving and reflection is not deep enough, and the key content of reflection is not clear.

The author hopes to solve the problems found in the survey through teaching practice, the practical research revolves around the content of the fifth chapter of the compulsory volume of trigonometric functions. Based on the analysis of the teaching content, key and difficult points, and common types of errors made by students in the chapter on trigonometric functions, combined with the problems discovered through investigation, the author proposes the following teaching strategies:

Firstly, use the weekly learning method guidance class to instill in students the concept of valuing reflection on wrong questions, and use it as a platform for exchanging experiences of wrong question reflection and improving skills in wrong question reflection.

Secondly, scientific and systematic note taking methods such as mind mapping and Cornell's note taking are used when organizing error notes.

Thirdly, based on Yu Ping's cognitive model theory of problem-solving, the author proposes the following four strategies for the key content of reflection: (1) Reflecting on the connections between mathematical knowledge and building a network of mathematical knowledge; (2) Reflect on the meaning of mathematical problems and concretize them; (3) Reflect on the process of solving mathematical problems and summarize problem-solving models; (4) Reflect on problem-solving methods for mistakes and focus on adapting variations.

The author applied the above strategy to conduct a practical study in the chapter on trigonometric functions for about a month and a half, there are a total of 50 students in the practical class. The following conclusions were drawn from the study: In a natural state, students' attitude towards problem-solving and reflection on incorrect questions is not given enough attention, and the management strategy for incorrect question notes is not systematic and scientific enough. The key content for reflecting on incorrect questions is not clear. In teaching practice, the author applied the proposed strategies and found that students' emphasis on problem-solving and reflection has been increased. Mistake notes are more systematic and standardized, and their academic performance has improved significantly compared to the control class.