随着社会发展，学生的创新意识培养越来越受到重视，高中数学教育也开 始注重培养学生的发散性思维和创新思维，在此背景下，数学开放题逐渐成为 数学教育研究的热点课题。 对数学开放题的设计和其带来的教育价值，本文分为五个部分内容进行 论述。第一部分分析本文的研究背景，指出数学开放题进入课程教学是当今趋 势，并介绍研究目的和研究意义。 第二部分对众多学者的研究做综述，对数学开放题的概念做界定，分析数 学开放题的类型和特点，并在开放题具有的特点的基础上论述开放题的教育 价值。 第三部分对近年高考中出现的开放题做编制分析，结合开放题的特点，提 出了数学开放题设计所需遵循的要点，并设计出不同类型的开放题作为本研 究的测验调查卷。 第四部分对北京市某中学高一年级学生进行测验卷、问卷调查，分析学生 成绩数据，与该学校期末考试成绩做检验，验证开放题设计合理，学生成绩整 体稳定。问卷调查得出：对比封闭题，学生大致上认为开放题更能引发思考和 联想，超过一半学生认为有提升到对数学的信心，对数学更有兴趣。在此基础 上对四名学生和两位数学教师做访谈调查，了解学生认为开放题对得分的影 响，以及教师对开放题教育价值的态度。 第五部分对本研究进行总结，根据本文对开放题的编制方法制定测验卷， 2 题目设计合理，能够作为考察学生学习水平和知识掌握情况的方式，学生整体 得分情况与以往成绩没有显著性差异。通过问卷调查和访谈了解师生对开放 题教育价值持正面态度，开放题教育能够培养学生发散性思维、有助于调动学 习积极性、帮助学生建构知识结构和教师形成开放式教学观念。本文最后给出 有关开放题的教学实践建议，并探讨本次研究中的不足之处。

With the development of society, more and more attention has been paid to the cultivation of students' innovative consciousness, and high school mathematics education has also begun to pay attention to the cultivation of students' divergent thinking and innovative thinking. Under this background, mathematics open questions have gradually become a hot topic in mathematics education research. This thesis is divided into five parts to discuss the design of mathematics open question and its educational value. The first part analyzes the research background of this thesis, points out that it is the current trend for mathematics open questions to enter the course teaching, and introduces the purpose and significance of research The second part summarizes the research of many scholars, defines the concept of mathematical open questions, analyzes the types and characteristics of mathematical open questions. And discusses the educational value of open questions on the basis of its characteristics. The third part makes an analysis of the open questions in the college entrance examination in recent years. Combines the characteristics of the open questions, puts forward the key points to be followed in the design of mathematics open questions, and designs different types of open questions as the test survey paper of this study. In the fourth part, the thesis and questionnaire survey are conducted on the students in the first grade of a middle school in Beijing. Analyze the grade data and the grade of the final examination, this verifies that the design of open questions is reasonable and the overall stability of students' performance is stable. According to the questionnaire survey, compared with the closed ended questions, the students generally think that the open questions can trigger more thinking and association. More than half of the students think open questions have improved their confidence and more interested in mathematics. On this basis, four students and two mathematics teachers were interviewed. To understand how students perceive the impact of open questions on scores, and teachers' attitude towards the educational value of open questions. The fifth part is a summary of this study. According to the preparation method of open questions in this thesis. The questions are reasonably designed and can be used as a test to examine students' learning level and knowledge mastery. There was no significant difference between the overall scores of students and the previous 4 scores. Through questionnaire survey and interview, it is understood that teachers and students hold a positive attitude towards the educational value of open questions. The education of open questions can develop students' divergent thinking, it is helpful to mobilize students’learning enthusiasm and construct knowledge structure. Also, it promotes teachers form open teaching concepts. Finally, this thesis gives some suggestions on the teaching practice of open questions, and discusses the shortcomings of this study.