中文题名: | 结构化情境下高三学生数学问题提出策略的现状研究 |
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保密级别: | 公开 |
论文语种: | chi |
学科代码: | 040102 |
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学生类型: | 硕士 |
学位: | 教育学硕士 |
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学位年度: | 2023 |
学校: | 北京师范大学 |
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第一导师姓名: | |
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提交日期: | 2023-06-30 |
答辩日期: | 2023-06-01 |
外文题名: | Research on Strategies for High School Seniors to Pose Mathematical Problems in Structured Situations |
中文关键词: | |
外文关键词: | Mathematical Problems Posing ; Structured Problem Situations ; Strategy Framework |
中文摘要: |
数学问题提出能力作为“四能”之一,在最新版的《普通高中数学课程标准 2017 年版2020年修订)》课程目标中占据重要地位 对相关问题进行理论和实践研究显得尤为重要和迫切。教师需了解学生提出问题的思维方式,才能帮助学生提高数学问题提出能力,揭示数学问题提出的过程以及数学问题提出的策略是亟需进 步深 研究的问题。基千此,本研究聚焦于高中生结构化情境下的数学问题提出,分析学生使用策略的倾向性及其原因,探讨不同情境下、解题前后学生提出问题的策略差异。 本研究在数学问题提出定义的基础上,结合已有研究 构建了数学问题提出策略的框架问题情境选取了更适用于我国学生提出问题的结构化情境 根据数学问题提出定义,给出问题提出的阶段;结合文献和数学问题提出实例,以如何改变问题和原情境下的初始条件作为策略分类标准 先确定数学问题提出策略的 级策略分类,即简化 系统改变、扩充、 般化 互换,然后进 步确定二级、三级策略,并明确每类策略的具体操作方式。 选取两个地区的高三学生共计 338 人,完成包含三类情境九道题的数学问题提出策略测试卷,其中 类情境为函数情境、立体几何情境和平面解析几何情境。基千数学问题提出策略的框架,将作答中提出的每个问题使用策略编码 并统计策略使用次数和人数。根据数据结果选取 名学生进行访谈,作为学生作答表现的补充。为从不同视角了解学生使用策略情况,访谈教师并进行课堂观察。 据此研究过程,研究发现对高三学生而言:(1)各类策略的使用情况存在显著差异;不论总体情况还是每个情境下,系统改变策略始终是使用次数和人数最多的策略,甚至均超过一半;互换和一般化策略的使用次数均较少;策略的使用过程中体现了日常学习对学生提出问题的影响,尤其在使用扩充、简化、系统改变中的改变问题策略时。(2) 不同情境下的数学问题提出策略存在差异,为学生提出问题提供了不同的发挥空间。(3) 解题前后数学问题提出策略使用次数差异显著,三类情境中解题前后每类策略的使用人数存在一致变化趋势,换言之,使用简化和系统改变的人数减少,使用互换、 般化、扩充的人数变多。 结合研究结果,本研究为教师提出两点建议:(1)选择不同青境和阶段为学生创设问题提出机会,学会预设学生使用的策略;(2)在日常课堂中适当穿插问题提出任务,渗透数学问题提出策略与数学思想方法。 |
外文摘要: |
The ability to pose mathematical problems, as one of the "Four Abilities", occupies an important position in the newly revised curriculum obj ectives of the Mathematics Curriculum Standard of Senior High School (2017 edition, revised in 2020). Theoretical and practical research on related problems is 兀i cularl important and urgent. Teachers need to understand students' ways of thinking when posing problems in order to help them improve their ability to pose mathematical problems, reveal the process of posing mathematical problems, and explore the strategies for posing mathematical problems, which urgently require further in-depth research. Based on this, this study focuses on high school students'mathematical problem posing in structured situations, analyzes their tendency to use strategies and their reasons, and explores the differences in strategies for mathematical problem posing among students in different contexts before and after problem-solving. Based on the definition of mathematical problem posing and existing research, this study constructs a theoretical framework for mathematical problem posing strategies: the problem situations selects a structured situations that is more suitable for Chinese students to pose problems; Propose a definition based on mathematical problems and provide the stage of problem posing; Combining literature and examples of mathematical problems, using how to change the initial conditions of the problem and the original situation as the classification criteria for strategies, first determine the primary strategy classification of mathematical problem posing strategies, Simplification, Systematic Variation, Extending, Generalizing, Reversing. Then further de er ne the secondary and tertiary strategies, and clarify the specific operation methods of each type of strategy. A total of 338 senior three students from two regions were selected to complete the mathematics problem posing strategy test paper containing nine questions in three types of situations, including functional situation, solid geometry situation and plane anal geometry situation. Based on the theoretical framework of proposing strategies for mathematical problems, each problem posed in the test is encoded with a strategy, and the number of times and number of people used are counted. According to the data results, 8 students were selected for interviews as a supplement to their response performance. To understand students'use of strategies from different perspectives, interview teachers and conduct classroom observations. Based on this research process, it was found that: (1) there are significant differences in the use of various strategies: regardless of the overall or each situations, Systematic Variation is always the strategy with the most frequency and number of users, even exceeding half; The frequency of use of Reversing and Generalizing has shown a sluggish state; The use of strategies reflects the impact of daily learning on students' problem-posing, especially when using strategies for Extending, Simplification, and Systematic Variation. (2) There are differences in the strategies for posing mathematical problems in different situations, providing students with different opportunities for problem-posing. (3) There is a significant difference in the number of times and numbers of strategies used to pose mathematical problems before and after problem-solving. In the three situations, there is a consistent trend in the number of people using each type of strategy before and after problem-solving. In other words, the number of people using Simplification and Systematic Variation decreases, while the number of students using Reversing, Generalizing, and Extending increases. Based on the research findings, this study proposes two suggestions for teachers: (1) Selecting different scenarios and stages to create opportunities for students to pose problems and learn to preset strategies for students to use; (2) Properly intersperse problem-posing tasks in daily classrooms, and incorporate mathematical problem posing strategies and mathematical thinking methods. |
参考文献总数: | 70 |
馆藏号: | 硕040102/23064 |
开放日期: | 2024-06-30 |