中学生排列组合解题策略的调查研究

发布时间：2017-12-28 06:39

本文关键词：中学生排列组合解题策略的调查研究　出处：《华东师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：排列组合是离散数学的重要分支,被视为最难教授与学习的数学领域之一,每年高考都会涉及但得分率较低。此外,通过文献阅读发现,国内的相关研究大部分是教学设计以及解题方法的总结归纳。鉴于以上背景,本研究主要调查中学生排列组合的解题策略以及错误类型。本研究通过调查测试卷和访谈研究以下四个问题:(1)中学生在排列组合测试中的整体表现如何?(2)在排列组合的应用中,中学生更偏好哪些解题策略?(3)在排列组合的应用中,中学生会出现哪些常见的错误类型?(4)学生对排列组合的理解与年级和性别因素有怎样的关系?研究结果发现,中学生在排列组合问题上的整体表现不佳,排列问题要难于组合问题,均匀分配问题要难于非均匀分配问题。在解题策略方面,中学生会使用纯枚举法、系统枚举法、图表法以及公式法。同种题型,当题目的数据较小时,使用纯枚举法的人数会变多,高中生一般用公式法,初中生一般用枚举法。错误类型主要是直观性的错误答案、计算错误、对问题的错误理解、次序错误、混淆对象类型、混淆单元类型、公式错误、忘记公式中参数的含义。另外,学生的表现与年级优势、性别优势相符,但是年级差异要比性别差异显著。最后根据本研究的结论,对排列组合的教学提出一些意见和建议。
[Abstract]:Permutation and combination is an important branch of discrete mathematics, which is regarded as one of the most difficult mathematical fields to teach and learn. Every year, the college entrance examination will be involved but the score is low. In addition, through literature reading, it is found that most of the relevant research in China is a summary of the teaching design and the method of solving the problem. In view of the above background, this study mainly investigates the problem solving strategies and the types of errors in the permutation and combination of middle school students. This study through the investigation tests and interview on the following four questions: (1) middle school students in the arrangement of how the overall performance of combination testing? (2) in the application of permutation and combination, students prefer what problem-solving strategies? (3) in the application of permutation and combination, students what are the common mistakes? (4) what is the relationship between understanding and gender and grade factors of students of permutation and combination of the results of the study showed that middle school students? Poor overall performance in the arrangement of the problem difficult to combinatorial problems, uniform distribution problems difficult to non-uniform distribution problems. In the field of problem solving strategy, middle school students use pure enumeration method, systematic enumeration method, chart method and formula method. In the same type, when the data of the subject is small, the number of the enumerated methods will be much more. The high school students usually use the formula method, and the junior high school students usually use the enumeration method. The types of errors are mainly visual errors, calculation errors, misunderstandings of questions, sequence errors, confused object types, confusion units, formula errors, and the meanings of parameters in forgetting formulas. In addition, the students' performance is consistent with the grade and sex superiority, but the grade difference is more significant than the gender difference. Finally, according to the conclusion of this study, some opinions and suggestions on the teaching of permutation and combination are put forward.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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