高中函数母题研究

发布时间：2018-01-03 14:39

本文关键词：高中函数母题研究　出处：《苏州大学》2016年硕士论文　论文类型：学位论文

【摘要】：函数揭示了客观世界中量的相互依存和相互制约的关系,函数思想广泛地渗透到数学研究的全过程,函数又是初等数学和高等数学衔接的枢纽.例题教学在数学教学环节中起着重要的桥梁作用,它是诠释解题方法,展现解题思路,形成数学逻辑的重要手段.本研究以高一年级学生和一线教师为研究对象展开调查研究,全面深入地了解函数母题的设计原则以及评价标准.本文主要采用定性与定量研究相结合的混合研究方法,包括文献法、问卷调查法和访谈法.在确定了研究问题之后,首先围绕研究问题收集梳理了已有相关文献.根据文献综述结果拟定了调查问卷和访谈提纲,进而实施调查.最后对调查问卷和访谈所反馈的数据进行分析得到结论,并将结论反馈给教师,从而确定了母题设计的原则.而后根据其原则设计出了函数概念部分的母题,总结反思后得出相关结论,并给出了针对性的建议.通过研究得出以下结论:(1)母题的设计需要遵循一定的原则:(1)密切联系知识点;(2)涵盖数学思想方法;(3)题目可模型化;(4)结构相对简单.(2)母题的设计主要有如下策略:(1)基于概念的本质;(2)基于通用的方法;(3)基于基本的数学思想;(4)基于典型的课本例题.(3)依据母题评价标准单个原则评分不为0分,且总评分达到6分的例题才能作为母题.(4)母题代表着一类题型,学好母题能有效帮助学生解题.(5)母题的学习并不只是母题本身的学习,需要深入到思想和方法的学习上.(6)利用母题解题需要将题目拆解为已知母题,因此解题技巧的训练至关重要.
[Abstract]:Function reveals the relationship between the interdependence and mutual restriction of quantity in the objective world, and the thought of function permeates the whole process of mathematical research. Function is the hub of the connection between elementary mathematics and higher mathematics. Example teaching plays an important role in mathematics teaching. It is the interpretation of problem solving method and shows the thinking of problem solving. The main means to form mathematical logic is to investigate and study the first grade students and first-line teachers of senior high school. Comprehensive and in-depth understanding of the functional motif design principles and evaluation criteria. This paper mainly uses a combination of qualitative and quantitative research methods, including the literature method. Questionnaire and interview methods. After determining the research questions, first of all, around the research questions collected and combed the existing literature. According to the results of literature review, the questionnaire and interview outline are drawn up. Finally, the questionnaire and interview feedback data were analyzed to get a conclusion, and the conclusions were fed back to the teachers. In order to determine the principle of motif design, and then according to the principle of the design of the functional concept part of the motif, summed up the reflection of the relevant conclusions. The following conclusions are drawn: 1) the design of the motif should follow certain principles: 1) closely related to the knowledge points; (2) covering mathematical methods of thought; (3) problems can be modeled; (4) the structure of the motif is relatively simple. 2) the design of the motif is as follows: 1) Conceptual essence; 2) based on general-purpose methods; (3) based on basic mathematical ideas; (4) based on the typical textbook example. 3) according to the evaluation standard of the motif, the single principle score is not 0, and the total score is 6) the motif can be regarded as the motif. 4) the motif represents a kind of question type. Learning the motif well can help the students to solve the problem effectively.) the study of the motif is not just the study of the motif itself. We need to go deep into the study of ideas and methods. 6) using the motif to solve the problem needs to disassemble the problem into a known motif, so the training of problem-solving skills is very important.
【学位授予单位】：苏州大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6

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