高中生函数问题解决过程中化归思想的案例研究
发布时间：2019-04-26 15:14
【摘要】：化归思想作为高中数学中最为重要和基本的思想之一,一直是数学教育工作者共同思考和研究的热点.可以说,整个高中数学内容都渗透了化归思想,而且它还统领着大多数的数学方法,在数学中有着不可替代的地位.然而,对目前数学学科中化归思想研究的文献查阅来看,比较常见的现象是对化归的策略和原则等进行举例说明,或者是对化归的各种手段和方法进行阐述,而针对学生本身的化归思维过程的研究较少,特别是学生化归思想的状况、发展特点及如何形成化归思想等研究还不够系统.为此,本研究力求对高中生数学化归思想进行系统的研究,并以函数教学为例对化归的思维过程进行分析,对化归思想的教学提供一些参考建议.本研究主要采用文献分析法、访谈法,对当前高中生数学函数化归进行了访谈调查与案例分析研究.本论文分为以下几部分:(1)问题的提出.通过对化归思想教学背景的分析,提出化归思想促进数学教学,并且在高中数学教学中,运用化归思想解决数学问题的机会较多.(2)相关研究综述,对国内外有关化归思想研究的文献的查阅与分析,掌握化归思想的研究现状和动态,为本研究的开展奠定基础.(3)问卷调查和访谈.选择某校高一学生学作为研究对象,进行问卷调查和访谈,了解目前学生的化归思想状况.(4)个案研究.通过对个案资料的研究,分析影响学生化归能力的因素主要有学生的原有知识结构、元认知水平及教师的教学观,并在此基础上提出一些思考建议.本研究得到的主要观点如下:学生的原有知识水平是化归得以实现的基石;高一学生的元认知水平普遍不高,导致不能对自身的化归过程进行有效的调控;很多学生都缺乏对自身原有知识内容进行归纳整理,难以快速的化到已知问题链.此外,我们通过访谈调查初步推断:原有数学知识、元认知水平和数学教师的教学观是高中生数学化归的主要影响因素.
[Abstract]:As one of the most important and basic thoughts in high school mathematics, the thought of conversion has always been a hot spot for mathematics educators to think and study together. It can be said that the whole high school mathematics content permeates the thought of transformation, and it also dominates most mathematics methods, and has an irreplaceable position in mathematics. However, looking up the literature on the thought of transformation in mathematics at present, the more common phenomenon is to give examples of the strategies and principles of transformation, or to elaborate on the various means and methods of transformation. However, there is little research on the process of students' thinking, especially on the condition, development characteristics and how to form the thought of transformation and so on, which are not systematic enough. Therefore, this study tries to make a systematic study on the thought of mathematical transformation of senior high school students, and takes the function teaching as an example to analyze the thinking process of transformation, and provides some reference suggestions for the teaching of the thought of transformation. This research mainly uses the literature analysis, the interview method, has carried on the interview investigation and the case analysis research to the current senior high school student mathematics function reduction. This paper is divided into the following parts: (1) the issue of the proposed. Through the analysis of the teaching background of the thought of transformation, this paper puts forward the idea of transformation to promote mathematics teaching, and in high school mathematics teaching, there are many opportunities to apply the thought of transformation to solve mathematics problems. (2) the related research is summarized. The review and analysis of domestic and foreign literature on the thought of transformation, the present situation and trend of the research on the thought of reversion, lay the foundation for the development of this study. (3) questionnaire investigation and interview. A survey and interview were conducted to find out the current situation of students' thinking. (4) A case study was carried out in the first year of senior high school as the object of study. (4) A case study was carried out in this paper. Through the study of the case data, this paper analyzes the factors that affect the students' ability to return to biochemistry, such as students' original knowledge structure, metacognitive level and teachers' view of teaching. On this basis, some suggestions are put forward. The main points obtained in this study are as follows: students' original level of knowledge is the cornerstone of the realization of transformation, and the metacognitive level of senior one students is generally low, which leads to the inability to effectively regulate and control their own process of transformation; Many students lack to sum up their original knowledge and content, so it is difficult to quickly turn to known problem chain. In addition, we infer that the original mathematics knowledge, metacognitive level and the teaching view of mathematics teachers are the main influencing factors of mathematics transformation of senior high school students.
【学位授予单位】：江西师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6
本文编号：2466183
[Abstract]:As one of the most important and basic thoughts in high school mathematics, the thought of conversion has always been a hot spot for mathematics educators to think and study together. It can be said that the whole high school mathematics content permeates the thought of transformation, and it also dominates most mathematics methods, and has an irreplaceable position in mathematics. However, looking up the literature on the thought of transformation in mathematics at present, the more common phenomenon is to give examples of the strategies and principles of transformation, or to elaborate on the various means and methods of transformation. However, there is little research on the process of students' thinking, especially on the condition, development characteristics and how to form the thought of transformation and so on, which are not systematic enough. Therefore, this study tries to make a systematic study on the thought of mathematical transformation of senior high school students, and takes the function teaching as an example to analyze the thinking process of transformation, and provides some reference suggestions for the teaching of the thought of transformation. This research mainly uses the literature analysis, the interview method, has carried on the interview investigation and the case analysis research to the current senior high school student mathematics function reduction. This paper is divided into the following parts: (1) the issue of the proposed. Through the analysis of the teaching background of the thought of transformation, this paper puts forward the idea of transformation to promote mathematics teaching, and in high school mathematics teaching, there are many opportunities to apply the thought of transformation to solve mathematics problems. (2) the related research is summarized. The review and analysis of domestic and foreign literature on the thought of transformation, the present situation and trend of the research on the thought of reversion, lay the foundation for the development of this study. (3) questionnaire investigation and interview. A survey and interview were conducted to find out the current situation of students' thinking. (4) A case study was carried out in the first year of senior high school as the object of study. (4) A case study was carried out in this paper. Through the study of the case data, this paper analyzes the factors that affect the students' ability to return to biochemistry, such as students' original knowledge structure, metacognitive level and teachers' view of teaching. On this basis, some suggestions are put forward. The main points obtained in this study are as follows: students' original level of knowledge is the cornerstone of the realization of transformation, and the metacognitive level of senior one students is generally low, which leads to the inability to effectively regulate and control their own process of transformation; Many students lack to sum up their original knowledge and content, so it is difficult to quickly turn to known problem chain. In addition, we infer that the original mathematics knowledge, metacognitive level and the teaching view of mathematics teachers are the main influencing factors of mathematics transformation of senior high school students.
【学位授予单位】：江西师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6
【参考文献】
相关期刊论文 前1条
1 曾峥,杨之;“化归”刍论[J];数学教育学报;2001年04期
相关硕士学位论文 前1条
1 余霞辉;高中数学解题中的化归方法及其教学研究[D];湖南师范大学;2007年
，本文编号：2466183
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