初中生数学作图能力的研究
发布时间：2018-08-30 12:36
【摘要】：在初中数学教材中,几何图形是一块很重要的学习内容。在实际生活、生产甚至是科技研发中,有很多实际问题是需要借助几何图形的知识来进行解决的,因此,学生对于几何图形的学习是很有必要的。数学作图能力是学生在学习几何图形时应该掌握的一种重要能力,不仅能提高学生的空间想象能力,还能促进学生问题解决能力的发展。本文以初中生数学作图能力的研究为研究内容,并分别对以下几个问题进行了深入的研究:数学作图能力的衡量标准有哪些?初中生数学作图能力的现状怎么样?影响初中生数学作图能力的因素是什么?培养初中生数学作图能力的原则、方法与途径有哪些?对数学作图教学的启示有哪些?本文基于教育学和心理学的相关知识,结合数学教学论、数学方法论以及多种版本的初中数学教材,从理论和实践两个方面进行了深入的研究。首先,在整理国内外数学图形研究现状的基础上,确定本文的研究内容为:初中生数学作图能力的研究,并对“数学作图能力”是什么进行了思考。紧接着,采用问卷调查法和访谈法对临沂第三十五中学的全体数学教师和七、八、九三个年级的300名学生进行了实证调查。根据教材中与数学作图相关的内容编制了测试卷,又对这300名学生进行了测试。然后,从多个角度分析了测试结果,分类总结出学生在数学作图时存在的问题并进行了归因。最后结合自身的教学体会,对如何培养初中生数学作图能力提出了六条培养原则和五种培养方法。本论文分为五个部分,主要内容如下:第一部分是问题的提出,分别从数学课程改革的需求、新课程标准的要求和数学作图对数学学习的重要性这三个方面提出了问题研究的背景及意义;又详细阐述了国内外关于数学图形的研究现状,并比较了本文的研究与国内外研究的联系和区别。第二部分是理论分析,主要阐述了数学能力的界定、数学作图能力的界定、数学作图能力与数学作图技能及空间想象能力的关系比较、对数学作图能力的衡量标准的分析和对培养初中生数学作图能力教材设置的解读。第三部分是初中生数学作图能力的调查与分析,这是本文的核心部分。通过对教师和学生的调查结果的分析,结合对学生测试结果的研究全面分析了初中生数学作图能力的现状,并找出了影响初中生数学作图能力的发展的因素。第四部分是培养初中生数学作图能力策略的研究,根据调查和测试的结果分析出初中生数学作图能力培养过程中存在的问题,提出了培养初中生数学作图能力的建议、培养原则、培养方法与途径,并以一个教学案例展示了教师在数学作图教学中对学生数学作图能力的培养情况。第五部分是反思与建议,总结了本文研究中存在的不足,并展望了进一步的研究方向。
[Abstract]:In junior high school mathematics teaching material, geometry is a very important learning content. In real life, production and even R & D of science and technology, there are many practical problems that need to be solved with the knowledge of geometry. Therefore, it is necessary for students to learn geometry. Mathematical drawing ability is an important ability that students should master when learning geometry. It can not only improve students' spatial imagination ability, but also promote the development of students' problem-solving ability. This paper takes the research of junior high school students' mathematical mapping ability as the research content, and carries on the thorough research to the following several questions separately: what is the measurement standard of the mathematics drawing ability? What is the current situation of junior high school students' mathematical mapping ability? What are the factors that affect the mathematical mapping ability of junior high school students? What are the principles, methods and approaches for developing the mathematical mapping ability of junior high school students? What is the enlightenment to mathematics drawing teaching? Based on the relevant knowledge of pedagogy and psychology, combined with mathematics teaching theory, mathematical methodology and various versions of junior high school mathematics teaching materials, this paper makes a deep research from two aspects: theory and practice. First of all, on the basis of sorting out the present situation of mathematical graphics research at home and abroad, this paper determines that the research content of this paper is: the study of junior high school students' mathematical drawing ability, and think about what "mathematical drawing ability" is. Then, the questionnaire and interview method were used to investigate all mathematics teachers and three hundred students in grade seven, eight and ninety-three in Linyi No. 35 Middle School. According to the content of mathematics drawing in the textbook, the test paper was compiled and the 300 students were tested. Then, the test results are analyzed from several angles, and the problems existing in mathematical mapping are summarized and attributed. At last, the author puts forward six training principles and five training methods on how to cultivate junior high school students' ability of drawing mathematics in combination with their own teaching experience. This paper is divided into five parts, the main contents are as follows: the first part is the problem raised, respectively from the needs of mathematics curriculum reform, The requirements of the new curriculum standard and the importance of mathematical drawing to mathematics learning are put forward in this paper, and the background and significance of the problem research are put forward, and the current research situation of mathematical graphics at home and abroad is described in detail. The relationship and difference between this paper and domestic and foreign research are compared. The second part is the theoretical analysis, mainly elaborated the mathematics ability definition, the mathematics drawing ability and the mathematics drawing skill and the spatial imagination ability relations comparison, This paper analyzes the measurement standard of mathematical mapping ability and the interpretation of teaching materials for cultivating junior high school students' mathematical mapping ability. The third part is the investigation and analysis of junior high school students' mathematical mapping ability, which is the core part of this paper. Through the analysis of the survey results of teachers and students, combined with the research of students' test results, this paper comprehensively analyzes the present situation of junior high school students' mathematical mapping ability, and finds out the factors that affect the development of junior high school students' mathematical mapping ability. The fourth part is the research on the strategy of cultivating junior high school students' mathematical mapping ability. According to the results of investigation and test, the problems existing in the process of developing junior high school students' mathematical mapping ability are analyzed, and some suggestions are put forward to cultivate the junior high school students' mathematical mapping ability. Training principles, methods and approaches, and a teaching case to show the teachers in mathematics drawing teaching students in the cultivation of mathematical mapping ability. The fifth part is the reflection and suggestion, summarizes the deficiency in this research, and prospects the further research direction.
【学位授予单位】：山东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6
本文编号：2213082
[Abstract]:In junior high school mathematics teaching material, geometry is a very important learning content. In real life, production and even R & D of science and technology, there are many practical problems that need to be solved with the knowledge of geometry. Therefore, it is necessary for students to learn geometry. Mathematical drawing ability is an important ability that students should master when learning geometry. It can not only improve students' spatial imagination ability, but also promote the development of students' problem-solving ability. This paper takes the research of junior high school students' mathematical mapping ability as the research content, and carries on the thorough research to the following several questions separately: what is the measurement standard of the mathematics drawing ability? What is the current situation of junior high school students' mathematical mapping ability? What are the factors that affect the mathematical mapping ability of junior high school students? What are the principles, methods and approaches for developing the mathematical mapping ability of junior high school students? What is the enlightenment to mathematics drawing teaching? Based on the relevant knowledge of pedagogy and psychology, combined with mathematics teaching theory, mathematical methodology and various versions of junior high school mathematics teaching materials, this paper makes a deep research from two aspects: theory and practice. First of all, on the basis of sorting out the present situation of mathematical graphics research at home and abroad, this paper determines that the research content of this paper is: the study of junior high school students' mathematical drawing ability, and think about what "mathematical drawing ability" is. Then, the questionnaire and interview method were used to investigate all mathematics teachers and three hundred students in grade seven, eight and ninety-three in Linyi No. 35 Middle School. According to the content of mathematics drawing in the textbook, the test paper was compiled and the 300 students were tested. Then, the test results are analyzed from several angles, and the problems existing in mathematical mapping are summarized and attributed. At last, the author puts forward six training principles and five training methods on how to cultivate junior high school students' ability of drawing mathematics in combination with their own teaching experience. This paper is divided into five parts, the main contents are as follows: the first part is the problem raised, respectively from the needs of mathematics curriculum reform, The requirements of the new curriculum standard and the importance of mathematical drawing to mathematics learning are put forward in this paper, and the background and significance of the problem research are put forward, and the current research situation of mathematical graphics at home and abroad is described in detail. The relationship and difference between this paper and domestic and foreign research are compared. The second part is the theoretical analysis, mainly elaborated the mathematics ability definition, the mathematics drawing ability and the mathematics drawing skill and the spatial imagination ability relations comparison, This paper analyzes the measurement standard of mathematical mapping ability and the interpretation of teaching materials for cultivating junior high school students' mathematical mapping ability. The third part is the investigation and analysis of junior high school students' mathematical mapping ability, which is the core part of this paper. Through the analysis of the survey results of teachers and students, combined with the research of students' test results, this paper comprehensively analyzes the present situation of junior high school students' mathematical mapping ability, and finds out the factors that affect the development of junior high school students' mathematical mapping ability. The fourth part is the research on the strategy of cultivating junior high school students' mathematical mapping ability. According to the results of investigation and test, the problems existing in the process of developing junior high school students' mathematical mapping ability are analyzed, and some suggestions are put forward to cultivate the junior high school students' mathematical mapping ability. Training principles, methods and approaches, and a teaching case to show the teachers in mathematics drawing teaching students in the cultivation of mathematical mapping ability. The fifth part is the reflection and suggestion, summarizes the deficiency in this research, and prospects the further research direction.
【学位授予单位】：山东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6
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