初三学生几何思维水平的调查研究

发布时间：2018-09-10 20:41

【摘要】：数学是思维的体操,而几何作为数学中的重要组成部分,对数学思维的培养与发展有着无可替代的作用。近年来由于数学改革的进行,教育部门对初中的几何内容进行了大刀阔斧的修改,对于繁、难的几何内容进行了删除,但对学生几何学习成果的检验却并没有松懈,而几何思维水平对几何学习成果有着很大的影响,因此学生的几何学习得怎么样及课程改革后初中学生几何思维水平处于什么样的层次很值得我们进行调查研究。根据研究的内容和研究方法,文章分为5个部分,分别如下：第1章是引言,主要介绍选题的背景与研究的意义、内容与方法以及国内外文献综述。第2章是几何思维水平的理论研究。第3章是调查的设计及调查结果与分析。第4章是根据调查结果针对性地提出教学建议。这次研究选取的是上完整个初中几何课程的学生,问卷采用的是经典的测试学生几何思维水平的范·希尔几何思维水平测试卷,分别从直观化水平、描述分析水平、抽象关联水平、形式推理水平、严密性水平这五个思维层次进行测试,测试结果如下：(1)处于水平1和水平2的学生人数较少,不到总人数的20%。(2)初中学生思维水平主要集中在水平3这一层次,也就说大部分学生具有一定的推理能力,能形成抽象的定义,能区分概念的必要条件和充分条件,能理解甚至做一些逻辑推理,能建立图形及图形性质间的关系,可以推出非形式化推论,了解构建图形的要素,能进一步探求图形的内在属性和其包含关系。(3)从统计表中我们可以看出,只有少部分学生达到水平4,也就是说大部分学生的推理能力并没有达到一个较高的水平。(4)通240名学生以及两个图表的数据我们可以知道,我国接近80%的学生的几何思维水平达到了水平2以上,只有不到20%的学生的几何思维水平处于水平2以下,几何思维水平处于水平2以下的学生只具有简单的推理能力,对各种图形的性质并不十分了解。根据美国芝加哥大学的Usiskin对美国学生的测试结果,在完成初中几何学习的2900学生中,仍有40%的学生的几何思维水平处于水平2以下。由此可见,我国初三学生的几何思维水平是要高于美国的,这也说明学校教育对学生的几何思维有促进作用。最后根据测试结果及对一些老师和学生的访问,笔者从教材、教师、学生三方面提了一些建议,希望对学生的几何学习特别是几何推理能力有所帮助。
[Abstract]:Mathematics is the gymnastics of thinking, and geometry, as an important part of mathematics, plays an irreplaceable role in the cultivation and development of mathematical thinking. In recent years, due to the reform of mathematics, the education department has made drastic changes to the geometry content of junior high school, and deleted the complicated and difficult geometric content, but the examination of the students' geometric learning results has not been lax. The level of geometric thinking has a great impact on the geometry learning results, so it is worth our investigation and research on how the students learn geometry and what level the junior middle school students' geometric thinking is in after the curriculum reform. According to the research content and research methods, the article is divided into five parts, as follows: the first chapter is the introduction, mainly introduces the background of the topic and the significance of the research, content and methods, as well as the literature review at home and abroad. Chapter 2 is the theoretical study of geometric thinking level. Chapter 3 is the design and analysis of the investigation. The fourth chapter is according to the investigation result puts forward the teaching suggestion pertinently. This study selected students who had completed the whole junior high school geometry course. The questionnaire used the classic Van Hill geometric thinking test paper, which tested the students' level of geometric thinking, and described the level of analysis from the level of intuitionism. Abstract relevance level, formal reasoning level and tightness level are tested. The results are as follows: (1) the number of students in level 1 and level 2 is small. Less than 20% of the total number. (2) the thinking level of junior high school students is mainly concentrated at level 3, which means that most students have certain reasoning ability, can form abstract definitions, and can distinguish the necessary conditions and sufficient conditions of concepts. Can understand and even do some logical reasoning, can establish the relationship between graphics and the nature of graphics, can deduce non-formal inference, understand the elements of constructing graphics, Can further explore the inherent properties of the graph and its inclusion. (3) We can see from the statistical table, Only a small number of students have reached level 4, which means that most students do not have a high level of reasoning. (4) 240 students and the data from the two charts. Nearly 80% of the students in our country have the level of geometric thinking above level 2, only less than 20% of the students have the level of geometric thinking below level 2, and the students whose level of geometric thinking is below level 2 have only simple reasoning ability. The nature of various graphics is not well understood. According to the results of Usiskin's test of American students at the University of Chicago, 40% of the 2900 students who have completed junior high school geometry study still have a level of geometric thinking below 2. It can be seen that the level of geometric thinking of junior high school students in our country is higher than that of the United States, which also shows that school education can promote the students' geometric thinking. Finally, based on the test results and interviews with some teachers and students, the author puts forward some suggestions from three aspects of teaching materials, teachers and students, hoping to be helpful to students' geometric learning, especially geometric reasoning ability.
【学位授予单位】：湖南师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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