高中数学核心概念及其教学的调查研究

发布时间：2018-02-28 07:44

本文关键词： 核心概念教学调查研究　出处：《陕西师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：自新一轮基础教育课程改革以来,素质教育一直指导着一线教师的教学工作,学校教育在形式、模式、理念等方面悄无声息的发生着变化。然而笔者在教育实习期间,发现许多学校过于注重形式,忽略了数学课堂教学本质的内容。特别是在概念的教学上,或仅仅提出而不讲来龙去脉,使得学生知其然,但不知其所以然,学生不能领会概念背后蕴含的数学思想方法,或者教师本身对数学概念理解有偏差,纠缠一些细节,引入数学概念形式丰富但依然停留在表面,这样就淡化了数学概念本身的内涵,忽视了数学概念的根基作用,降低了课堂效率,浪费了增强学生数学人文素养的机会。那么在现行的高中数学必修教材中,哪些数学概念可作为核心概念?如何界定?与一般概念有怎样的脉络关系?核心概念的教学有哪些模式?与一般概念的教学有什么不同?数学史在核心概念教学中有怎样的作用?本文以人教A版数学必修1-5为对象,主要研究以上问题。文章采用文献分析法对数学核心概念的研究现状做出总结。鉴于“核心”的相对性,文章将高中数学知识分为“代数”“几何”“概率与统计”三大模块,研究模块中的核心概念及核心概念体系,并提出界定高中数学核心概念的标准：1、在高中数学必修课程中占有重要地位,处于主干位置；2、在模块内,或生成其他概念,或与其他概念有紧密联系；3、高中生的数学知识结构中有不可替代的根基作用；4、符合高中生认知的水平,是其逻辑思维发展上是必要的一环。然后利用问卷调查法、访谈法,从教师、学生两个视角得到数学核心概念的选项,结合文献与分析,最终确定“函数”“向量”为“代数”模块的核心概念,“斜率”“正余弦函数”“异面直线”为“几何”模块的核心概念,“随机事件”“概率”为“概率与统计”模块的核心概念,并作出了核心概念网络图。最后文章核心概念的教学教学现状做了调研,选取数学史为切入角度,分析调研数据,并提出了有关核心概念教学的建议。第一,重视数学核心概念的教学,广泛收集素材,做好教学准备。第二,数学核心概念引入阶段,选取适当数学史素材,结合现今生活实际,激发学生兴趣。第三,利用数学史知识加强对核心概念的解读。第四,利用数学史、概念图等多种手段帮助核心概念体系的构建。第五,利用丰富的实例对核心概念多次运用,达到对概念的巩固。
[Abstract]:Since the new round of basic education curriculum reform, quality education has been guiding the teaching work of front-line teachers, and school education has been quietly changing in form, mode, concept and so on. It is found that many schools pay too much attention to form and neglect the essential content of mathematics classroom teaching, especially in the teaching of concepts, or simply put forward without the context, so that students know what they are, but do not know why. Students can not understand the mathematical ideas behind the concept, or the teachers themselves have a deviation in understanding mathematical concepts, entangled in some details, the introduction of mathematical concepts rich in form but still remain on the surface. In this way, the connotation of mathematics concept itself is desalinated, the basic function of mathematics concept is ignored, the classroom efficiency is reduced, and the opportunity of enhancing students' humanities accomplishment in mathematics is wasted. What mathematical concepts can be considered as core concepts? How to define it? What is the relationship with general concepts? What are the teaching models of core concepts? What is the difference from the teaching of general concepts? What role does the history of mathematics play in the teaching of core concepts? This paper mainly studies the above problems in order to study the subject 1-5 of the required mathematics subject in the A edition. This paper summarizes the present situation of the research on the core concepts of mathematics by using the method of literature analysis. In view of the relativity of the "core", In this paper, the mathematics knowledge in senior high school is divided into three modules: algebra, geometry, probability and statistics. It also puts forward the standard of defining the core concept of senior high school mathematics: 1, which occupies an important position in the required course of senior high school mathematics, is in the main position, and in the module, or generates other concepts. Or has a close connection with other concepts. The mathematical knowledge structure of senior high school students has an irreplaceable fundamental role. It conforms to the cognitive level of high school students and is a necessary link in the development of their logical thinking. Then, by means of questionnaires and interviews, The choice of the core concepts of mathematics is obtained from the perspectives of teachers and students, and combined with literature and analysis. Finally, it is determined that "function" "vector" is the core concept of "algebra" module, "slope" sine cosine function "cross-plane line" is the core concept of "geometry" module, "random event" "probability" is the core concept of "probability and statistics" module. Finally, the paper makes a survey on the current teaching situation of core concepts, selects mathematics history as a cutting point, analyzes the survey data, and puts forward some suggestions on the teaching of core concepts. Pay attention to the teaching of the core concepts of mathematics, collect materials extensively and prepare for teaching. Second, introduce the core concepts of mathematics into the stage, select appropriate historical materials of mathematics, combine with the reality of today's life, stimulate students' interest. Third, Using mathematical history knowledge to strengthen the interpretation of core concepts. 4th, using mathematical history, concept map and other means to help the construction of core concepts system. 5th, using rich examples to use the core concepts many times, to achieve the concept of consolidation.
【学位授予单位】：陕西师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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