初高中数学函数教学衔接性的实践研究

发布时间：2019-03-27 20:03

【摘要】：函数知识是初高中教学的重点和难点,是高考试题中相关度最高的一个考点。所涉及的分类讨论、数形结合、联系与转化等数学思想方法也能为高等数学的深入学习奠定良好的基础。但是,基于当前各个学校师资配备的小循环特性,初高中的教学脱节现象非常严重,尤其是重要的函数知识学习,初高中教学的侧重点差异很大。本文利用文献研究法、问卷调查法、案例分析法,对初高中教材、初高中函数概念以及函数与方程、不等式的关系等进行了深入对比和研究。发现初中函数概念教学中讲解函数发展史衔接高中函数集合论的定义;一次函数与一次方程、一次不等式的联系学习加强学生识图、绘图、说图的能力衔接高中函数与方程、不等式的关系及应用;重视渗透数形结合的数学思想衔接高中函数的综合应用。以初高中函数概念的调查研究、函数与方程关系的案例研究,形象地阐述了教学衔接性的要点。指出初中的学习重点在于让学生感知函数与方程之间是存在联系的,并可以借助函数图像,利用数形结合的数学思想,解决一些方程的问题,旨在渗透函数思想。此外,还可以潜移默化地为高中继续学习函数与方程的关系以及函数的其它应用做了很好的铺垫,这样循序渐进的过程,使得高中学习函数与方程不是那么的突兀,学生容易接受。针对作者所在城市初高中不同版本的教材,从初高中教材函数部分的内容安排、联系与区别、编写特色、思维差异以及初高中实践教学中的体会进行了分析,介绍了初高中函数教学的衔接策略。
[Abstract]:The function knowledge is the key and difficult point of the initial high school teaching, and it is the highest correlation in the high test. The methods of mathematical thinking, such as the discussion of the classification, the number-form combination, the relation and the transformation, can provide a good foundation for the in-depth study of higher mathematics. However, based on the small cycle characteristics of the current school teachers, the disjunction of the teaching in the first high school is very serious, especially the important function knowledge study, and the focus of the initial high school teaching is very different. In this paper, the author makes an in-depth comparison and research on the concept of the initial high school teaching material, the concept of the initial high school function, the function and the equation and the inequality by using the literature research method, the questionnaire method and the case analysis method. It is found that the development of the function of the teaching in the concept of the junior high school function is the definition of the set theory of the high school function. The relationship between the function of the elementary function and the basic equation and the one-time inequality enhances the student's identification, drawing, and the ability to connect the high-and high-school function with the equation and the inequality. In this paper, we attach importance to the integrated application of the mathematical idea of the combination of the penetration number and the high-school function. Based on the investigation of the concept of the initial high school function, the case study of the relation between the function and the equation, the main points of the teaching cohesion are set forth. It is pointed out that the main point of the study in junior middle school lies in that the student's perception function and the equation are related, and the problem of some equations can be solved by means of the function image, using the mathematical idea of the number-form combination, and the aim is to penetrate the function thought. In addition, the relationship between the continuing learning function of high school and the equation and the other applications of the function can be well paved, so that the high school learning function and the equation are not so abrupt, and the students are easy to accept. In view of the different versions of the teaching materials in the first high school of the author's city, the paper analyzes the content arrangement, the relation and the difference, the writing characteristic, the thinking difference and the experience in the practice teaching of the junior high school from the first high school teaching material function part, and introduces the connection strategy of the initial high school function teaching.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

【参考文献】