高中指数函数教学研究

发布时间：2018-04-29 02:26

本文选题：高中数学 + 指数函数　；参考：《内蒙古师范大学》2015年硕士论文

【摘要】：指数函数在高中数学课程中扮演着重要的角色,它是学习对数函数的基础。从实际应用方面来看,指数函数被广泛应用于本人们的日常生产、生活和科学研究的各个领域之中,尤其体现在细胞分裂、放射衰变、人口控制、疾病预测、贷款利率的计算和考古中的年代测算等方面。指数函数的学习,不但有助于学生加深函数概念的理解,而且具有广泛的现实意义。所以指数函数的理解和掌握显得尤为重要。本文从《指数函数及其性质》出发,通过对乌海市第一中学高一389班、390班学生104人进行问卷调查和交流,并进行问卷统计与数据处理,得出学生在指数函数学习方面存在的问题,查找这些问题存在的原因,针对这些问题给出相应的教学策略,并给出《指数函数及其性质》的教学设计。本研究的主要结论为：学生对于指数函数理解和掌握方面所存在的主要问题有：(1)部分学生不会指数幂的运算；(2)对指数函数概念理解不够深刻,系数和指数的要求考虑不够周全；(3)对指数函数图象理解不到位；(4)利用指数函数解决实际问题不关心定义域。影响学生指数函数理解和掌握的主要因素有：(1)学生数学基础差、知识掌握不扎实；(2)学生的辩证思维还不够成熟；(3)教师对于指数函数概念的讲解不够深入；(4)教师在引导学生自主地建构知识方面做得不够好。提出的教学策略主要有：(1)创设问题情境让学生建构指数函数概念；(2)借助多媒体技术让学生更加形象直观地理解指数函数；(3)适时渗透数学思想方法培养学生的思维能力；(4)引导学生亲身经历探究过程总结指数函数的性质。本研究创新之处是从指数函数这一核心概念出发,通过问卷调查,统计分析乌海市第一中学高一389班、390班学生学习指数函数方面存在的问题,教师在教学方面存在的问题等。针对所存在的主要问题,给出相关的教学策略,并给出《指数函数及其性质》的教学设计。
[Abstract]:Exponential function plays an important role in high school mathematics curriculum, and it is the basis of learning logarithmic function. In practical applications, exponential functions are widely used in our daily production, life and scientific research fields, especially in cell division, radiation decay, population control, disease prediction, Loan interest rate calculation and archaeological dating and other aspects. The study of exponential function not only helps students to understand the concept of function, but also has wide practical significance. So it is very important to understand and master the exponential function. Based on the exponential function and its Nature, this paper makes a questionnaire survey and exchange among 104 students of Class 39, Class 389 of No. 1 Middle School in Wuhai City, and carries out statistical analysis and data processing of the questionnaire. The problems existing in the study of exponential function are obtained, the reasons for these problems are found out, the corresponding teaching strategies are given, and the teaching design of "exponential function and its properties" is given. The main conclusions of this study are as follows: the main problem in understanding and mastering exponential function among students is: (1) some students do not have a deep understanding of the concept of exponential function. The requirements of coefficients and indices are not fully considered (3) the image of exponential function is not well understood. 4) the use of exponential function to solve practical problems does not care about the domain of definition. The main factors that affect students' understanding and mastery of exponential function are: 1) students' poor mathematical foundation. (2) the dialectical thinking of students is not mature enough. 3) the teacher's explanation of the concept of exponential function is not deep enough. 4) the teacher does not do well in guiding students to construct knowledge autonomously. The teaching strategies put forward are: (1) creating problem situation for students to construct the concept of exponential function; (2) making students understand the exponential function more vividly and intuitively by means of multimedia technology; (3) infiltrating mathematics thinking method to cultivate students' thinking at the right time Ability 4) to guide students to experience the inquiry process and summarize the nature of the exponential function. The innovation of this study is that from the core concept of exponential function, through the questionnaire survey, this paper statistically analyzes the problems existing in the study of the exponential function among the students of Class 1, 389, Class 390 in Wuhai No. 1 Middle School, and the problems existing in the teaching of the teachers, and so on. In view of the main problems, the related teaching strategies are given, and the teaching design of "exponential function and its properties" is given.
【学位授予单位】：内蒙古师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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