高中生对数函数学习困难的研究

发布时间：2018-02-03 15:47

本文关键词： 高中生对数函数学习困难　出处：《东北师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：对数函数是高中生新接触的一类重要的基本初等函数,但是由于对数符号的抽象性,函数学习的复杂性,对数函数的综合性等诸多因素,导致学生关于对数函数的学习和理解明显存在困难。尽管国内数学教育工作者关于对数以及对数函数的研究成果颇丰,但是他们大多数都是在对数的发展史、对数函数的教学设计、对数函数的概念、性质、解题及应用等方面提出自己的观点,而以对数函数为主实证研究却很有限。笔者通过对部分高中教师和学生的访谈发现,教师并不知道学生在对数函数学习过程中具体存在哪些学习困难,学生也无法通过教师的讲解完全消除学习障碍。因此笔者以高中生对数函数的学习困难为研究内容,选取吉林省长春市三所高中的不同年级学生为调查对象展开研究。在正式研究之前,笔者首先选取学校一高一的部分学生进行预研究,根据预研究调查问卷反映出的问题,适当修改问卷后才对三所学校的高中生展开正式调查。接下来笔者使用Excel和SPSS软件对调查问卷的数据进行了分析和处理,得到高中生关于对数函数知识的理解现状,并总结了他们在这部分知识学习的过程中存在的四类学习困难：1.对数函数的概念辨析困难。在这类困难范围内,学生分别有关于对数函数概念的陈述性知识记忆困难,对对数函数概念中变量的限定条件掌握不准确,无法应用对数函数的概念进行辨析三类具体困难类型。2.数学思想的应用困难。在高中阶段要求学生掌握的七类基本数学思想中,有三类常常被应用于解决对数函数的相关问题,分别是分类与讨论思想、数形结合思想和转化与化归思想,而这三类数学思想的应用也是学生的主要学习困难所在。3.对数型复合函数的理解困难。对数函数和复合函数都是高中数学学习的重点和难点,而将两者结合成对数型复合函数对学生来说无疑是“雪上加霜”。学生在学习这部分知识主要存在三类困难：缺乏整体换元意识、忽略对函数定义域的考察和单调性的判断困难。4.对数函数的相关知识基础薄弱。有些学生之所以出现对数函数的学习困难,并不是对数函数知识掌握不足,而是对于对数函数相关的知识理解存在障碍。结合上述研究结果,笔者针对高中生关于对数函数的学习困难提出了五点教学建议：首先教师应该尽量激发学生对对数函数的学习兴趣,并且鼓励学生勇于发现错误、提出疑难,然后设计适应高中生认知发展水平的教学活动,接下来引导学生建构对数函数的知识框架,最后注重培养学生在数学学习过程中的反思习惯。
[Abstract]:Logarithmic function is an important basic elementary function in high school students' new contact. However, because of the abstraction of logarithmic symbol, the complexity of function learning, the comprehensiveness of logarithmic function and so on. As a result, there are obvious difficulties in learning and understanding logarithmic functions. Although there are many researches on logarithms and logarithmic functions by domestic mathematics educators, most of them are in the history of logarithmic development. The teaching design of logarithmic function, the concept, property, problem solving and application of logarithmic function are put forward. Through interviews with some senior high school teachers and students, the author finds that teachers do not know what learning difficulties students have in the process of learning logarithmic functions. Students can not completely eliminate the learning barriers through the teacher's explanation. Therefore, the author takes the learning difficulties of the logarithmic function of high school students as the research content. Three high schools in Changchun, Jilin Province, different grades of students as the research object. Before the formal study, the author first selected a part of the first high school students to carry out a pre-study. According to the pre-study questionnaire reflected the problem. After the proper revision of the questionnaire, three high school students were formally investigated. Then the author used Excel and SPSS software to analyze and process the data of the questionnaire. The present situation of high school students' understanding of logarithmic function knowledge is obtained, and the four kinds of learning difficulties existing in the process of learning this part of knowledge are summarized. 1. The concept of logarithmic function is difficult to distinguish. Within this kind of difficulty range. Students have difficulty in memorizing declarative knowledge about the concept of logarithmic function, and they are not accurate in grasping the qualification conditions of variables in the concept of logarithmic function. The concept of logarithmic function can not be applied to distinguish three kinds of concrete difficulty types. 2. The application of mathematical thought is difficult. In the senior middle school students are required to master the seven basic mathematical ideas. There are three kinds of problems which are often applied to solve the problem of logarithmic function, namely, classification and discussion, the combination of number and form, and the thought of transformation and transformation. The application of these three mathematical ideas is also the main learning difficulties of students .3.The understanding of logarithmic complex function is difficult. Logarithmic function and compound function are the key points and difficulties of senior high school mathematics learning. The combination of the two into a logarithmic complex function is undoubtedly "aggravated" for students. There are three main difficulties in learning this part of knowledge: the lack of overall awareness of changing elements. Ignoring the investigation of function definition and the difficulty of judging monotonicity. 4. The relative knowledge base of logarithmic function is weak. Some students have difficulty in learning logarithmic function, not because of lack of knowledge of logarithmic function. However, there are obstacles to understanding the knowledge related to logarithmic functions. The author puts forward five teaching suggestions for the difficulties of studying logarithmic function in senior high school students: first, teachers should try to arouse students' interest in logarithmic function, and encourage students to find mistakes and put forward difficulties. Then it designs the teaching activities to adapt to the cognitive development level of senior high school students, then guides the students to construct the knowledge frame of logarithmic function, and finally pays attention to the cultivation of students' reflective habits in the process of mathematics learning.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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