基于APOS理论的反比例函数教学研究

发布时间：2018-01-11 14:09

本文关键词：基于APOS理论的反比例函数教学研究　出处：《上海师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：“数学理解”是现今数学教育研究与实践的焦点之一,理解数学概念是数学课堂教学的关键。函数是初中代数的重要内容,是刻画和研究现实世界变化规律的重要模型。反比例函数是最基本的初等函数之一,是初中学生理解函数的重要载体。但是对于刚学习函数的八年级学生而言,在反比例函数概念形成和理解上存在难度。基于以上背景,本文试图研究以下问题:1、学生理解反比例函数概念的困难所在2、利用APOS理论优化反比例函数的教学,对学生是否产生积极的影响3、将APOS理论应用于概念教学应注意的问题为解决这些问题,本文将人教版与上教版反比例函数教学内容、教学安排进行对比分析,例析了学生学习反比例函数的困难所在,阐述应用APOS理论在反比例函数教学中的可行性与必要性,探索出基于APOS理论的反比例函数的教学设计。根据同年级对照班和实验班,采用不同教学设计进行同一内容的教学,设计测试问卷、访谈,基于问卷调查的数据进行分析,得出学生在反比例函数的操作、过程、对象、图示等不同阶段的理解情况,通过反比例函数概念课的课堂对话分析、学生活动分析,教学设计评价、学生认知评价,发现基于APOS理论的教学确实可以提高学生对反比例函数的理解水平,探索一些教学规律。学生对反比例函数操作阶段的知识总体掌握良好,对反比例函数的形式化定义的认知不够全面。绝大多数学生对反比例函数的理解位于操作、过程阶段,少数学生上升到对象、图式阶段,综合应用的能力较弱。对于概念课的教学,操作、过程、对象、图式循序渐进,教师要重视学生对概念本质的体验和丰富内涵的理解,引导学生经历概念本质特征构建和形成的过程。本文总结了对反比例教学的启示:(1)关注课与课之间的内在联系,(2)关注反比例函数概念形成的过程,(3)用问题引导学生学习,(4)突破难点,理解概念本质。对概念教学的启示:(1)扎实做好概念教学,(2)通过多种形式提高学生概念理解水平,(3)注重引导反思、归纳提炼。对数学教学的启示:(1)关注过程,促进数学理解,(2)提高教学设计的有效性。
[Abstract]:"Mathematical understanding" is one of the focuses of mathematics education research and practice nowadays. Understanding mathematical concepts is the key of mathematics classroom teaching. Function is an important content of junior high school algebra. Inverse proportional function is one of the most basic elementary functions and an important carrier for junior high school students to understand the function. But for the eighth graders who have just learned the function. It is difficult to form and understand the concept of inverse proportional function. Based on the above background, this paper attempts to study the following question: 1, the difficulty for students to understand the concept of inverse proportional function 2. Using APOS theory to optimize the teaching of inverse proportion function has a positive effect on students. 3. The problem that should be paid attention to when applying APOS theory to concept teaching is to solve these problems. In this paper, the teaching contents and teaching arrangements of the inverse proportional function are compared and analyzed, and the difficulties of students in learning the inverse proportion function are analyzed. This paper expounds the feasibility and necessity of applying APOS theory in the teaching of inverse proportional function, and explores the teaching design of inverse proportional function based on APOS theory. Using different teaching design for the same content of teaching, design test questionnaires, interviews, based on the questionnaire data for analysis, the students in the inverse proportion function operation, process, object. Through the analysis of classroom dialogue, student activity analysis, teaching design evaluation, student cognition evaluation. It is found that teaching based on APOS theory can improve students' understanding of inverse proportional function and explore some teaching rules. The understanding of inverse proportional function is not comprehensive enough. Most students' understanding of inverse proportional function lies in operation, process stage, a few students rise to object, schema stage. The ability of comprehensive application is weak. For the teaching, operation, process, object and schema of concept class, teachers should pay attention to students' experience of concept essence and understanding of rich connotation. This paper summarizes the enlightenment to inverse teaching: 1) paying attention to the internal relationship between class and class. 2) paying attention to the process of forming the concept of inverse proportion function. (3) to guide students to study with questions) to break through the difficulties and to understand the essence of concepts. The enlightenment to concept teaching is to do a good job in concept teaching. (2) to improve students' level of conceptual understanding through various forms. The enlightenment to mathematics teaching is to pay attention to the process, to promote mathematics understanding and to improve the effectiveness of teaching design.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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