波利亚解题理论在高中导数教学中的应用研究

发布时间：2018-06-07 17:24

本文选题：波利亚解题理论 + 怎样解题表　；参考：《五邑大学》2017年硕士论文

【摘要】：解题是数学活动的重要组成部分,波利亚的解题理论在解题上给予理论基础,它与我国的高中课程标准的理念相符合。导数是高中数学的重要概念之一,它连接了高中数学内容和大学数学内容。在高中阶段导数部分的学习,学生觉得导数的学习太抽象,理解不了导数的基本内容,从而导致出现学困生。因此本研究结合数学课程标准,将波利亚的解题理论应用到高中导数教学中,以期望能解决这个问题。本文主要分为三部分:第一部分介绍解题理论核心概念和波利亚的解题理论,其中包括他的“怎样解题表”、启发思想、四种解题模式、合情推理、学习原则和教师十诫。第二部分是对解题理论在导数教学中应用必要性的分析。第三部分是研究波利亚的解题理论在高中导数教学中的应用案例,其中包括波利亚“怎样解题表”在导数几何意义教学中的应用案例、在函数单调性与导数的例题教学中的应用案例,以及在函数最值与导数的习题教学中的应用案例。本文在波利亚解题理论指导下,结合课程标准,探究波利亚的“怎样解题表”在高中导数教学中的应用,这具有很大的现实意义和作用。教师运用波利亚的解题理论来进行导数的教学,可培养学生良好的审题习惯、一题多解与一题多变的思维习惯和解题后反思的习惯;能培养学生创造性思维,激发学生探索知识的意识;培养学生的合情推理能力;可以提高学生解题的能力,从而达到教学目的和提高教学效果。
[Abstract]:Problem-solving is an important part of mathematical activities. Poolia's theory of problem-solving gives a theoretical basis for solving problems, which accords with the concept of curriculum standards of senior high schools in China. Derivative is one of the most important concepts in senior high school mathematics, which connects the content of high school mathematics with that of college mathematics. In the study of derivative in senior middle school, students feel that the learning of derivative is too abstract to understand the basic content of derivative, which leads to the emergence of students with learning difficulties. Therefore, combining with the mathematics curriculum standard, this study applies Poolia's problem solving theory to the derivative teaching in senior high school, in order to solve this problem. This paper is divided into three parts: the first part introduces the core concepts of problem-solving theory and Poolia's problem-solving theory, including his "how to solve the problem list", heuristic thoughts, four problem-solving models, reasonable reasoning, learning principles and the Ten Commandments of Teachers. The second part is the analysis of the necessity of applying problem solving theory in derivative teaching. The third part is to study the application of Polia's problem solving theory in derivative teaching in senior high school, including how to solve the problem list in derivative geometric meaning teaching. The application cases in the teaching of function monotonicity and derivative, and in the exercise teaching of function most value and derivative. Under the guidance of Polia's problem solving theory and curriculum standard, this paper explores the application of Polia's "how to solve problem Table" in derivative teaching in senior high school, which has great practical significance and function. By using Poolia's theory of solving problems to carry out derivative teaching, teachers can cultivate students' good habit of examining questions, the habit of thinking more and more questions, the habit of reflection after solving problems, and the cultivation of students' creative thinking. It can stimulate students' consciousness of exploring knowledge, cultivate students' ability of reasonable reasoning, improve students' ability to solve problems, and thus achieve teaching purpose and improve teaching effect.
【学位授予单位】：五邑大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

【参考文献】