《数形结合在中学数学教学中的探究》毕业学术论文.doc

\* MERGEFORMATi- 摘要 数、形是数学中两大基本概念，数学大体上都是围绕这两个基本概念的提炼、演变、发展而展开的。数形结合是根据数学问题的条件与结论之间的内在联系，既分析其代数意义，又揭示其几何直观，使数量关系的精确刻划与空间形式的直观形象巧妙、和谐地结合在一起。在中学数学里所接触到的一些思想方法中，数形结合的思想方法无疑是比较重要的一种。本文从数形结合在函数，不等式，三角函数，解析几何问题等有关方面的解题应用，探究在中学数学教学中数形结合的解题思想的必要性以及对中学生解题思想的渗透。 关键词：数形结合；数学教学；教学探究 ABSTRACT Both number and shape is two basic concepts in mathematics, while mathematics are expanded in general around the extraction, evolution, development to the two basic concepts. The method on combining number with shape is that analysis both of the algebraic sense, but also reveals the geometric intuition based on the intrinsic link between the conditions and conclusions, so that accurate characterization of the relationship between the number of forms of visual image and space cleverly and harmoniously together. In middle school mathematics come into contact with some of the thinking methods, the combining number with shape is undoubtedly the more important one. From problem solving application problems and other parties of the combining number with shape in function, inequality, trigonometric functions, analytic geometry, the present dissertation explores the necessity for problem-solving thinking of the combining number with shape in teaching as well as the penetration of problem-solving thinking. Keywords: combining numbers with shapes; Mathematics teaching; Teaching inquiry 湖南科技大学本科生毕业设计（论文） \* MERGEFORMAT- 33 - 目 录 TOC \o 1-3 \h \z \u HYPERLINK \l _Toc293894226 第一章 前言 1 HYPERLINK \l _Toc293894227 1.1 数形结合思想方法概述 1 HYPERLINK \l _Toc293894230 1.2 数形结合思想方法历史演进 2 HYPERLINK \l _Toc293894231 第二章 数形结合在中学数学教学中的应用 5 HYPERLINK \l _Toc293894232 2.1 数形结合思想在函数问题中的应用 6 HYPERLINK \l _Toc293894233 2.2 数形结合思想在不等式问题中的应用 11 HYPERLINK \l _Toc293894234 2.3 数形结合思想在三角函数问题中的应用 13 HYPERLINK \l _Toc293894235 2.4 数形结合思想在解析几何问题中的应用 17 HYPERLINK \l _Toc293894237 第三章 中学生数形结合解题能力现状及原因分析 23 HYPERLINK \l _Toc293894238 3.1 中学生数形结合解题能力现状 23 HYPERLINK \l _Toc293894239 3.2 原因分析 23 HYPERLINK \l _Toc293