摘要数与形是数学中两大基本概念,既相互独立,又互相渗透,数学就是围绕这两个基本概念的发展而展开。进一步加强对数学思想方法的学习与理解,让学生在原有的解题技能的基础上,有效运用数形结合的思想方法,能有效的提高学生的解题能力。因此,数形结合的思想方法毫无疑问是中学数学中比较重要的一种。本文举例论述了数形结合在函数,不等式,三角函数,解析几何问题等有关方面的应用,探究在中学数学及教学中数形结合思想的必要性以及对中学生解题思想的渗透。47011
Abstract The number and shape are the two basic concepts in mathematics, both independent of each other, but mutual penetration, while mathematics was largely based on the development of the two basic concepts. This article is to help strengthen the learning and understanding of mathematics thinking and further more to improve the students' ability to solve problems, connected with the idea of number shape union. It is effective to improve students' ability to solve problems that teachers pay attention to training the idea of number shape union of students. Therefore, the idea of number shape union is undoubtedly the more important one in middle school mathematics. In the article, some applications of the idea of number shape union is illustrated in function, inequality, triangle function, analytic geometry problems and other relevant aspects, and the author also explores the necessity of the idea of number shape union in middle school mathematics teaching and the penetration in middle school students’ problem solving thoughts.
毕业论文关键词:数形结合; 数学解题; 应用; 中学
Keyword: Number Shape Union; Solve Mathematics Problems; Application; Middle School
目 录
1 引言 4
1.1 数形结合思想概述 4
1.2 数形结合的历史演进 4
2 数形结合思想方法在教学中的作用 4
2.1 数形结合在中学数学教学中的体现 4
2.2 数形结合在中学数学教学中的作用 5
3 在过去的课堂教学中利用数形结合的思想解题的类型 5
3.1 以数助形 5
3.1.1 利用坐标法解决几何问题 6
3.1.2 利用三角法解决几何问题 6
3.1.3 利用向量法解决几何问题 6
3.2 以形助数 7
3.2.1 数形结合思想在集合问题中的应用 7
3.2.2 数形结合思想在函数问题中的应用 8
3.2.3 数形结合思想在方程与不等式问题中的应用 10
3.2.4 数形结合思想在三角函数问题中的应用 11
3.2.5 数形结合思想在线性规划问题中的应用 12
3.2.6 数形结合思想在数列问题中的应用 12
3.2.7 数形结合思想在解析几何问题中的应用 13
3.2.8 数形结合思想在立体几何问题中的应用 14