摘要在中学数学中有很多数学方法,其中数形结合思想是中学数学中一种重要方法。它将代数与几何相结合,利用数形之间相互转换,有利于分析题中的数量之间关系,丰富想象,化繁为简,化难为易。分析当下数学结合思想研究的作用及意义,并且结合当下的教育形式来分析数形结合思想在中学教学中的地位。最后用几个典型的例子来具体说明数形结合思想在中学数学中的应用:实数运算、不等式、简单几何、简单函数图像、集合、解方程、函数最值与值域、抽象函数及立体几何图形与解析几何。通过具体例题的分析、比较和归纳,可以体会到数形结合思想解决问题的直观性以及简捷性,在实际教学中,教师要将数形结合思想融汇到课堂中,培养学生加强数形结合思想的意识。44094
【Abstract】 In the middle school mathematics has lots of mathematical methods, and combining numbers with shapes is one of the most important methods. It combines algebra and geometry, and the transformation between them, is helpful for analyzing problem of the relation between the quantity, enrich imagination, change numerous hard things simple, easy.
We can know the importance of studying the way to combine numbers with shapes from the background of studying the theory, and analyze the position in middle school. Finally I will discuss the application form combining numbers with shapes of the middle school Mathematics from the following several aspects: Real arithmetic, inequality, simple geometry, simple graphics functions, sets, solving equations, functions best value and range, and three-dimensional geometric abstraction function and analytic geometry. Through the analysis, comparison and induction, it shows the application form combining numbers with shapes of the middle school Mathematics in the characteristic and advantages, which in actual teaching will form together with several ideas to the classroom, training students' strengthen the consciousness of combining numbers with shapes.
毕业论文关键字:中学数学;数形结合;应用;思想方法
【Key words】 Middle school mathematics;combining numbers with shapes;The application;Thought method
目 录
1、数形结合思想基本知识 5
2、数形结合思想的研究背景 5
3、数形结合思想的研究意义与作用 5
4、数形结合思想在中学数学教学中的地位 6
4.1、从新课程标准对思维能力的要求看数形结合 6
4.2、从新课程教学内容的特点来看数形结合 6
4.3、从高考题设计背景来看数形结合 6
5、数形结合思想在中学中的应用 6
5.1、数形结合涉及的数学内容 6
5.2、数形结合解决的问题 7
6、数形结合的实例 7
6.1、数形结合与实数运算 7
6.2、数形结合与不等式 8
6.3、数形结合与简单几何 9
6.4、数形结合与简单函数图像 9
6.5、 数形结合与集合 11
6.5.1、利用韦恩图法解决集合之间的关系问题 11
6.5.2、利用数轴解决集合的有关运算 11
6.6、数形结合与解方程