江西师范大学数学与信息科学学院
学士学位论文
中学数学中的数形结合思想Several of the middle school Mathematics form combining ideas
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学号：0807010040
学院：数学与信息科学学院
专业：数学与应用数学指导老师：
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中学数学中的数形结合思想
【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，一方面, 借助于图形的性质可以将许多抽象的数学概念和数量关系形象化、简单化, 给人以直觉的启示．另一方面,将图形问题转化为代数问题, 以获得精确的结论．提高分析和解题的能力从而达到简易的解题方法，最终方便我们的解题．我将从以下几个方面来探讨数形结合思想在中学数学中的应用：（1）在集合中的应用；（2）在解方程中的应用；（3）在解不等式中的应用；（4）在解析几何上的应用；（5）在解决最值、值域问题上的应用．通过分析、比较和归纳充分展现数形结合思想在解题中的特点和优越性，从而在实际教学中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．
关键词】中学数学数形结合应用思想方法
Several of the middle school Mathematics form combining
ideas
【Abstract】In the middle school mathematics has lots of mathematical methods, including several form combining ideas middle school mathematics is one of the most important methods,
it will algebra and geometry, and the combination of using several shape transformation between, be helpful for analysis problem of the relation between the quantity, rich imagination, change numerous hard things simple, easy, on the one hand, graphic nature of many of the abstract will math concepts and visual and quantitative relationship between simplified, give a person with intuitive enlightenment. On the other hand, will graphics problem into the algebra problem, in order to obtain the accurate conclusions. Improve the analysis and problem solving ability so as to achieve simple problem solving method, the final convenient our problem solving. I will from the following several aspects to discuss several form combining ideas middle school mathematics in the application: (1) the application of the set; (2) in the process of the application of the solution; (3)the application of inequality in solution; (4)in the application of analytic geometry; (5)to solve the most value, domain in its application. Through the analysis, comparison and induction show several form combining ideas of problem 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 ideas number form.
【Key words】Middle school mathematics Several form combined with An application example Thought method
目录
1引言 (1)
2数形结合思想的概念 (1)
3数形结合思想在中学数学中的应用 (2)
3.1 (2)
3.1.1利用韦恩图法解决集合之间的关系问题 (2)
3.1.2利用数轴解决集合的有关运算 (3)
3.2数形结合思想在解方程中的应用 (3)
3.3数形结合思想在解不等式中的应用 (4)
3.4数形结合思想解决最值、值域问题 (6)
3.5数形结合思想在解析几何中的应用 (7)
4培养学生数形结合思想的一些教学措施 (8)
结束语 (9)
参考文献 (10)
