数形结合在初中数学中的应用
Abstract"Number" and "form" are the two most basic concepts in mathematics, they are unified but also opposite. Each geometric shape is closely related to the size, shape, position and so on. In contrast, the quantitative relation can also be used to make the intuitive description and reflection. The essence of the number line combination is to combine the visual graphics and the abstract mathematical language together, to combine the two kinds of thinking of abstract thinking and image thinking. In solving the corresponding algebraic problem is to think of its graphics, so as to inspire their thinking and tries to find the solution of ideas, or in mathematical research pattern when using the algebraic properties to solve geometry problems. The final purpose of the number shape combination is to make all the difficult problems become simple and clear, to make the complicated problems simple, and to achieve the combination of numbers and shapes. I will from the several aspects to tell application of number shape union thinking in middle school mathematics: (1) in the collection of application; (2) in the solution of equations in the application; (3) application of inequality in the solution; (4) in the analytic geometry application; (5) in solving the most value and range of application. Through the analysis, the induction and the comparison of several methods fully showed combination of number and shape in helping students to deal with practical problems of superiority and characteristics, to take the number shape union thinking binding to class although rear lost to students, and cultivate students' ideological consciousness of number and shape node.
毕业论文关键词：中学数学； 数形结合； 应用； 思想方法
Keyword: Middle school mathematics; Several form combined with; An application example; Thought method
目 录
1.引言5
2.数形结合思想概述5
3.数形结合的作用与地位5
4.数形结合的原则6
5.数形结合在中学数学中的应用6
5.1解决集合问题6
5.2解决解方程问题8
5.3解决不等式问题9
5.4数形结合在数列问题中的应用10
5.5数形结合思想解决最值、值域问题11
5.6数形结合思想在解析几何中的应用12
6.培养学生数形结合思想的一些教学措施12
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