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数学学习离不开思维,数学探索需要通过思维来实现,在初中数学教学中逐步渗透数学思想方法,培养思维能力,形成良好的数学思维习惯,数形结合的思想贯穿初中数学教学的始终。数形结合思想的主要内容体现在以下几个方面:(1)建立适当的代数模型(主要是方程、不等式或函数模型)。(2)建立几何模型(或函数图象)解决有关方程和函数的问题。(3)与函数有关的代数、几何综合性问题。(4)以图象形式呈现信息的应用性问题。采用数形结合思想解决问题的关键是找准数与形的契合点。如果能将数与形巧妙地结合起来,有效地相互转化,一些看似无法入手的问题就会迎刃而解,产生事半功倍的效果。
Mathematical learning can not be separated from thinking. Mathematical exploration needs to be realized through thinking. Gradually permeate mathematical thinking and methods in junior high school mathematics teaching and cultivate thinking ability to form good mathematical thinking habits. The idea of combining numerical and form teaching runs through junior high school mathematics teaching. The main contents of the idea of combination of numbers are reflected in the following aspects: (1) to establish an appropriate algebraic model (mainly equation, inequality or function model). (2) to establish geometric model (or function image) to solve the problem of equations and functions. (3) function-related algebra, geometry synthesis problem. (4) the application of information in the form of images. The key to solve the problem by using the combination of number and shape is to find the fit point between number and shape. If we can skillfully combine numbers and forms and transform each other effectively, some seemingly impossible issues will be solved and a multiplier effect will be produced.