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数形结合思想就是将抽象的数学语言与直观的图形结合起来,使抽象思维与形象思维结合。通过对图形的认识、数形转化,以提高思维的灵活性、形象性、直观性使问题化难为易,化抽象为具体。它包含“以形助数”和“以数辅形”两个方面。数形结合的思想方法能扬数之长、取形之优,使得“数量关系”与“空间形式”珠连壁合,相映生辉。“数”和“形”是不能分开的,它们是数学研究的两个侧面,它们互相渗透,互相转化,使得以代数为法研究几何,以几何法为研究代数成为可能。数形结合思想初中数学的重要思想之一,也是学好数学的关键之一。本文通过实例谈数形结合思想在初中代数学教学的渗透。
The idea of combining numbers with numbers is to combine abstract mathematical language with intuitive graphics to combine abstract thinking with thinking of images. Through the understanding of graphics, digital transformation, in order to improve the flexibility of thinking, visual and intuitive so that the problem is difficult, easy to abstract as a concrete. It contains two aspects: “form aids” and “a few figures”. The idea of combining numbers and numbers can take as long as possible and take the advantages of taking shape, making the relationship between quantity and space form a perfect match. “Number” and “shape” can not be separated. They are the two sides of mathematical research. They permeate each other and transform each other, making it possible to study the geometry by the method of algebra. It is possible to study algebra by the method of geometry. One of the important ideas of combining mathematics with mathematics in junior high school is also one of the keys to learning mathematics. This article talks about the infiltration of algebraic mathematics teaching in junior middle school through the examples.