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数学是研究现实世界的空间形式和数量关系的科学,数与形是数学的两大基石。从“数”中去认识“形”和从“形”中去认识“数”构成了数学思维的基本方法之一。“数形结合百般好,隔裂分家万世休”。这说明数学是数与形的统一,用“数形结合”的思想方法研究问题,就是注意“数”与“形”两个方面的结合,或者借助于“数”的精确性来阐述“形”的某种属性,或者借助于“形”的几何直观性来阐明“数”之间的某种关系。结合多年的教学经验,本文探讨了数形结合在概念教学、方程、不等式、函数、复数、证明中的应用。
Mathematics is a science that studies the relationship between the spatial form and the quantity in the real world. Numbers and forms are the two cornerstones of mathematics. One of the basic methods of mathematical thinking is to recognize “shape ” from “number ” and “number ” from “shape ”. “Shape with all sorts of good, separated from each other world break ”. This shows that mathematics is the unity of numbers and forms, and the problem of studying the problem with the method of thinking of “combination of numbers and forms” is to combine the two aspects of “number” with “form” or “ ”To explain some of the“ shape ”of a certain attribute, or by means of the geometric intuition of the“ shape ”to clarify some relationship between the“ number ”. Combined with years of teaching experience, this article explores the application of the combination of numbers and forms in concepts teaching, equations, inequalities, functions, complex numbers, and proofs.