摘要
任何思维都离不开抽象.形象思维借助于形象的抽象,逻辑思维借助于概念的抽象.本文指出了数学形象思维的基本特征,即数学形象是抽象化了的形象想象中的形象;数学形象是通过变换找出典型表示,因而数学形象思维通常成为表示论和典型化:数学中的形象不断地与数学抽象和数学逻辑互相融合互相转化,形成数学思维模块.
No thinking can be without abstraction. Thinking in terms of images depends on the abstraction of images and logical thinking depends on the abstraction of concept. The basic characteristics of mathematical thinking in terms of images is pointed out in this paper, that is, the mathematical image is an abstracted and imaginative one and it is to find out the typical representation through transformation. Therefore the mathematical thinking in terms of images often becomes representation theory and typi-cation. The image in mathematics and mathematical abstraction and logic keep being mixed and transformed with each other to form mathematical thinking models.
关键词
形象思维
表示论
思维模块
数学
thinking in terms of images
representation theory thinking model
