论数学思维能力中的分类思想

On the classifcation of mathematical thinking ability

数学思想是数学知识和方法在更高层次上的抽象与概括,分类是一种重要的数学思想,分类思想是根据数学本质属性的相同点和不同点,将数学研究对象分为不同种类的一种数学思想。分类以比较为基础,比较是分类的前提,分类是比较的结果。分类应在同一标准下具有完备性和互斥性,不同的类之间的逻辑关系是"或",因此,分类的结果是集合运算的"并",通过分类思想的学习,培养学生思维的条理性,缜密性,提高学生的思维能力。初中数学中,分类问题总体归结为两类,涉及数与代数、空间与图形,因此,分类思想是安徽省中考每年必考的核心思想方法。

Mathematical thinking is the abstraction and generalization of mathematics knowledge and methods on high level.Assorting thought is an important kind of mathematical thinking which is based on similarities and differences in the nature of mathematics and classifies objects for study into different kinds.Classification is on the basis of comparison,comparison is the precondition of classification,and classification is the result of comparison.Classification should have completeness and exclusiveness according to the same standard.The logical relationship between different classes is ＂or＂.Therefore,the result of the classification is ＂union＂ of set operation.By studying assorting thought,logic and rigor of students＇ thinking are cultivated and students＇ thinking ability is improved.In junior high school mathematics,classification problems overall boils down to two categories,number and algebra,space and graphics.Therefore,assorting thought is a core thought which must be involved in senior high school entrance examination in Anhui province every year.