Generalization In Mathematics Learning

Generalization is one of the most essential characters of mathematics.What mathematics concerns is highly generalized materials of thoughts,and generalization is a way to mathematics research,what's more,the development of mathematics is also a process of generalization. Therefore, in the sense of the characters of mathematics,generalization is needed in mathematics learning. On the other hand, generalization is the base of mathematics learning,and generalization ability is the key to the development of mathematics ability,and mathematics generalization level is an important mark of mathematics learning level/The basic and important role played by generalization calls for generalization in mathematics learning.Generalization is aimed at the essential attribute and common character of mathematics object,generalization has such character as duality,process,and gradation.Generalization is found everywhere in mathematics learning.This paper,enumerates the generalization of the meaning of mathematical symbol,number and form,relation, structure, operation and inference,and thinking modes of mathematics.Generalizing is a process of several thinking acts coordinating,and it contains five steps:watching,taking,filtering,extending,and affirmation. In the process of mathematics learning,students should always look for and take a certain effective way of generalization as a thinking thread,and make perceptual knowledge rise to rational knowledge, thus improve generalization of mathematics knowledge/There are several kinds of generalization in mathematics learning: analogical generalization, inductive generalization, abstract generalization and brief generalization.The ultimate purpose of studying generalization in mathematics is to put the common theoretical knowledge about generalization into the process of mathematics teaching and learning,so as to instruct the teaching of teachers and improve the learning of students.On the base of survey of student' s mathematics generalization ability ,the paper puts forward some advice on improving student' s mathematics generalization level in concept teaching,proposition teaching,problem solving teaching and revision.