数列极限定义教学的认识与实践

Understanding and Practice on the Limit Definition Teaching of Sequence of Number

数列极限定义是微积分学习的起点，也是一个难点．高等数学教育不仅是数学知识的教育，同时也是数学语言的教育和数学文化的教育．数列极限定义的教学可分4个阶段，教师与学生可共同观察、归纳、抽象概括，让学生参与到知识的发生过程中来，主动建构知识，并学会用数学语言刻画某一现象，体验由自然语言到数学语言的转化过程，增强他们学习和使用数学语言的信心．

The limit definition of sequence of number is the starting point of learning calculus, but also a difficulty. The higher mathematics education is not only a knowledge of mathematics education, but also the language of mathematics education and the education of mathematics culture. The limit definition teaching of sequence of number can be divided into four stages. The teacher and the student can observe and conclude and abstract summarize together, let the students involved in knowledge occurrence process, to construct knowledge actively, and learn to use the language of mathematics depict a phenomenon, to experience transformation process from a natural language to mathematics language, to enhance their confidence of learning and using the mathematical language.