§1 引言在高中代数课程里讲到“数列”这一单元时,由于要牵涉到绝对值不等式和实数理论,使大部分定理无法证明,因而在教学过程中造成了一定的困难。其实最主要的原因可能还是在于研究对象的改变。过去只研究有限多个数,而在极限中要讨论无限多个数,同学感到不习惯。在有限多个数里认为当然正确的事实,而在无限多个数里就未必尽然。例如在有限多个数中至少有一个最大和最小的数,而在1/n(n=1,2,3,…)中只有最大而无最小的数。再因过去同学的思维方法,基本上属于形式逻辑的范围,从静止的孤立的来看问题,一旦要它转变为从运动的全面的唯物辩证的思维方法来考虑问题时,必然会产生困难。因此怎样来讲好这一个单元,怎样根据大纲精神,课本系统,同学的接受水平来 § 1 Introduction When we talk about the “series” unit in the algebra of high school curriculum, we must involve absolute value inequality and real number theory to make most of the theorems impossible to prove, thus causing some difficulties in the teaching process. In fact, the main reason may still lie in the change of research object. In the past, only a limited number of studies were conducted, and in the limit, there was an infinite number of discussions. Students were not used to it. The fact that, of course, it is correct in a limited number of cases, it may not necessarily be in an infinite number of numbers. For example, there are at least one largest and smallest number in a finite number of numbers, and only the largest number and no smallest number in 1/n (n=1, 2, 3,...). Again, due to past students’ thinking methods, they basically belonged to the scope of formal logic. From the perspective of static isolation, once we turn it into a comprehensive materialistic dialectical thinking method from sports, it will inevitably cause difficulties. So how do you say this unit well, and how can it be based on the spirit of the curriculum, the textbook system, and the acceptance level of the students?