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“指数概念普遍化”这一章节,一向被认为是代数教学中的一个难点。实际上,让学生記住一些指数的定义,并且会运算,达到这个目的是极其容易的。但是,我們絕不能滿足于这种形式主义的教学成果。应該使学生透彻地理解指数概念普遍化的內容、方法和意义。实現此目的,确非易事。教学中,关键在于必須解决两个問題。首先应解决为什么要把指数概念普遍化的問題。学习之始,不明确目的,則学习的积极性就不会很高;学过之后,不理解其重要性,那么认識就不可能进一步深化和提高。其次是应該改进指数概念扩充的叙述方法,使得这部分知識更加明朗化。本文是围繞上述两个問題說明一些认識和体会,笔者的教学經驗是不足的,希望批評指教。
The “universalization of index concept” section has always been considered a difficult point in algebra teaching. In fact, it is extremely easy for students to remember the definition of some index and calculate it. However, we must not be satisfied with this formalistic teaching achievement. Students should be given a thorough understanding of the content, methods and significance of the generalization of the concept of the index. It is not easy to achieve this goal. The key to teaching is to solve two problems. First of all, we should solve the problem of why we should generalize the concept of the index. If the beginning of learning is not clear, the enthusiasm for learning will not be very high; after learning, if you do not understand its importance, then understanding cannot be further deepened and improved. The second is the narrative method that should improve the expansion of the index concept, making this part of the knowledge more clear. This article describes some understandings and experiences centering on the above two issues. The author’s teaching experience is insufficient and he hopes to criticize and teach.