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我在长期的职工大学数学教学中,针对成人学员的特点,我经常采用类比对照、分析归纳和注释的方法,取得了较好的教学效果,现介绍如下。一、类比对照所谓类比对照,既是说,要弄清楚相类似的东西是什么,同时也要弄清楚相区别的东西是什么。“没有比较就没有鉴别”。比较是相类似事物之间的比较,鉴别是指找出类似事物之间的差别。从而使对要掌握的内容的理解更深刻更牢固。具体的说应该从以下几方面入手。1.概念的类比对照在高等数学中,多元函数微积分中的概念,从定义到定理公式,以至于到计算方法,都可以与一元函数类比对照。如,二元函数的积分(即二重积分)的定义其主要数学思想是,构造出一个和式的极限: (?)sum from i=1 to (?)f(ζ_i,η_i)⊿σ_i此与一元函数的积分(即定积分)定义的数学思想是一致的,即构造出一个和式的极限(?)sum from i=1 to (?)f(ζ_i)⊿x_i其区别仅在于空间由一维扩充到二维了(这里“空间”
In my long-term teaching of college mathematics, in view of the characteristics of adult students, I often use analogy, analysis and annotation method, and achieved good teaching results are as follows. First, the analogy The so-called analogy control, both to say, to find out what a similar thing, but also to find out what is the difference between what. “There is no comparison without comparison.” Comparison is a comparison between similar things, discrimination refers to find the difference between similar things. So that you have a deeper and stronger understanding of what you need to know. Specifically speaking, we should start from the following aspects. 1. Concept analogy In higher mathematics, the concept of multivariate calculus, from the definition of the theorem formula, so that the calculation method can be compared with the univariate function control. For example, the definition of the integral of a binary function (that is, the double integral) is that the main mathematical idea is to construct a limit of sum: () sum from i = 1 to (?) F (ζ_i, η_i) ⊿σ_i It is consistent with the mathematical idea defined by the integral (ie, definite integral) of a unitary function, that is, the sum of the summation i = 1 to (?) F (ζ_i) ⊿x_i is constructed from the limit One-dimensional expansion to two-dimensional (here “space”