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数学练习题从难度上看,可分为两部分:一部分是直接应用定义、定理、公式、法则等基本知识就可解决的基本题,另一部分是要经过“转化”才能解的提高题(或称综合题)。典型题对如何把综合题转化为基本题具有示范作用,它的转化方法具有通性、通法的意义,所以应该让学生掌握一定数量的典型题。为此,在数学中注意选取典型题,揭示其通性、通法的典型本质,使学生掌握转化规律,提高转化能力,是非常必要的。下面举例说明。例1 如图1,已知AC⊥AB,BD⊥AB,AD和BC相交于E,EF⊥AB。求证:
From the difficulty point of view, mathematics exercises can be divided into two parts: one is the basic problem that can be solved by directly applying basic knowledge such as definitions, theorems, formulas, and rules, and the other is the improvement problem that can be solved through “transformation” (or Comprehensive question). A typical question has a demonstration effect on how to convert a comprehensive question into a basic question. Its transformation method has the meaning of generality and common sense. Therefore, students should be allowed to master a certain number of typical questions. For this reason, it is necessary to select typical questions in mathematics to reveal the typical nature of its generality and common practice, and to enable students to grasp the laws of transformation and improve their transformation ability. The following is an example. Example 1 As shown in Figure 1, AC⊥AB, BD⊥AB, AD and BC are known to intersect at E, EF⊥AB. Verification: