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在数学教学中,引导学生探索命题结论的来源,培养学生的数学猜想能力,是有益的。笔者在平面几何教学中对这方面进行了一些实践,方法是: 1、提出问题即更改命题结论,变命题结论为不确定性,激发学生积极思考; 2、探索结论引导学生寻求命题在特殊条件下的结论; 3、猜想根据命题在特殊条件下的结论猜想命题的一般结论; 4、证明猜想。例1 如图1,AB是⊙O的直径,CD是弦,AE、BF垂直于CD.
In mathematics teaching, it is useful to guide students to explore the source of the conclusions of the propositions and to cultivate students’ mathematical conjecture. In the teaching of plane geometry, the author has carried out some practice in this respect. The methods are as follows: 1. Ask the question to change the conclusion of the proposition, change the conclusion of the proposition into uncertainty, inspire students to think positively; 2. Explore the conclusion to guide the student to seek the proposition in special conditions The following conclusions; 3. Guess the general conclusion of the proposition according to the conclusions of the proposition under special conditions; 4. Prove the conjecture. Example 1 As shown in Figure 1, AB is the diameter of ⊙O, CD is the string, and AE and BF are perpendicular to the CD.