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练习是数学教学重要的组成部分,恰到好处的习题,不仅能巩固知识,形成技能,而且能启发思维,培养能力。在教学过程中,除注意增加变式题、综合题外,适当设计一些开放型习题,可以培养学生思维的特性。一、利用缺少条件型开放题,培养学生思维的灵活性缺少条件型开放题,按常规解法所给条件似乎不足,但如果换个角度去思考,便可得到解决。如:在一个面积为12平方厘米的正方形内剪一个最大的圆,所剪圆的面积是多少平方厘米?按常规的思考方法:要求圆的面积,需先求出圆的半径,根据题意,圆的半径就是正方形边长的一半,但根据题中所给条件,用小学的数学知识无法求出。换个角度来考虑:可以设所剪圆的半径为r,那么正方形的边长为2r,正方形的面积为2r×2r=4r2=12,所以r2=3,圆的面积是3.14×3=9.42(平方厘米);还可以这样想:把原正方形平均分成4个小正方形,每个小正方形的边长就是所剪圆的半径,设圆的半径为r,那
Exercise is an important part of mathematics teaching, just the right exercises, not only to consolidate knowledge, skills, and can inspire thinking and develop ability. In the teaching process, in addition to pay attention to increase the variant questions, comprehensive questions, the appropriate design of some open-type exercises, you can develop the characteristics of student thinking. First, the use of the lack of conditional open questions, to develop the flexibility of thinking Students lack of conditional open questions, according to the conventional solution given the conditions seem inadequate, but if you think from another point of view, can be resolved. Such as: in an area of 12 square centimeters within a square cut a maximum circle, the area cut is the number of square centimeter? According to the conventional method of thinking: the required area of the circle, you must first find the radius of the circle, according to the title , The radius of the circle is half the length of the square, but according to the conditions given in the question, it can not be found in the elementary mathematics. From another point of view: you can set the radius of the circle is r, then the side of the square length of 2r, the square area of 2r × 2r = 4r2 = 12, so r2 = 3, the area of the circle is 3.14 × 3 = 9.42 ( Square centimeters); You can also think: the original square is divided into four small square, the small side of each small square is the radius of the circle, set the radius of the circle r, that