老问题 新变式

• 作 者: 阳娟娟
• 机 构: 北京市宏志中学,
• 出 处: 中学生数学
• 发表日期: 2014年24期
• 关键词: 变式 波利亚 解题方法 图形的 数量关系 基本图形 全等三角形 反思过程 等腰直角三角形 逆时针旋转

在解题方面,波利亚堪称“高人”.他认为,我们可以选择一道有意义又不太复杂的题目,去发掘它的各个方面,在解题过程中提高我们的才智和推理能力.这些见解启示我们,通过解题活动和反思过程,总结归纳解题方法,提炼图形的本质特征,概括思想方法,达到举一反三、触类旁通的效果,其中对问题进行变式练习是发掘题目价值的重要途径之一.下面我们通过对一道平面几何问题的变式探究,体会变中不变的性质.

In terms of solving problems, Polyana is called “superman.” He believes that we can choose a meaningful and less complex topic to explore all aspects of it, to improve our intelligence and Reasoning ability of these insights inspired us through the problem solving activities and reflection process, summed up the problem-solving methods to extract the nature of the graphic features, ideas and methods summarized to achieve the goal of giving top priority, touch by analogy, of which the variant practice is to explore the value of topics One of the important ways below.We will understand the changeable nature by a variant inquiry of a plane geometry problem.