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数学问题的解决,首先依据解题方案的获得。但解题方案的产生过程常表现为一系列缺少逻辑依据和清晰推理的联想,因而难以产生形式化。这就使学生认识和实践这一过程更加困难。对思维的研究表明,解题方案是由解题者依据题目信息和已有经验,联想到有关概念、原理和方法而获得。一、从基本知识、原理角度联想依据题目条件和结论的信息联想与之有关的知识和原理,常可以触发灵感获得解题思路。正如波利亚在“解题表”中指出的“你知道一个可以用上的定理吗?”。例1 已知直角三角形周长为1,求其面积最大值。联想一:由题目条件及所求信息联想到,
The solution to mathematics problems is based on the solution to problems. However, the process of solving a problem solution often appears as a series of associations lacking logical basis and clear reasoning, and thus it is difficult to produce formalization. This makes it more difficult for students to understand and practice this process. The research on thinking shows that the problem solving program is obtained by the problem solver based on the topic information and existing experience, associating with relevant concepts, principles and methods. First, from the perspective of the basic knowledge, the principle of association with the information based on the conditions and conclusions of the article associated with the knowledge and principles, often can trigger inspiration to get ideas. As Polya pointed out in the “Question Table”, “Do you know a theorem that can be used?”. Example 1 It is known that the perimeter of a right-angled triangle is 1, and find the maximum area. Lenovo 1: Assimilated by the condition of the subject and the requested information,