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波利亚说过“掌握数学意味着什么呢?就是要善于解题。”从某种意义上讲,学习数学就是学会解题,数学教学就是以解题为中心的教学。通过培养学生在解题过程中的方向性、目标性,不断地自动调整思维的角度,避免盲目的思维,从而顺利地解决问题,真正有效地实现学生自己主动建构知识的过程和意义。从心理学上看,解题是一种思维活动的过程。而思维的目标性是思维的主要特征,没有目标就没有思维。而怎样快速地到达目标,这就是思维的方向性的问题。
Polly said: “What does it mean to master mathematics? It is to be good at solving problems.” In a sense, learning mathematics is to learn to solve problems, and mathematics teaching is problem-centered teaching. By training students in the process of solving the problem of the direction, the goal, and constantly automatically adjust the perspective of thinking, to avoid blind thinking, so as to successfully solve the problem, the real and effective realization of the process of students and their own initiative to construct knowledge and significance. From a psychological point of view, problem solving is a process of thinking activities. The goal of thinking is the main feature of thinking, there is no goal without thinking. And how to quickly reach the goal, this is the direction of the problem of thinking.