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解题教学是数学教育的重要组成部分,近年来,怎样解题已经成为现代数学方法论研究的一项重要内容.在研究怎样解题时,既要研究解决一类问题一般化的通性通法,又要注意解决具体问题特殊化的特殊技巧.一般化与特殊化贯穿于整个解题过程之中,构成整个解题过程的基础.通性通法,是从解同类若干问题成功的实践中总结归纳出的一般方法或模式,是解决一类问题的共性方法,具有较强的程序性和迁移性,对解类似的问题起着启发和指导作用;特殊技巧,是对具体问题的“极端”条件进行思考而得到的特殊方法或方式,是解决具体问题的个性方法,具有较强的技巧性和简洁性,为一般
Problem-solving teaching is an important part of mathematics education. In recent years, how to solve problems has become an important content of modern mathematics methodology research. When studying how to solve problems, it is necessary to study and solve common problems in a class of problems. It is necessary to pay attention to the special techniques for solving specific problems. Generalization and specialization are used throughout the problem-solving process to form the basis of the entire problem-solving process. The general method is a successful practice in solving several problems of the same kind. The general methods or models summarized and summarized are common methods for solving a class of problems. They have strong procedural and migratory properties and they serve as inspiration and guidance for solving similar problems. Special techniques are the extremes of specific problems. "The special method or method for considering the conditions is a personal method for solving specific problems. It has strong skill and simplicity and is general.