分类讨论思想在数学解题方式中的应用研究

Application of Classified Discussion in Mathematical Problem Solving

当前数学解题期间教师大量应用分类讨论思想,很多一线教师和教学领域人员在多年教学历程中发现,通过分类讨论思想的指引可将许多复杂的数学问题有效解决。但很多学生在具体应用分类讨论思想期间依旧存在许多不合理之处和问题,例如平常在解题和考试期间,由于自己的分类不到位、讨论不仔细等原因就会出现丢失分数的现象,其中最主要的原因还是在于学生无法按照题目要求进行针对性、科学的分类。与此同时学生不知以何种标准来进行分类;有些学生虽然可进行分类,但分类的过程不是很完善,漏洞百出,导致分类的不完整、讨论的不合理;甚至部分学生的分类完全错误,这样的答题效果就与实际要求严重脱离。

At present,teachers use the idea of classified discussion extensively in solving mathematical problems,many front-line teachers and teaching staff have found that many complex mathematical problems can be effectively solved through the guidance of the idea of classified discussion in many years of teaching process.However,many students still have many unreasonable points and problems in the course of discussing the idea of classification,for example,during solving problems and examinations,students will lose scores because of their lack of classification and careless discussion.The most important reason is that students can not classify according to the requirements of the topic pertinently and scientifically.At the same time,students do not know what criteria to classify;some students can classify,but the process of classification is not perfect,there are many loopholes,leading to incomplete classification,unreasonable discussion;even some students classify completely wrong,so the effect of the answer is severely divorced from the actual requirements.