The Survey Study On The Solution To Mathematics Variant Problems

Mathematics, as the important basis of the science, is extensively applied in both people’s study and their daily lives and it has an inestimable influence on the development of human society. Correspondently, there is a longstanding history of the research on mathematics so that mathematics builds its own reputation in the exploration into those solved and unsolved problems on itself. "Problem solving" in mathematics, being the focus in the study of math teaching all the time, is considered as the central topic in educational circle. The solution to one mathematics problem is not regarded as the ultimate goal for math teachers but to cultivate students’ ability in drawing inferences about other cases from one instance, that is to say, the ability in solving variant math problem. As is known to all, variant teaching has been popular in Chinese traditional math teaching, which can make students further understand and consolidate their basic knowledge and practice their proficient basic skills. However, the fact is that students at the same level (equal in intelligence quotients and basic knowledge) show different levels in problem solving when dealing with the same variant problem in math. Therefore, the research question comes to that:what factors cause these differences? This paper mainly aims to address this problem. In this paper, tests, case analysis and interviews are employed to assist this empirical research, aiming at finding out those factors which influence the solutions to variant teaching in mathematics. Moreover, some effective suggestions for variant math problem solving will be distilled by the analysis of both interviews for math teachers and their teaching plans.The first part of this paper is introduction, mainly including research background, existing research status both home and abroad, research content. The second part is theoretical basis, in which some concepts concerned and theory and practice about variant teaching will be illustrated, such as the variant, variant math problems, problem solving, variant math problem teaching theory and its manifestation, etc. The third part is the design and implementation of the survey study, embracing research purpose research instruments, the implementation plan and its procedures. Then the fourth part is results analysis, including variance analysis, teaching cases analysis on math variant problem solving and the interview analysis on variant teaching of teachers. The final part comes to the conclusion.