An Experimental Study On Developing Mathematics Normal Students' Variation Problem Constructing Abilities From The Perspective Of Problem Posing

As a pre-service teacher,the professional development of mathematics normal students,especially the acquisition of complete professional knowledge,is crucial.As a kind of mathematics normal students' ability to pose mathematical problems,the construction of mathematics variation problem is an important part of the professional knowledge of mathematics normal students.Developing the ability of mathematics normal students to construct the variation problem is not only the need for the ability development of mathematics normal students,but also the need of traditional mathematics variation teaching in China.The research on the construction of mathematical variation problems is still scarce,and most of them remain on perceptual cognition.Researchers lack a certain degree of attention and understanding of “mathematical variation problem constructing",and do not regard it as an “ability” of mathematics teacher,especially a pre-service mathematics teacher with less teaching experience or even no teaching experience.This research regards the construction of mathematical variation problems as part of the ability to pose problems.It is an independent mathematical activity that pose mathematical variation problems in relatively independent situations or reexplain the problems in the process of problems solving.In this study,firstly,the connotation of the mathematical variation problem constructing ability is defined on the basis of literature review.Then,the strategy diagram for the development of mathematical variation problem constructing ability is built on the basis of comparing the similarities and differences between "what-If-Not" and the variation strategy.Finally,the evaluation framework of the mathematical variation problem constructing ability is constructed by referring to the relevant research of the evaluation of mathematical problem posing.The proposed research questions are as follows:(?)what is the current situation of the mathematics normal students' variation problem constructing ability?(1)What is the overall performance of mathematics normal students in the test of variation problem constructing ability?What's the difference between different grades of mathematics normal students in the test of variation problem constructing ability?(2)What is the understanding of mathematics normal students on the knowledge of variation teaching?(?)What effect will the teaching case designed according to the training strategy diagram of mathematical variation problem constructing ability have on the training of mathematics normal students' variation problem constructing ability?In view of the research question one,we mainly use the test paper survey method and the questionnaire survey method to investigate the current situation of 246 mathematics normal students,in order to explore the performance of mathematics normal students' variation problem constructing ability and their knowledge of variation teaching.Aiming at the second problem,we mainly used two groups of experiments to study 89 mathematics normal students.Among them,50 mathematics normal students in the experimental class were intervened for two months,39 mathematics normal students in the control class were not intervened in any way.Finally,89 mathematics normal students were tested for their ability to construct mathematical variation problems,and then tested whether the teaching cases can effectively improve their ability to construct mathematical variation problems.Through the analysis of the interview content of 18 mathematics normal students,we can understand the mastery of the variation strategies in different situations.The results show that:(1)in the test of the variation problem constructing ability,most of the normal students,including the senior students,are in the medium or lower level.(2)Mathematics normal students' knowledge of variation teaching,especially the knowledge of non-standard variation and vertical variation,is at a relatively narrow or shallow level,even for the senior mathematics normal students who have some educational practice experience.(3)Teaching cases can effectively improve the mathematics normal students' variation problem constructing ability.The constructing ability of mathematics normal students in the experimental class has been improved in different degrees in three situations.At the same time,mathematics normal students also have a deeper grasp and understanding of non-standard variation and vertical variation strategies.This research lays a foundation for further research on the ability of teachereducation educators in China,and has a high reference value for the teaching of mathematics teaching skills in the classroom teaching of university mathematics teachers,especially the teaching of mathematical variation problem teaching skills.