| It can be seen from the work of new curriculum standard,mathematics core accomplishment and other researchers that mathematical reverse thinking is an important mathematical thought,which can help the diversity and innovation of thinking.also It can be seen from the students’ cognition,the arrangement of teaching materials and the current teaching status that it is urgent to train the students’ mathematics reverse thinking.This paper did a review of reverse thinking at home and aboard,found that elementart school is very lack of mathematics reverse thinking,so the study of this aspect as follows:first,analysis of Beijing normal university version of the mathematics teaching material,then research on the current situation of grade four mathematics reverse thinking,finally Threw out teaching suggestions of cultivating students’ reverse thinking by combining cases.In the second chapter,this paper first define the related concepts of“thinking,mathematics thinking,mathematics of reverse thinking”,and then summarizes the theory of elementary student’s psychological characteristic,to determine the grade four students for testing the main object,and finally summarizes the theory of the zone of proximal development and the main content of the theory of constructivism,for subsequent case analysis provides a theoretical basis.The third chapter,through the frequency of reverse thinking in math textbook,determines the main content of teaching material analysis: application of reverse thinking in the problem,in the relationship,in the calculation,in the math formula.Then through the Sorting and statistics of reverse thinking in 12 teaching materials,found the changing trend for four kinds of reverse thinking rising by grade,the percentage for four kinds of reverse thinking in primary school,in content of new lesson,exercises and extended exercises,in number and algebra,graphics and geometry,probability and statistics,synthesis and practice.It provides the basis for the design of test questionnaire and the suggestion of teaching.In the research on the current situation of reverse thinking of fourth-grade students,this paper takes four kinds of application of reverse thinking as the main content,selects the mathematics teaching materials and the development topic to adapt,and makes the test volume from the positive and the negative aspects.Then test,code,assign and input data,use SPSS for reliability analysis,and judge whether there is significant difference between mathematical reverse thinking and gender,mathematical reverse thinking and school.Whether there is significant difference between positive thinking and reverse thinking;In the final analysis of the students’ consciousness of disproof,fill "cut" and "the use of the characteristics of problem solving" consciousness,provide the basis for subsequent provide valuable teaching advice,for primary school teachers to cultivate students reverse thinking mathematics teaching provides the reference.In the fourth chapter,this paper combined with the above research results and teaching cases,from three aspects which are before class,in class and after class give the following advice: advice teachers to put reverse thinking into the design of the prelab assignment;Suggest teacher to teach in class by using the common usage of reverse thinking such as analysis,cut and complement,hindcasting,subjunctive,complement thought,reverse calculation,counter-exampe;suggest teacher using reverse thinking way to build the problem chain;Finally suggest teacher to encourage students to organize and review after class,Organize the knowledge of mutual exclusion,and let students truly understand the usage of reverse thinking in calculation or in solving problems. |
