A Study On The Correlation Between High School Students’ Ability Of Mathematical Abstraction And Proposing Mathematical Problems

Mathematics is the foundation of natural science.Six core qualities are the important connotations and manifestations of mathematical teaching objectives,among which,mathematical abstract quality,as the first thought,is the necessary prerequisite for human rational thinking.At the same time,the development of the new era needs innovative talents.Active thinking is a necessary condition for innovation,while proposing questions by oneself is an important prerequisite for initiative.The psychology of students in senior high school has become more mature,and their subjectivity has also entered an important period of high development.They have the ability to calculate and think on the abstract level without being restricted by specific objects,and are in a critical period of the development of abstract ability.Therefore,in order to develop mathematics teaching and cultivate students’ thinking,it is necessary to study the ability of mathematical abstraction and proposing mathematical problems of senior high school students.Since both of them reconstruct existing information from the perspective of mathematics,this thesis attempts to study their correlation,so as to expand the research field and provide new ideas for teachers’ teaching.In this thesis,through literature research,mathematical representation and abstract thinking are set as secondary indexes of mathematical abstraction ability.Fluency,flexibility and originality are set as secondary indexes of mathematical problems raising ability.Combined with interview and survey methods,compile ability test topics and set up scoring standards,then test the students and retrieve the test papers.Through quantitative analysis,statistics and analysis of measured data with SPSS and EXCEL,to understand the status quo of students’ mathematical abstraction ability and ability to propose mathematical problems in grade one,and then establish a structural equation model to analyze the correlation between the two abilities and their secondary indicators with AMOS.Through the research,the following conclusions are drawn.On the whole,the students of grade one are at the medium level in mathematics abstraction ability and mathematics problems proposing ability.There is a high correlation between mathematical abstraction ability and mathematical problems proposing ability and their secondary indexes,and the internal structure of the model is good.The ability of mathematical abstraction and proposing mathematical problems are closely related and have significant positive correlation.In the actual teaching process,teachers should create more abundant and inductive situations to cultivate students’ mathematical abstraction ability.In class,teachers should actively organize open,discussion and divergent teaching activities to cultivate the ability to propose mathematical problems.Teachers also should set up reasonable teaching strategies and carry out teaching activities that complement and permeate each other through the relevant links of ability training.It can better develop students’ ability and effectively improve teaching efficiency.