Investigation And Research On The Current Situation Of Mathematical Reverse Thinking Ability Of Senior Two Students

Innovation is the main theme of the times,and the times need innovative talents.Reverse thinking,as an important source of innovative thinking generation,is an important indicator of innovative talents.The ability of reverse thinking in mathematics is a kind of ability that high school students must have in the process of learning mathematics.Understanding the current situation of students’ability of reverse thinking in mathematics can effectively cultivate students’ability of reverse thinking in mathematics and help promote the development of students’mathematical ability.In this paper,we use the contents of four topics,namely,preparatory knowledge,functions,geometry and algebra,and probability and statistics,to study the mathematical reverse thinking skills of senior two students.Firstly,we collected relevant literature to construct a framework for measuring mathematical reverse thinking ability,and evaluated students’thinking process in three dimensions:correctness of answers,reasonableness of strategies and clarity of expression,and compiled test papers,questionnaires and interview outlines,taking into account textbooks,standards,college entrance examination questions and other literature;secondly,we selected a total of 282 senior two students from six classes in a middle school in D,Yunnan Province to participate in the survey,and six students and six teachers to participate in the interviews;finally,the survey data were compiled to statistically analyze the students’level of mathematical reverse thinking ability,and to analyze the variability between students’mathematical reverse thinking ability and class level,gender,and the correlation between it and their usual grades in mathematics.The problems in the process of developing mathematical reverse thinking skills were further analyzed through student interviews and teacher interviews to provide a basis and direction for teaching suggestions.Based on the above study,teaching suggestions were made with the goal of improving students’mathematical reverse thinking skills.The study found that students’ability to think backwards in mathematics was generally at an intermediate level n the second year of senior secondary school,and that there was no difference between boys and girls in their ability to think backwards in mathematics,but there was a significant difference between key classes and regular classes,and a positive correlation with their usual performance in mathematics;the results of the interviews showed that students did not have the awareness and habit of thinking backwards,and that teachers’attention to and cultivation of students’ability to think backwards in mathematics.the four factors,namely students,teachers,schools and families,all have a certain influence on the development of students’reverse thinking skills in mathematics,with the two factors of students and teachers having the most significant influence,and the regression equation is y=1.521+0.515x₁+0.187x₂,where y represents students’ability to think backwards,₁x represents the student factor and ₂x represents the teacher factor.The teacher factor.Combining the characteristics of high school mathematics teaching and learning,based on motivating students to learn and take the initiative,the teaching suggestions for developing students’ability to think backwards in mathematics are proposed.