A Survey Of High School Students' Mathematical Reverse Thinking Ability

It is a hot research topic to construct a scientific and systematic education system of subject core literacy.It is the basic principle of curriculum reform and the concentrated embodiment of educational value to cultivate students’ mathematics core literacy.It is also one of the important contents of cultivating students’ rational thinking from the perspective of subject thinking to teach students how to effectively use mathematical reverse thinking to settle issues.The cultivation of students’ reverse thinking capacity in classroom teaching can not only cultivate students’ thinking flexibility and sensitivity,but also help to improve the students’ mathematics core literacy.First of all,this study analyzes the research background from the requirements of senior school mathematics curriculum standards and the current situation of senior school mathematics classroom teaching,and through literature review to understand the current situation of the cultivation of high school students’ mathematics core literacy and reverse thinking capacity,and clarify the purpose and significance of the research.Secondly,combined with the definition and theoretical basis of related concepts in this study,through tests and student interviews,this study investigates the current situation of the cultivation of mathematical reverse thinking ability of sophomores in a senior school in S City,and makes a quantitative and qualitative analysis of the test consequence.Finally,combined with the analysis conclusion,it puts forward some suggestions on the cultivation of senior school students’ mathematical reverse thinking capacity.Through the inquiry,we draw the consequence: the current situation of senior school students’ mathematical reverse thinking capacity is below the medium level;In the application of complement thought and finding paradoxes,the accuracy with strategy hint is significantly higher than that without hint;The reverse use of formula and theorem are significantly different from other kinds of reverse thinking strategies of mathematics;Boys are in the reverse of theorem The ability of using and finding counter examples is significantly better than that of female students.Moreover,the study also found that there are the following issues in the course of cultivating senior school students’ mathematical reverse thinking: The connotation and essence of formulas and theorems are not thoroughly grasped;The consciousness of using mathematical reverse thinking to settle issues is lacking;The training of using mathematical reverse thinking strategy to settle issues is insufficient.Addressing the identified issues,the following suggestions are given from three aspects of mathematical formula teaching,mathematical theorem teaching and mathematical problem solving teaching:Understanding the essence of formula,guiding students to master the inverse use of formula;Gradient variant training to improve students’ ability to use formula inversely;Mastering the relationship of propositional structure of theorems,effectively infiltrating the application of mathematical reverse thinking;Conducting mathematical theorem teaching from multiple perspectives and reinforcing the drilling of mathematical reverse thinking;To reinforce the application of structural counterexamples,to develop students’ awareness of mathematical reverse thinking;To reinforce the teaching of analytical method to solve problems,and to develop students’ ability to carry out the results.