Optimization Research On Polya's Problem-solving Ideas In The Teaching Of The Maximum Value Problem Of Function In The First Grade Of High Schoo

Teachers’ teaching thinking directly affects students’ problem-solving thinking."Mathematics Curriculum Standard for Ordinary Senior High Schools(2017 Edition)" points out: "Mathematics education should start from the actual situation of students,create problems that are helpful for students to expand their thinking,and guide students to acquire relevant knowledge and form good problem-solving thinking through thinking,communication and practical inquiry".Maximum value problem of function in Grade One is the basis of Maximum value problem in senior high school.In practical teaching,the biggest problem teachers encounter is that there are many knowledge points,miscellaneous solutions and rich questions.Therefore,teachers should expose their thinking of solving problems to students,guide students to review and reflect,and cultivate students’ consciousness of summing up,"solving more than one problem" and "drawing inferences from others".However,in the actual teaching,teachers’ teaching is more to complete the corresponding teaching tasks,and some students will still be helpless when they encounter similar problems.In this case,it does not play its due role in cultivating the thinking ability to solve problems.Therefore,based on Polya’s thought of solving problems,this paper puts forward the optimization of Polya’s "’how to solve it’ list" with the characteristics of the present era,and integrates the optimization strategy of "’how to solve it’ list" with the teaching of the maximum value problem of the high school function to guide the teaching design of the maximum value problem of the function,aiming at providing methods for the optimization of teaching thinking of senior high school mathematics teachers.The research problems of this paper are shown in four aspects: first,the true level of solving the maximum value problem of the students in Grade One of Y Middle School in Z City,the present situation of teaching thinking of mathematics teachers in the teaching of the maximum value problem of function,the degree of understanding of Polya’s problem-solving thought,and the degree of agreement with the teaching of solving the maximum value problem of function;Secondly,combined with the research results,whether we can put forward corresponding optimization strategies for Polya’s problem-solving thought;Thirdly,with the help of Polya’s "’how to solve it’ list" optimization strategy,whether it can design a teaching scheme to improve mathematics teachers’ teaching thinking of function maximum value problem;Fourthly,whether the teaching scheme designed by the optimization strategy of Polya’s "’how to solve it’ list" is effective in improving mathematics teachers’ teaching thinking.Based on the above problems,the research process and results are as follows.First,using the method of questionnaire survey and interview,it is found that the main problems in solving the problem of the maximum value of functions are as follows:(1)The degree of integration of the problem-solving ideas and the "’how to solve it’ list" is not high;(2)After the problem solving Weak consciousness.Through the teacher questionnaire and interview investigation,the main problems in the teaching of teachers in the most valuable problem of functional functions are:(1)understanding of Polya at a shallow level;(2)the teaching process is not high with the "’how to solve it’ list";(3)The "retrospective" session is limited to the answering questions itself.Second,in view of the problems in the research,with the help of Polya’s problem solving ideas,we propose the optimization strategy of "’how to solve it’ list" :(1)Observing and doubting-finding the crux of the problem;(2)Multivariate analyzing doubts-exploring the path of solving the problem;(3)Accurately solving doubts-accurately implementing the plan;(4)Reviewing and doubting-perceive the problem-solving process;(5)Reflecting and doubting-the problem of sublimation and expansion.Third,the optimization strategy is incorporated into the case "The Most Value to the Triangle Function" in teaching design,and the effectiveness of the optimization strategy is verified by teaching practice.It can provide a certain direction for teachers ’teaching thinking,which is conducive to the improvement of the teaching effect and the improvement of students’ ability to solve problems.