Investigation And Research On The Cultivation Of Mathematical Reverse Thinking Ability In High School Function Teaching

With the continuous progress of the times,the society's demand for innovative talents has gradually increased.How to improve innovation ability and cultivate innovative talents has become a subject of widespread concern at home and abroad in the new era.The key to improving the ability of innovation is to form innovative thinking.As a kind of innovative thinking,reverse thinking plays an important role in all fields of production and life.Function,as one of the main contents of high school mathematics knowledge,runs through the high school mathematics curriculum and contains many conversions between forward and inverse.Therefore,it is necessary to cultivate students' mathematical inverse thinking ability in high school function teaching.It is helpful for students to deeply understand the essence of the function and enhance the flexibility of thinking.The research on reverse thinking and function teaching in our country has been increasing year by year,but there are few related researches on students' reverse thinking ability and function teaching.Therefore,on the basis of existing research,an attempt was made to test the current situation of the cultivation of mathematical reverse thinking ability in the function content of high school students,and the following tasks were mainly completed: First,sort out and analyze domestic and foreign thinking,reverse thinking,mathematical reverse thinking,and functions.Teaching related literature,discussing and summarizing the related concepts of mathematical reverse thinking suitable for this research.Secondly,the function content of the high school mathematics textbook of People's Education A version is sorted out and statistics,and the teacher-student questionnaires and test papers are compiled according to the sorted content and existing related research.The students in two high school science classes in each of the two high schools in K city(total 190(Name)and 50 teachers conducted a survey to analyze the current situation and influencing factors of students' mathematics reverse thinking ability training.Finally,based on the analysis of the survey results and related theoretical research,suggestions on the cultivation of mathematics reverse thinking ability in high school function teaching are proposed.The main conclusions are as follows:(1)The current situation of students' mathematical inverse thinking ability:students' mathematical inverse thinking ability in function content is at the middle or lower level.There are significant differences in mathematics reverse thinking ability between students of different classes and levels,and key classes are better than ordinary classes;there is no significant difference in mathematics reverse thinking ability between students of different genders.In addition,there is a significant positive correlation between the mathematics reverse thinking ability and the students' mathematics daily performance.With regard to cultivating students' mathematics reverse thinking ability in high school function teaching,from the cognitive perspective,teachers and students generally understand and affirm the effect of mathematical reverse thinking on students' personal development;from the perspective of training attitudes,teachers and students Generally speaking,they are in favor of cultivating students' mathematics reverse thinking ability in the content of high school functions;from the perspective of training methods,teachers and students generally agree with the teaching mode of guiding inquiry,teaching methods such as one question with multiple solutions,variant training,and designing open questions.It is suitable for cultivating the ability of reverse thinking in mathematics.(2)Factors affecting the development of students' mathematical reverse thinking ability: through analysis of the results of student test papers and teacher-student questionnaires,combined with interviews,it is concluded that the main factors affecting students' mathematical reverse thinking ability include students' thinking ability,teachers' teaching concepts and abilities,Teaching mode.(3)Suggestions for the cultivation of reverse thinking ability in high school function teaching: change teachers' teaching concepts and improve teaching ability;create reverse situations to create a good learning atmosphere;improve mathematical reverse thinking ability in problem-solving reflection.