Research On The Application Of Mathematical Thinking Methods In The Teaching Of Compound Functions In High School

This paper focuses on the two questions.They are as following."What Is the Current Situation of the Application of Mathematical Ideas and Methods in Senior High School Compound Function Teaching?"."How to Improve and Strengthen the Infiltration Teaching of Mathematical Ideas and Methods Compound Function Teaching in Senior High School ?".The literature method,investigation method,case method and other research methods are used in this study.This paper investigates the application of mathematical ideas and methods in compound function teaching in two high schools in Yun Gang area of Da Tong city.This paper analyzes reasons of the current problems and difficulties and finally puts forward the possible effective improvement strategies.The strategies are verified in practice through study and analysis of the two cases including the Definition Domain and Value Domain of Composite Function and the Monotonicity of Composite Function.The results are as follows:Firstly,this paper finds that there are the following problems in the application of mathematical thoughts and methods of senior high school on compound function teaching: 1.Teachers have not formed the conscious behavior in the active application of mathematical ideas and methods.The systematicness and externality of mathematical ideas and methods in teaching designs are insufficient.2.Students are afraid of the complex function modules and lack of scientificity in specific transformation and summary.3.When it comes to the teacher-student interaction,the teacher guidance is insufficient and the means of integration and evaluation on teaching and learning are single.Secondly,combined with classroom observation and teaching practice,the main reasons are summarized as follows according to the data analysis of surveys and interviews: 1.Teachers lack the initiative to research and lack the systematic learning.And their teaching design ability is initiative.The grasp of the learning situation,the teaching experience and wit are insufficient.2.Students lack motivation and have great differences in the foundation.They lack the clear understanding of mathematical ideas and methods and are not flexible.3.When it comes to the teacher-student interaction,teachers' modern technical literacy is weak.Students' abilities to learn from each other and the demonstration learning are insufficient.Finally,the following possible effective improvement methods are obtained with the help of teaching practice summary and the problem analysis:1.For teachers: The research and training and the teaching and research activities should be carried out to strengthen their self-consciousness in action;Based on the situation of examination and learning,they should optimize the teaching designs and add explicit tips and the train of thought guidance;They should teach students according to the courses and students' learning conditions and strengthen the guidance and scientific evaluations of the standard college entrance examination;They should improve the ability of modern educational technology and enrich the integration means.Teachers should make scientific incentive evaluations and play a role in guiding learning and teaching.2.For students: The investigations of learning situation should be strengthened and the supplementary materials should be provided to deepen students' intuitive understanding of mathematical thinking methods;The guide demonstration and mutual learning are needed.Strengthen the explanation of typical examples of composite functions and infiltrate mathematical ideas and methods.Improve the abilities of students' logical thinking,group cooperation and communication skills and display excellent error correction summary and the mind map.3.Interaction between teachers and students: Teachers should improve the ability to integrate mathematical ideas and methods into the teaching designs and implementation of specific lessons.They should provide guidance according to time and make good use of technical means.They should create the atmosphere of mutual learning and assistance.They should give students opportunities to exercise,express and communicate.They should improve the level of team cooperation by displaying learning achievements and the standardization of the blackboard writing.The research conclusion:This paper finds that the problems of integrating and infiltrating high school mathematics ideas and methods in compound function teaching are complex and diverse in the investigation of the current situation.There are five problems in the teachers' teaching.There are five problems in the learning of students.There are three problems in the teacher-student interaction.The level of teachers' teaching involves the overall cognition and practice as well as the specific teaching behaviors.The level of students' learning involves problems in learning basis,learning emotions,learning methods and specific application.The level of teacher-student interaction involves the neglect of learning situation,singleness of ways and insufficient guidance.This paper puts forward possible effective improvement methods and strategies through strategy exploration and the analysis of reasons from the aspects of teachers,students and teacher-student interaction.The reasons focus on research and learning,information literacy,teaching ability,teaching wit and learning situation differences(the learning starting point,the learning interest,the learning method standardization,the logical thinking and the expression ability).The strategies are also put forward in three aspects.The teaching level includes the unified understandings,the literacy improvement.It should base on practice,pay attention to the examination situation,base on the learning situation,design teaching carefully,integrate class hours,focus on the systematic teaching from point to area,benchmark the college entrance examination,strengthen guidance and pay attention to the evaluations.The level of learning is related to optimizing design,improving learning methods,participating the class actively,the system construction,the organic infiltration,the active accumulation,strengthening design,benchmarking guidance,training the abilities,studying college entrance examination,paying attention to the learning situation,optimizing explanation and team cooperation.The level of teacher-student interaction is related to enriching ways,stimulating the class,strengthening research,improving abilities,understanding the learning situations,improving teaching methods,creating the platform to form specifications.The enlightenment obtained from this study proves that these strategies have a certain effectiveness through the case study.To a certain extent,they can improve the problems existing in the integration of high school mathematics ideas and methods in the teaching of compound function.As front-line teachers,we can practice the above optimization strategies and be good at using high school mathematics ideas and methods in compound function teaching to boost the improvement of teaching efficiency.