Research Oh The Difficulties And Teaching Strategies Of High School Students In Learning “Application Of Derivatives-Monotonicity”

The emergence and development of calculus is known as "one of the key events in the emergence of modern technological civilization".It is a milestone in the history of mathematics.Derivative,the core concept of calculus,plays a crucial role in senior high school mathematics.Derivative is a powerful tool for students to learn about the properties of functions and solve optimization problems in real-world life.Applying derivative in analysing the monotonicity of functions is one of the basic applications of derivatives It is also the basis for advanced properties of functions such as extreme values,local extreme values,and zeros.The definition of monotonicity in high school only provides a focus of strictly monotonicity,without any strict theoretical systems.In the mean time,the application of derivatives is based on students’ sound knowledge of function and strong comprehensive ability.Evidences of most students meeting certain difficulties iwhile learning and applying derivatives are provided in literatures and studying cases.So it is imminent to adopt reasonable teaching strategies for effective teaching.According to the actual teaching experiences,students tend to use derivatives in analysis of the monotonicity of functions and subsequent application problems.For topics with higher abstraction level,most students even give up directly because they have no idea where to start.In addition,students’ knowledge transfer ability is relatively weak,and there may be a fixed mindset when it comes to the connection with other related knowledge such as solid geometry,maximal problems in analytic geometry,and optimization problems in real life.In order to further understand and analyze the practical difficulties encountered by senior three students in our school in the study of “Application of Derivatives-Monotonicity”,find out the reasons and put forward effective teaching strategies for such phenomena,provide reference for students and high school teachers,and enhance students’ confidence in learning derivatives,this article adopted following experimental methods:1.Understand the common problems that may exist in the students’ learning process through the literature review method,refering to the existing teaching research results,and combining the actual teaching experience to guide the completion of the teaching design;2.Through the comprehensive use of questionnaire survey method and subject test method,carefully designed Questionnaire on the derivative learning situation of senior three science students and the monotonicity ability test of derivative research function,and obtain the corresponding data;3.Through the interview method,take the students and the front-line backbone teachers as the object,carry out the types of students’ learning difficulties and their causes,etc.4.Analyze data qualitatively and quantitatively through statistical analysis,summarize laws and draw preliminary conclusions.Summarize the survey results and analyze the difficulties of students in the "Application of Derivatives-Monotonicity" from the three levels of knowledge,ability and emotion.The main reasons are: the basic knowledge is not solid enough;the thinking is not flexible enough,and the knowledge transfer ability is poor;learning The method is not clear;the psychological quality of mathematics learning is poor.According to the above situation,the corresponding teaching strategies are put forward as follows:1.Pay attention to the formation process of basic concepts and the explanation of the meaning of the concepts;2.Pay attention to the connection between knowledge and consolidate the basic knowledge of students;3.Pay attention to the training of students’ problem-solving steps and writing norms in the teaching process;4.Pay attention to thinking training and improve the flexibility of using methods;5.Pay attention to the emphasis on mathematical thinking methods,so as to get rid of rote memorization and rote problem solving methods;6.Pay attention to cultivating students’ interest in learning in the teaching process,Enhance students’ self-confidence.