The Research On High School Calculus Teaching From The Problem-driven Perspective

The calculus is an important foundation of modern mathematics,and as an important research tool in the field of multiple applications in physics,astronomy,economics,and other areas of the science.Calculus contains abundant mathematical ideas and methods,Its "creative" characteristics provide students with new ideas and methods,understand functions and other knowledge,and help students form innovative thinking ability.Based on that,many countries offer calculus courses in high school,which is regarded as the connection between primary mathematics and higher mathematics.High school calculus teaching in China has been innovating,and the new curriculum standard points out that high school calculus is an important content of cultivating students' subject core literacy.However,what is the current situation of calculus teaching in senior high school? What kind of classroom should be created to drive Calculus Teaching in senior high school? It has become an urgent problem to be solved in promoting Calculus Teaching in senior high school.On the basis of literature research,this paper discusses the above problems with the help of questionnaire survey,interview analysis and other research methods.Through the analysis of the empirical research results of calculus in senior high school,it can be found that there are some problems in Calculus Teaching in senior high school,such as teachers pay more attention to the explanation of calculus calculation and pay less attention to the teaching of calculus concepts and ideological methods,which leads to students' learning of calculus in senior high school mainly based on memory and lack of understanding of the essence of calculus.Therefore,based on the current situation of calculus teaching in senior high school,combined with the problem driven theory,this paper uses the teaching ideas of "why","what" and "what's the use" to design the corresponding teaching problems,and carries out case teaching from the perspective of problem driven through practical research to explore the rationality of teaching thinking.The case teaching practice research is divided into two stages.The first stage is to design and implement the derivative concept teaching practice research from the problem driven perspective,carry out questionnaire and interview research on students according to the teaching effect,analyze the teaching feedback,and understand the teaching effect of this teaching practice research.Then,it puts forward optimization strategies for the deficiencies of the first stage of teaching practice research,so as to improve the teaching design and teaching practice research process in the teaching practice research.In the second stage,design and implement the practical research on the teaching of geometric meaning of derivative from the perspective of problem driven.According to the teaching effect,carry out questionnaire and interview survey and Research on students again,and analyze the teaching feedback.Combined with the results of two teaching practices,this paper summarizes the impact of problem driven theory on Calculus Teaching in senior high school.Through the above research,the conclusions of this study are as follows:1.Studying the current situation of calculus teaching in senior high school from the perspective of students and teachers,it is found that many students are difficult to deeply understand the essence of knowledge,lack of calculus background knowledge,weak application ability and so on.However,fewer teachers use problems to guide students' thinking,pay attention to the concept teaching of calculus and infiltrate the mathematical cultural knowledge of calculus.Many teachers pay more attention to the explanation of exercises,ignore the concept and ideological methods of calculus,and are not good at using information technology to assist calculus teaching.2.Through teaching case practice research,it is found that,the problems that effectively drive Calculus Teaching in senior high school have the characteristics of historical situation,realistic situation,humanity,interest,intuition,inspiration and scientific rationality.3.The mathematics classroom carried out from a problem-driven perspective emphasizes the connection between knowledge,which helps to reveal the essence of high school calculus knowledge,and students experience innovation in the process of solving "why","what" and "what's the use" problems Mathematics,discovering mathematics and the fun of using mathematics are helpful for students to learn and master corresponding knowledge from a holistic perspective,improve their core mathematical literacy,and cultivate the quality of seeking novelty,truth-seeking and realistic-seeking.According to the research conclusion,this paper puts forward corresponding thinking for Calculus Teaching in senior high school,in order to promote Calculus Teaching in senior high school from the perspective of problem driven.