Research On Teaching Design Of Derivative Unit Based On Problem-Driven

The thought method of derivative as the content of calculus has greatly promoted the development of modern mathematics and physics.Since the 20 th century,after several reforms of the syllabus,it has been decided to take the derivative part of calculus as the teaching requirement of high school.The content of the derivative chapter as the finale of the college entrance examination has always been a difficult point for students to break through.On the one hand,students do not know where to start to apply derivative knowledge and other knowledge to solving problems.On the other hand,although they master various problemsolving skills,they do not understand what is derivative,why derivative can be used to judge the monotonicity of function and other essential problems.The ’’ General High School Mathematics Curriculum Standards(2017 Edition)’’ points out that ’’ overall design and implementation of teaching,situation creation and problem design should be conducive to the development of the core literacy of mathematics ’’,and emphasizes the view of the overall teaching of mathematical knowledge.Therefore,based on the unit teaching theory that focuses on knowledge relevance,this paper determines the teaching elements and teaching objectives of derivatives from an overall perspective,and combines the problem-driven theory to form the class teaching design of derivatives to realize the ’’ recreation ’’ of knowledge,hoping to help teachers grasp the teaching content of derivatives as a whole and penetrate the essence of the discipline.Based on the theory of problem-driven and unit teaching design,this study analyzes the current situation of derivative teaching through unit teaching design,classroom record and teacher interview : teachers pay less attention to the connection between class hours and units,the setting of problem situations and problems lacks certain rationality,and teaching is separated from the cultivation of students critical thinking ability.Under the guidance of problem-driven theory,the paper further explores the basic context and thinking methods of the emergence and development of calculus,and re-examines the treatment of derivative limits in high school based on this,so as to clarify the core of derivative teaching in middle school.Through the above research,combined with the characteristics of unit teaching and problemdriven teaching,a problem-driven unit teaching design model is constructed,and a unit teaching design from the perspective of derivative as a case is formed.The author mainly based on the problem-driven teaching theory and the related mathematical history thought contained in the derivative,based on the students existing cognitive structure,the ’’ concept of derivative ’’,’’ the derivative of basic elementary function’’,’’ the four arithmetic rules of derivative ’’ and ’’ the application of derivative in the study of function-the monotonicity of function ’’ four contents of the specific class teaching design,it can answer the students following questions : why should we learn derivative ? Why can derivative judge the monotonicity of function ? What is the essential idea of derivative ? With the help of the above design,we hope to help students grasp the primitive problems in derivative knowledge to understand the essence of concepts,build a more systematic knowledge structure,and also provide some reference for the connection between derivative and university calculus knowledge,so as to further cultivate students critical thinking ability and mathematical core literacy.