Research On Teaching Design Of "Derivativeand Its Application" Based On Mathematical Modeling Literacy

With the rapid development of modern society,mathematics plays a more and more important role,especially in social science.The application of mathematics has already penetrated into modern society and every field of people's daily life.The social demand for mathematics turns to the use of mathematical knowledge and mathematical thinking to solve the actual problems in social life in order to achieve practical economic and social benefits.Mathematics is derived from the abstract of the real world,and mathematical modeling has built the bridge between mathematics and the outside world,which is an important form of mathematical application.In 2017,our country formally promulgated "Ordinary Senior High School Mathematics Curriculum Standard",and the development of students' core literacy of mathematics has become the focal point of the present new mathematics curriculum reform.Mathematics modeling literacy is regarded as one of the six core mathematics literacy in senior high school.Derivative is one of the core contents of calculus,is the basic concept of modern mathematics and the basic tool to study the nature of function.The application of derivative is also very rich in real life.It is of great significance to connect the content of "derivative and its application" with mathematical modeling literacy to improve students' mathematical modeling ability and develop mathematical modeling literacy.This paper systematically combs the current situation of mathematical modeling and mathematical modeling literacy and the related research of "derivative and its application" teaching,and puts forward the analytical framework of mathematical modeling literacy in senior high school.Then,based on the analysis framework of mathematical modeling literacy in senior high school,this paper analyzes "derivative and its application",and then puts forward the instructional design principles and instructional design strategies of "derivative and its application" based on mathematical modeling literacy.Finally,based on these instructional design principles and strategies,the author chooses two representative contents of the part of "derivative and its application" for teaching design.Through the research,it is found that mathematical modeling literacy is composed of three aspects: the correct value concept,the necessary qualities and the key ability of mathematical modeling.Referring to the Curriculum Standard,the paper established analysis framework for the senior high school mathematical modeling literacy from the four dimensions of situation and problems,knowledge and skills,thinking and expression,communication and reflection.It is concluded that students' mathematical modeling literacy can be developed through the teaching of "derivative and its application".It also puts forward four instructional design principles for "derivative and its application" based on mathematical modeling literacy,including mathematical principle,activity principle,creative principle and enlightening principle,as well as teaching strategies.Creating life-like circumstances,putting forward enlightening questions,creating the opportunity of the development of the modeling literacy;adjust the learning mentality,build up the confidence of modeling,provide the guarantee of the development of modeling literacy;clarify the knowledge context,establish the relationship between new and old knowledge,and lay the foundation for the development of modeling literacy;promote exploration-style learning,cultivate the ability of autonomous learning,and open up a way to develop modeling literacy.Finally,it designed the two specific teaching contents of the concept of derivative and the examples of optimization in life.