Research On High School Function Teaching Based On Model Thinking

The concept of functions is an important basic concept in mathematics courses.With the release of the latest edition of the General Senior High School Mathematics Curriculum Standard(2017 Edition),the teaching of functions has received more and more attention.Functions are the focus of learning,and functions are also the basis for mastering other mathematical knowledge.Model thinking is an important mathematical thought,and it is also one of the six basic ideas proposed by the Standard.Functions are important mathematical models for studying the relationship between variables and variables.Function problems are closely related to actual problems.Combining functions with mathematical models,analyzing the problems that students have when answering questions,and exploring the causes will help students to use Model ideas solve functional problems.Model thinking is an important thinking method to cultivate students' ability to apply mathematics.It first emerged from mathematical modeling competitions and gradually gained more and more attention in primary and secondary education."Compulsory Education Mathematics Curriculum Standards(2011 Edition)" lists "model thinking" as one of the ten "core concepts",and "Ordinary Senior High School Mathematics Curriculum Standards(2017 Edition)" takes model thinking as the six basic mathematical ideas.The application of model thinking to functions is to regard functions as models and the process of exploring functions as the process of model construction,model analysis and model application,and the process of establishing connections between models.The construction of a function model is an abstraction process based on the characteristics of expressions.The definitions of functions are all form definitions(exponential functions,logarithmic functions,trigonometric functions,etc.are functions with a certain form).The analysis of the nature of a function depends on the transformation process of the model.The function is transformed between tables,graphs,and expressions to discover and demonstrate the basic properties of the function.The application of the function is a process of problem analysis and resolution based on the nature of the function.The function teaching process is the process of model construction,understanding and application.This research explores how to infiltrate model ideas into classroom function teaching,so as to effectively improve students' mathematical application ability and reflect the true application value of mathematics.It is a theory that has both theoretical significance and meets the actual needs of mathematics teaching and the needs of current educational teaching.The author made a survey of high school students and teachers.The survey found that students' grasp of model ideas in function learning is not optimistic,and their knowledge of functions is not sufficient.For this reason,in this article,the characteristics of the author's mathematical disciplines,combined with their own teaching practices,discuss the model thinking in high school mathematics teaching and its penetration into function teaching content,and cultivate students' ability to model thinking.The author believes that teachers should first choose appropriate modeling problems in teaching,and then teachers should strengthen students' understanding of model ideas in the classroom.Third,they should strengthen the actual connection between functions and life,and use model ideas.Finally,use information clever Technology to help students understand functional models.