Teaching Research On Functional Concept And Properties In High School Based On Problem Driven

Function is an important mathematical model to describe the movement of things in the real world.The nature of function describes the regularity and invariance of the movement of things.Functions do not simply teach students the concept of functions and their related properties,but use the tools of functions to solve problems and learn the mathematical ideas behind them.Compared with junior middle school,senior middle school functions are more complex and abstract,which has some difficulties and challenges to students’ function learning and teachers’ function teaching.Therefore,it is very important to analyze the teaching difficulties of function concept and nature,find out the reasons and put forward the corresponding teaching strategies.This study first analyzes and combs the knowledge about problem-driven teaching theory and function by means of literature research,and forms its own opinions: problemdriven teaching theory aims to make students "recreate" mathematical knowledge,experience the process of knowledge development,understand the nature of knowledge,develop mathematical thinking ability,and cultivate mathematical thought.This paper analyzes the historical development of function and the teaching material content system to find the core and essence of function concept and nature and integrate it into teaching.Further,this study investigated the obstacles in the functional knowledge learning of the first-year students through the test volume,mainly the weak geometric intuitiveness,weak mathematical abstraction ability,mathematical modeling literacy to be improved and too narrow concept understanding,interviewed the understanding and knowledge of functional concepts and properties of teachers on the front line,to understand the existing difficulties in functional teaching.According to the present situation of teaching,the following teaching strategies are put forward: First,flexible use of teaching materials,changing teaching concepts;Secondly,focus on understanding and learning the core concepts of mathematics,experience and feel the advantages of mathematical abstraction,so that students can experience the abstract process from special to general,and cultivate their abstract generalization ability.Thirdly,in the process of teaching,students are guided to use functional images to describe mathematical problems,and in this process,numerical patterns are combined with ideas to solve problems.This paper analyzes the main points of relevant teaching design.After analyzing the present situation of functional teaching,this research is based on the problem-driven teaching theory,and combines the cognition of functional knowledge in the existing cognitive structure of students as the starting point to design the functional concept and nature of the teaching strategy,which conforms to both the cognitive development characteristics of students and the development of knowledge.In the related teaching of function concept and nature,based on problem-driven theory and inspired by the mathematical history of relevant knowledge,a more comprehensive teaching system is constructed,which will help students understand the essence of function-related knowledge.Finally,a problem-driven functional case study design is formed,which can contribute to students’ understanding of the nature of knowledge through comparative analysis.