| Mathematical thought is the soul of mathematics,hidden in the application process of mathematical knowledge,is the further abstraction and generalization of specific knowledge,is the bridge of knowledge into ability,is the key to solve problems.The thought of naturalization is one of the most important ideas in mathematics,and it is also one of the mathematical ideas reflected in the solving process of many function problems.Therefore,the function problem-solving ability of high school students largely depends on the high and low ability of students to use naturalization thought to solve problems.Therefore,this paper focuses on the investigation and research of high school students’ function problem-solving ability based on naturalization thought.Function is an important content of high school mathematics course,almost runs through the whole process of high school mathematics teaching,is the core knowledge point of students to learn.In order to better improve the solving ability of high school students’ function-related problems,this paper focuses on the analysis of the types of functional problem-solving ability based on the naturalization thought,and analyzes the specific performance of five types of problem-solving ability with typical examples.Based on this,a reasonable research questionnaire and test paper are designed to carry out a survey and research on the current situation of high school students’ functional problem-solving ability based on the naturalization thought.Through the analysis of the survey results,some suggestions are given to improve the function problem-solving ability of senior high school students.The full text mainly includes the following four parts: the first part is the introduction of this paper,which mainly introduces the research status of "thought of transformation","function problem solving ability" and "function problem solving ability based on thought of transformation",and explains the research significance,methods and theoretical basis of this paper.The second part is the second chapter of this paper.According to the characteristics of solving problems with naturalization thought summarized by scholar Yuan Shouyi,the method of naturalization was summarized,and then the problem-solving ability based on naturalization thought was divided into five types: the ability of combining number and form,the ability of transforming function and equation,the ability of reverse thinking,the ability of classification and discussion and the ability of construction.The concrete performance of these five kinds of abilities in solving problems with function was analyzed with examples.The third part is the third chapter of this paper.On the basis of the previous research content,combined with Du Wenping and Luo Zengru’s "Level division of mathematical problem solving",the evaluation framework of function problem solving ability in this paper is developed.With the students of senior high school in Ying Kou City as the research object,questionnaires and test papers are distributed to investigate the current situation of function problem solving ability of high school students based on the thoughts of transformation.SPSS was used for statistical analysis of the data.The fourth part is the fourth chapter of this paper.Aiming at the current situation of high school students’ problem-solving ability,it puts forward strategies from four aspects: basic knowledge,transformation consciousness,rigor of transformation process and broadness of transformation ideas,hoping to give teachers some practical suggestions on function teaching in high school. |
