A Survey Of Junior High School Students Applying Functional Thinking To Solve Problems

China’s education is in a stage of rapid development,followed by a change in educational goals,for the study of mathematics,not only stay in the mastery of basic knowledge,but also pay attention to the cultivation of mathematical ideas.As one of the important mathematical ideas,the idea of functions runs through the whole process of mathematical learning.As far as junior high school mathematics is concerned,functions are one of the main lines of the teaching process,the key content of the junior high school mathematics curriculum,one of the knowledge that students think is the most difficult to understand,and also the difficult point and hot spot of the proposition of the middle school entrance examination.Therefore,it is of certain significance to investigate and study the current situation of junior high school students applying function ideas to solve problems.After reading and sorting out the literature,it is found that the current research on the application of functional ideas to solve problems is mostly to list typical examples in high school mathematics,there is little research in the junior high school stage,and even less investigation and research on the current situation.Based on this,this thesis mainly uses a variety of research methods to investigate and study the ability level and current situation of junior high school students to apply functional thinking to solve problems,and mainly does the following work:1.On the basis of previous research,a functional thought level analysis framework is established,which is divided into four horizontal dimensions: simple embellishment(level 1),process replication(level 2),structural conformance(level 3),and comprehensive application(level 4).Starting from the special column of the renjiao version of the junior high school mathematics textbook,the functional thought level analysis framework is used to analyze the functional ideological level contained in the three chapters of primary function,quadratic function and inverse proportional function in the textbook,which is intended to investigate the requirements of the curriculum standard and textbook for the application of function thinking to junior high school students to solve problems.The results of the survey and analysis show that the functional ideas contained in the three types of functions in the textbook all contain four horizontal dimensions,of which level two and level three contain the most.It can be seen that the requirements of the curriculum standards and textbooks for the ability of junior high school students to apply the level of functional thinking are to achieve level three-structural conformity.2.Implement questionnaire surveys and interviews to understand the attitude of junior high school students in Sichuan Province A to mathematics learning,their understanding of function ideas,and the penetration of teachers’ implementation of function ideas in classroom teaching.The analysis of questionnaires and teacher interviews found that students and teachers believe that function ideas are very important,but students need to further understand and apply them in the learning process,and teachers need to further analyze and infiltrate in the teaching process;3.Conduct a test paper examination of students,investigate the ability and current situation of junior high school students in Sichuan Province A to apply function thinking to solve problems,and the analysis found that the overall application function thinking problem-solving ability of junior high school students is not high,and the vast majority of students’ ability is at level two,very few have fully reached level three,and fewer students have reached level four.4.Based on the above investigation and research,a six-point teaching strategy for junior high school students to apply function thinking to solve problems is proposed.4.Based on the conclusions of investigation and research,the following teaching strategies are proposed:(1)improve the teacher’s function level and improve their own teaching skills;(2)understand the current situation of students and teach according to their aptitudes;(3)create problem situations and cultivate learning interest;(4)consolidate basic knowledge and infiltrate function ideas;(5)pay attention to the introduction of examples in the teaching of function concepts and cultivate mathematical modeling awareness;(6)attach importance to learning methods and cultivate good problem-solving habits.