A Survey On The Application Of Metacognition In The Process Of Solving Function Problems Among High School Student

Metacognition is an important factor affecting mathematical problem solving,which runs through the whole problem solving process.Function is an important and difficult subject in high school mathematics.As the main line to carry out the compulsory,optional and elective courses in high school,it has an extremely important position.In order to improve students’ function problem solving process,effectively implement the fundamental task of moral cultivation and cultivate students’ innovation ability,we need to start from the key factors affecting the function problem solving process and have a target.Metacognition has plasticity.Training students’ metacognition and optimizing its function problem solving process can achieve the purpose of improving students’ mathematics achievement and mathematics teaching quality.Focusing on the field of functions in senior high school,this study explores the application status of metacognition in the process of solving function problems of senior high school students from the perspective of quantitative research,and uses vocal thinking to deeply explore the role of metacognition in the process of solving function problems from a qualitative perspective,aiming at clarifying the role of metacognition in the process of solving function problems and enriching relevant researches on metacognition and mathematical problem solving.Moreover,it provides teaching guidance on function problem solving for high school mathematics teachers.The research questions include:(1)How about the application of metacognition in the process of functional problem solving?(2)What role does metacognition play in the process of solving functional problems of senior high school students?(3)What are the metacognitive application strategies in the process of functional problem solving for senior one students?In order to solve research question 1,166 survey data were statistically analyzed from the perspectives of overall metacognition application,sub-dimension metacognition knowledge,metacognition experience and metacognition monitoring and monitoring,using questionnaire survey method and statistical analysis method,to comprehensively explore the application status of metacognition in the process of functional problem solving of senior high school students.In order to solve the second research problem,the method of thinking out loud is adopted based on three metacognitive dimensions: metacognitive knowledge,metacognitive experience and metacognitive monitoring and four stages of functional problem solving process: Exploration and understanding,representation and formation,planning and execution,monitoring and reflection,combined with the analysis of oral record,movement and expression of six subjects,from the qualitative perspective to explore the role of metacognition of senior high school students in the process of functional problem solving,and analyze the reasons,to provide the basis for writing the conclusion.Research conclusions:(1)The overall metacognitive application,metacognitive knowledge,metacognitive experience and metacognitive monitoring of senior high school students in the process of functional problem solving are at an average level,which needs to be further improved.(2)Students’ functional problem solving thinking path has three characteristics.Firstly,students’ thinking of functional problem solving is sequential;Secondly,solid basic knowledge and excellent problem-solving skills are the basis for students to solve function problems;Thirdly,students lack monitoring and reflection on the whole,and do not dig deeply enough for problems.(3)Students’ metacognition plays an important role in the process of functional problem solving.Firstly,metacognitive knowledge is the basis for students to solve functional problems successfully,and also the basis for the whole process of solving functional problems.Second,students lack metacognitive experience in unfamiliar problems.Metacognitive experience is the internal driving force for the whole functional problem solving process.Thirdly,the application of metacognitive monitoring is not enough,which is the key to solve the function problem.Teaching strategies:(1)Pay attention to reasonable infiltration guidance to help master metacognitive knowledge;(2)Focus on stimulating emotional factors to fully mobilize metacognitive experience;(3)Adopt metacognitive questioning strategy to effectively improve metacognitive monitoring.