An Investigation On The Metacognitive Level And Open Problem Solving Of Mathematics In Senior High School Students-a Case Study Of Senior High School Students In Xining City

Metacognition is implemented in the whole learning process of students,and it is the advanced cognitive skills required by high school students.Mathematical metacognition is the cognition and monitoring of mathematical cognitive activities under the guidance of mathematical concepts and in the process of mathematical thinking.It plays an important role in mathematical learning.The open question itself has the characteristics of divergence,innovation and inquiry,and plays an irreplaceable role in cultivating students' abilities of experiment and inquiry.Over the years,the cultivation of students' mathematical metacognition level has been widely paid attention to,but the research on mathematical metacognition level and mathematical open problem solving is far less than that on mathematical metacognition level and mathematical closed problem solving.Meanwhile,the research objects mainly focus on the primary and middle school grades,but lack of high school grades.Based on the review of the existing mathematical metacognition level and literature,and based on the open mathematics questions in Xining city part of the three high school high school students as subjects,the high school mathematics metacognition level questionnaire and senior high school students mathematics open-ended problem solving test as a survey tool,designed to understand the Xining region high school mathematics metacognition level and present situation of mathematics open-ended problem solving,then explore the relationship between the two,and finally put forward the corresponding training suggestions to the perspectives of teachers,students and parents.The data processing,correlation analysis and linear regression analysis in this paper mainly use SPSS and MATLAB software.The conclusions of the study include the following:(1)The metacognitive scores of senior high school students are generally in the middle level;Grade has a significant impact on the mathematical metacognition level of senior high school students.From grade one to grade three,the mathematical metacognition level of senior high school students shows an increasing trend year by year.The mathematical metacognition level of senior two students is significantly improved compared with that of senior one student,and gradually reaches stability in grade three.Grade has significant influence on knowledge dimension and monitoring dimension of metacognitive knowledge,but has no significant influence on metacognitive experience.Gender has no significant effect on the metacognitive level of high school students.(2)The scores of open problems solving in mathematics of senior high school students are generally at a low level;Grade of high school students have a significant effect mathematical open-ended problem-solving ability,the open problem-solving ability of senior three students is higher than that of senior one and senior two students.Grade has significant influence on the open problem solving dimension of mathematical strategy and open problem solving dimension of mathematical conclusion,but has no significant influence on the open problem solving dimension of mathematical condition and open problem solving dimension of mathematical synthesis;Gender has no significant effect on open problem solving ability of high school students.(3)The degree of correlation between mathematical metacognition and mathematical open problem solving is as follows: mathematical condition open problem solving(29)mathematical comprehensive open problem solving(29)mathematical strategy open problem solving(29)mathematical conclusion open problem solving;The degree of correlation between the three dimensions of mathematical metacognitive and mathematical open problem solving is: mathematical metacognitive monitoring(29)mathematical metacognitive knowledge(29)mathematical metacognitive experience;There is a positive correlation between mathematical open problem solving ability and mathematical metacognition level in the range of quantitative evaluation.Therefore,the mathematical metacognition level of senior high school students has a certain influence on the mathematical open problem-solving ability.