A Study On Meta-Cognitive Level Of Mathematical Problem Solving For Sophomore Students

Mathematical meta-cognition is students’ understanding and monitoring of mathematical cognitive activities in the process of mathematics learning and problem solving.The curriculum standard of mathematics in senior high school points out that teaching should take improving students’ problem-solving ability as one of the basic goals.Moreover,many studies show that mathematical problem solving is a process of cognitive and meta-cognitive interaction and continuous influence.Therefore,studying students’ meta-cognitive level of problem solving has certain theoretical and practical significance for teachers to guide students’ mathematics learning and carry out mathematics teaching activities.The research adopts the method of investigation and teaching experiment,and uses the Questionnaire of High School students’ meta-cognition level compiled by Wang Guangming’s team to formulate the Questionnaire of high school students’ meta-cognition level,so as to investigate the development of high school students’ meta-cognition level.Based on the development characteristics of students’ meta-cognition level,this paper adopts the three dimensions of mathematical meta-cognition level as an intervention means,and takes high school students learning elliptic knowledge as an example to carry out the teaching experiment of mathematical meta-cognition development in problem solving.Through the evaluation of teaching experiment results,the paper analyzes whether students’ meta-cognition level has been developed.Specifically,there are the following research conclusions:(1)Uneven development of students’ meta-cognitive level of mathematics.Specifically,students can face up to their own learning ability,but lack cognition of strategies when solving math problems,hold a negative attitude toward the cognitive experience of math learning,and lack of monitoring ability such as planning,adjustment and reflection of learning.(2)The teaching experiment in which problem-solving process integrates meta-cognitive level development can improve students’ meta-cognitive level of mathematics:the knowledge level and experience level of mathematical meta-cognition are significantly improved,and the monitoring level is improved to some extent.Specifically,the students have a clearer understanding of their own mathematics learning and are more adept at solving mathematical problems.In this process,students get the perceptual experience,stimulate the curiosity of exploration,cultivate the awareness of monitoring and adjustment,and thus promote the formation and development of the overall level of mathematical meta-cognition.Based on this,some suggestions for further teaching are given:(1)Organize interesting experiment teaching to improve students’ meta-cognitive experience level;(2)Pay attention to the process of knowledge generation and improve students’ meta-cognitive knowledge level;(3)Guide students to explore independently and improve students’ meta-cognitive monitoring level;(4)Develop students’ overall level of meta-cognition and improve their problem-solving ability.