A Study On The Representation Level Of "problem-solving Strategies" In Elementary School Mathematics

As an important learning content of elementary mathematics,"problem-solving strategies"play an important role in developing students’ ability of problem-solving and strategy application.The strategy of solving problems can deepen students’ understanding of mathematics and develop their concepts of mathematical analysis,but it also requires students to have a high level of mathematical representation.Good mathematical representation can help students concretize mathematical problems,simplify complex mathematical problems,deepen students’understanding of mathematical problems and improve their mathematical structure.Therefore,it is indispensable to explore the level of mathematical representation of primary school students and effectively improve their level of mathematical representation.In order to accurately describe the level of mathematical representation of pupils in the field of "problem solving strategies",referring to the suggestions of front-line teachers and consulting relevant experts,the level of mathematical representation is divided into four levels.According to the characteristics of knowledge in the field of "problem-solving strategies" and pupils’learning characteristics,the paper constructs a test paper of representation level for sixth-grade students,with 210 students from four classes of Grade 6 in Yangzhou M Primary School as subjects.The main results are as follows:(1)The representation level of the sixth grade students in Yangzhou is different on all kinds of mathematical problems.Generally speaking,most of the sixth grade students are at the representation level of 3;(2)There is no significant difference between male and female students in the representation level of various mathematical problems;(3)There is significant difference between students of different ages in the representation level.According to the research results and interviews,the reasons for the above representation level are analyzed,which are mainly related to the difficulty of different types of mathematical knowledge,teachers’ educational concepts and professional qualities,students’ physical and mental development level and pupils’ learning characteristics.Based on the research results and the needs of teaching practice,some suggestions are put forward for teachers to improve mathematical representation level.Teachers should pay attention to the diversification of representation modes in teaching and teach from the introduction of intuitive representation.With the in-depth attention of teaching content,the intuitive representation mode should be transformed into abstract representation mode,and the combination of multiple representations should be interacted.Finally,they should deal with practical problems in life.Combine them to consolidate ability of abstract representation.