A Study Of Junior High School Students’ Conceptual Representation Ability In Mathematics

The Mathematics Curriculum Standards for Compulsory Education(2022 Edition)expresses the core literacy of students to be developed in the mathematics curriculum as "three skills",among which "to express the world in the language of mathematics" emphasizes the important role of mathematical representation in mathematics.Mathematical concepts are the logical starting point of mathematics,and mathematical representations cannot be separated from concrete mathematical concepts.This study takes four mathematical concepts,namely,equation,squared difference formula,circle,and angle,as carriers,and focuses on the current situation and characteristics of seventh grade students’ mathematical concept representation ability and its connection with problem solving.A conceptual representation test was administered to seventh-grade students in Shanghai X Middle School,and the data were analyzed to clarify the relationship between several dimensions of conceptual representation ability and problem-solving performance,and interviews were conducted with students whose conceptual representations were typical and unique.This study focused on the following two research questions:1.What is the current status of middle school students’ ability to represent concepts in mathematics? What are the characteristics?2.How does students’ ability to represent mathematical concepts relate to their problem-solving performance?Through the analysis of students’ test papers and interviews with typical students,the study came to the following conclusions:(1)In terms of richness,7th grade students’ conceptual representations in mathematics were dominated by single representations,and students’ performance on the richness of conceptual representations in the domain of number and algebra was better than their performance on the richness of conceptual representations in the domain of graphing and geometry.In terms of tendency,students’ tendency to represent concepts was closely related to the content areas to which the concepts belonged.In terms of connectedness,students were able to construct a basic network of conceptual representations with rich connections,but the nodes of the mind maps were dominated by single nodes,and some students were able to integrate and classify the written concepts with clear and coherent logic.(2)In general,the richness and connectedness of students’ conceptual representations were positively correlated with their problem-solving performance,but the correlation between the richness and connectedness under each concept and the corresponding problem solving varied slightly depending on the concept.On this basis,the author makes several suggestions for teacher teaching and student learning.When teaching concepts,teachers should deeply understand the advantages and disadvantages of various types of representations and choose reasonable ones,while they should encourage students to generate their own representations.When students learn concepts,they should take the initiative to build a conceptual learning system and establish a solid network of conceptual representations.