An Exploratory Study of Mathematical Representation and Algebraic Thinking of Elementary School Students
This study provided various representation problems with which to evaluate students’ performance in generalization. The types of representation appropriate for generalization were determined according to the difficulty and characteristics of the representation problems. A total of 423 fifth and sixth grade students underwent generalization tests and interviews, the results of which were subjected to both quantitative and qualitative analysis. The results showed that sixth grade students significantly outperformed fifth grade students in generalization problems. In addition, students performed most favorably in table representation problems, followed by text, graphs, and pictorial representations. The students felt that numeric representation was the most difficult. We found that representation problems adopting tables, graphs, and text are suitable for thinking in the process of generalization problems, variable recognition, and the connection and development of structural relationships. Pictorial and numeric representations were shown to stimulate students to speculate about variable relationships and form rules with which to solve problems. We believe that the results of this study provide a valuable reference for researchers in terms of algebraic thinking and instructional development.