김리나 Kim Leena
DOI:10.7468/jksmee.2025.39.1.19 JANT Vol.39(No.1) 19-40, 2025
Keyword:
The identity element is a fundamental component of an operation’s structure, and the process of justifying its properties is closely linked to students' logical and critical thinking. This study examines how elementary school students in grades 3 to 6 justify the properties of the identity element, explores the relationship between justification types and generalization types, and investigates the connection between justification methods for the identity elements in addition and multiplication. To address these objectives, a survey was conducted with 939 elementary school students, and their responses were classified into justification types (incorrect answers, invalid justifications, justifications using representative examples, and justifications using general expressions) and generalization types (generalization using specific numbers, written language, and symbolic expressions). The results indicate that as grade level increased, the proportion of incorrect answers decreased, while the proportion of students employing representative examples and general expressions in their justifications increased. Notably, more students justified using representative examples than general expressions. Furthermore, students who demonstrated the ability to generalize the identity element’s properties in multiple ways exhibited a higher success rate in justification. A strong correlation was found between the justification methods for the identity element in addition and those for the identity element in multiplication. Based on these findings, this study discusses the educational implications of instructional activities related to justifying the properties of the identity element.