Communications of Mathematical Education (한국수학교육학회지시리즈E:수학교육논문집)

Korean Society of Mathematical Education (한국수학교육학회)
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An analysis of justification types for the properties of the identity element: Focusing on elementary school students in grades 3 to 6

항등원의 성질에 관한 정당화 유형 분석: 초등학교 3~6학년을 중심으로

  • Received : 2025.02.18
  • Accepted : 2025.03.12
  • Published : 2025.03.31
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Abstract

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.

본 연구는 초등학교 3~6학년 학생들이 항등원의 성질을 어떻게 정당화하는지를 분석하고, 정당화 유형과 일반화 유형 간의 연관성 및 덧셈, 곱셈에 대한 항등원의 성질을 정당화하는 유형 간의 관계를 탐색하는 것을 목적으로 하였다. 이를 위해 초등학생 939명을 대상으로 자료를 수집하였고, 학생들의 응답을 정당화 유형(오답, 타당하지 않은 정당화, 포괄적인 예를 사용한 정당화, 일반적인 표현을 사용한 정당화)과 일반화 유형(특정한 수, 언어를 사용한 글, 기호를 사용한 식을 활용한 일반화)으로 구분하여 분석하였다. 연구 결과, 학년이 증가할수록 오답 비율은 감소하는 반면, 포괄적인 예를 활용한 정당화 및 일반적인 표현을 사용한 정당화 유형에 해당하는 학생의 비율은 학년이 올라갈수록 증가하는 경향이 있었다. 또한, 다양한 방법으로 항등원의 성질을 일반화할 수 있는 학생일수록 정당화에 성공하는 비율이 높아지는 경향이 있었다. 덧셈에 대한 항등원의 성질과 곱셈에 대한 항등원의 성질에 대한 정당화 방식 간에는 강한 상관관계가 확인되었다. 이러한 결과를 바탕으로, 항등원의 성질에 관한 정당화 활동의 교육적 시사점을 논의하였다.

Keywords

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