세 자리 수의 불규칙 배열 대상에 대한 초등학교 2학년의 수 세기 분석
Analysis of Second Graders’ Counting an Irregular Arrangement of Three-Digit Objects
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수 세기는 수 개념 및 연산과의 관련성으로 인해 수학 학습에서 기초적이면서도 중요한 위상을 차지한다. 특히 큰수 세기는 수학 학습 초기의 수 개념 도입시 수 세기가 요구하는 일대일 대응이나 기수의 원리 등은 물론 자릿값의이해를 포함하는 구조적 세기라는 점에서 핵심 학습 요소라 할 만하다. 본 연구는 현행 교과서 활동으로 구성되어있지 않아 학생들의 경험이 전무할 것으로 예상되는 큰 수에 대한 수 세기 가능 여부 및 세기 전략을 파악하여 교수학적 시사점을 도출하는 것을 목적으로 한다. 이를 위해 세 자리 수까지 학습하였고 교과서 활동으로서 묶어 세기와뛰어 세기를 경험한 초등학교 2학년 학생 89명을 대상으로 세 자리 수만큼의 대상이 불규칙적으로 배열된 그림에서수 세기 및 세기 방법을 묻는 문항으로 구성된 검사지를 제공하였다. 학생 응답을 정오답률과 사용한 세기 전략 및인지적 특징 측면에서 분석한 결과, 오답률이 매우 높고 십진 원리, 묶어 세기, 1씩 세기, 부분합 전략 등의 사용이확인되었다. 이와 같은 분석 결과에 기초하여 교과서 활동으로서 큰 수 세기 활동을 포함할 필요성을 비롯한 몇 가지 교수학적 시사점을 도출하였다.
Abstract
Counting occupies a fundamental and important position in mathematical learning due to its relation to number concepts and numeral operations. In particular, counting up to large numbers is an essential learning element in that it is structural counting that includes the understanding of place values as well as the one-to-one correspondence and cardinal principles required by counting when introducing number concepts in the early stages of number learning. This study aims to derive didactical implications by investigating the possibility of and the strategies for counting large numbers that is expected to have no students’ experience because it is not composed of current textbook activities. To do this, 89 second-grade elementary school students who learned the three-digit numbers and experienced group-counting and skip-counting as textbook activities were provided with questions asking how many penguins were in a picture where 260 penguins were irregularly arranged and how to count. As a result of analyzing students’ responses in terms of the correct answer rate, the strategy used, and their cognitive characteristics, the incorrect answer rate was very high, and the use of decimal principles, group-counting, counting by one, and partial sum strategies were confirmed. Based on these analysis results, several didactical implications were derived, including the need to include counting up to large numbers as textbook activities.
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