유아들의 비형식적 수학과 형식적 수학의 만남: 소집단 프로젝트 과정의 수학적 의미 구성 사례 분석
Children's Informal Mathematics Encounters Formal Mathematics: An Analysis of Mathematical Discourse During Small Group Project Work
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초록
본 논문은 사회적 활동이며 의사소통으로서 수학이라는 관점에서 소집단의 ‘동전 세기’ 프로젝트의 담화 분석을 통해 어떻게 유아들의 비형식적 수세계가 형식적 수세계와 만나며 다양한 수학적 의미를 구성해 나가는 지를 살펴보고자 한 것이다. 다양한 단위의 동전으로 이루어진 전체 동전의 합을 알아내고자 하는 문제해결 상황에서, 유아들은 교사의 지원을 받아 협력 작업을 하면서 단위별 동전의 합과 전체 동전의 합을 셈하고, 그 수량을 숫자 표기로 전환시켰다. 이 과정에서, 유아들은 발화의 참조적 관점을 조율하면서 일상적 언어의 수학적 의미를 구성하였고, 집단 또래의 책략을 재해석하고 교류하면서 수세기 책략을 습득하였으며, 숫자 표기를 비관례적 방식으로 재고안해 내면서 숫자 표기체계에 대한 이해를 획득할 수 있었다. 결론에서는 교사와 유아 또래가 수학담화 구성에 어떻게 기여 하였는지를 살펴보고 교육적 함의를 제시하였다.
Abstract
This study examined the process of mathematical meaning construction from the perspective of mathematics as a social and communicative activity, by performing a discourse analysis on the data gathered during the small group project, called “counting coins.” Working toward the goal of calculating the total sum of coins with various denominations, 5-year-old children collaborated to find out the sums for each denomination and to represent the sum with numbers, supported by the classroom teacher. During this process, children could, first, construct mathematical meanings for plain vocabulary by coordinating referential perspectives of utterances, secondly, they could learn how to calculate the sum by transforming group strategies into their own, and finally, gain an understanding of the number notation system by re-inventing their own unconventional notations. In conclusion, how the teacher and the children, respectively and collaboratively, contributed to the construction of mathematical discourse was discussed, and implications for classroom teaching were also offered.
참고문헌 (39)
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