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

다국어 초록 (Multilingual 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.

국문 초록 (Abstract)

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.

참고문헌 (Reference)

1 조희연, "한국과 프랑스 부모-유아 간 놀이 속에 나타난 수 표기법 비교" 한국영유아교원교육학회 15 (15): 277-298, 2011

2 이정욱, "유치원 교사의 발화에 나타난 수학교육 내용 분석" 한국유아교육학회 29 (29): 281-300, 2009

3 홍혜경, "유아의 수표상능력 발달에 대한 분석과 교육적 활용" 19 (19): 95-118, 1999

4 Hughes, M, "어린이와 수" 창지사 1992

5 이종희, "수학적 의사소통의 관점에 따른 수학 수업" 5 (5): 69-86, 2001

6 오제연, "수어림하기 활동이 유아의 수세기와 수표상에 미치는 영향" 한국열린유아교육학회 9 (9): 1-21, 2004

7 오문자, "사회적 차원의 인지 행위로서 유아 학급담화" 한국열린유아교육학회 16 (16): 129-156, 2011

8 나귀옥, "만 4, 5세 유아의 수학적 표상활동이 비형식적 더하기 및 빼기에 미치는 영향" 미래유아교육학회 9 (9): 39-57, 2002

9 오문자, "레지오 알아가기:한국 현장에서 레지오 교육의 재구성" 정민사 2010

10 O'Connor,M, "“Can any fraction be turned into a decimal?”: A case study of a mathematical group discussion" 46 : 143-185, 2001

11 Sfard,A, "Two metaphors in learning mathematics : Acquition metaphor and participation metaphor" 27 (27): 4-13, 1998

12 Carpenter, T, "Thinking mathematically: Integrating arithmetic and algebra in elementary school" Heinemann 2003

13 Sfard,A, "There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematics" 46 : 13-57, 2001

14 Walshaw, M, "The teacher's role in classroom discourse: A review of recent research into mathematics classrooms" 78 (78): 516-551, 2008

15 Forman, E. A, "The multiple voices of a mathematical classroom community" 46 : 115-142, 2001

16 Yackel, E, "The interactive constitution of mathemtatical meaning in one second grade classroom: An illustrative example" 17 (17): 469-488, 1999

17 Rogoff,B, "The cultural nature of human development" Oxford University Press 2003

18 Wertsch, J. W, "The concept of internalization in Vygotsky's account of the genesis of higher mental functions" Cambridge University Press 162-179, 1985

19 Bakhtin,M.M, "Speech genres and other late essays" University of Texas Press 1986

20 Issac, E. A, "References in conversation between experts and novices" 116 (116): 26-37, 1987

21 Ford, J, "Redefining disciplinary learning" 30 : 1-34, 2006

22 National Council of Teachers of Mathematics, "Principles and standards for school mathematics" NCTM 2000

23 Vygotsky,L.S, "Mind in society" Harvard University Press 1978

24 Granott, N, "Microdevelopment: a process-oriented perspective for studying development and learning" Cambridge University Press 1-28, 2002

25 Richards,J, "Mathematical discussion" Kluwer 13-51, 1991

26 Zack, V, "Making mathematical meaning through dialogue: “Once you think of it, the Z minus three seems pretty weird.”" 46 : 229-271, 2001

27 Goos,M, "Learning mathematics in a classroom community of inquiry" 35 (35): 258-291, 2004

28 Kieran, C, "Learning discourse: Sociocultural approaches to research in mathematics education" 46 : 1-12, 2001

29 Rommetveit,R, "Language acquisition as increasing linguistic structuring of experience and symbolic behavior control" University of Cambridge Press 183-235, 1985

30 Wiegel,H.G, "Kindergarten students' organization of counting in joint counting task and the emergence of cooperation" 29 (29): 1-17, 1998

31 Cobb, P., "Discourses, mathematical thinking, and classroom practice" Oxford University Press 91-119, 1993

32 Resnick, L., "Discourse, tools and reasoning" Springer-Verlag 1-21, 1997

33 Bloome, D., "Discourse analysis and the study of classroom language and literacy events: A microethnographic perspective" Lawrence Erlbaum Associates, Inc 2005

34 Mercer, N, "Dialogue and the development of children's thinking: A sociocultural approach" Routeledge 2007

35 Shotter,J, "Cultural politics of everyday life: Social constructionism, rhetoric, and knowing of the third kind" University of Toronto Press 1993

36 Bruner,J, "Child's talk.: Learning how to use language" Norton and company 1983

37 O'Connor, M, "Aligning academic task and participation status through revoicing: Analysis of a classroom discourse strategy" 24 (24): 318-335, 1993

38 Wertsch,J.W, "Adult-child interaction as a source of self-regulation in children" Academic Press 1985

39 Wertsch, J. W, "A sociocultural approach to socially shared cognition" the American Psychological Association 85-100, 1991