초등수학 영재의 문제설정 단계와 사고과정 분석: 성냥개비 과제에 대한 사례분석을 중심으로 = Analysis of thinking process and steps in problem posing of the mathematically gifted children

다국어 초록 (Multilingual Abstract)

The purpose of this study is to find how the mathematically gifted children pose difficult problems and articulate the characteristics of their thinking process in problem posing. The following research topic is established to be investigated: Through what steps of thinking process do the mathematically gifted children pose problems? To obtain answer to this question, we surveyed 4 mathematically gifted students from the Gifted Science Education Center of Pusan National University in Busan. Matchstick problems are carefully chosen or developed according to their level of academic performance, in the ways of creating problems, classification of mathematics, and degree of ill-structuredness of initial circumstance for problem posing. 4 subjects are asked to pose difficult problems from 'matchstick problem tasks` in thinking aloud method for 45 minutes each (2 times for 2 subjects, 1 time for other 2 subjects) and all their performance were videotaped. The results were investigated by testers and two educational psychology Ph.D`s. Researchers analyzed the protocols focused on the posed problems. Our main results of research topic are described as follows. The mathematically gifted children pose problems through thinking steps and process shown as below 1) Exploration (understanding of the situation, imaging), 2) Planning(idea dedication, plan deployment, plan expansion) 3) Temporary problem posing, 4) Examination(problem solving, reconstruction).

참고문헌 (Reference)

1 김판수, "초등수학영재의 문제설정 과정분석" 2003

2 하주현, "창의적 인성의 관계 교육심리연구 17" 17 : 2003

3 김정효, "창의적 문제해결력 중심의 수학 교육과정 개발 및 적용 초등학교수준을 중심으로" 4 (4): 2000

4 전윤식, "창의성 교육의 새로운 접근: 문제찾기" 한국교육학회 41 (41): 10-238, 2003

5 김정섭, "창의성 교육을 위한 패러다임의 전환:문제 해결에서 문제 찾기로" 2002

6 이대현, "수학교육에서 직관적 모델에 관한 연구" 11 (11): 2001

7 임문규, "수학교육에서 문제설정과 문제해결의 관련에 관한 연구" 대한수학교육학회 1992

8 주정언, "수학 문제 만들기 학습이 문제 발견 능력에 미치는 영향" 2002

9 박학규, "물리문제 해결과정에서 중학생들의 사고과정의 특성 분석" 1993

10 은희철, "문제에 바탕을 둔 학습" 1998

11 정지호, "문제설정의 교수-학습에 관하여" 31 (31): 1992

12 이석희, "문제설정 방법이 문제해결력과 창의력에 미치는 효과 분석" 1996

13 La Valeur de la Science, "과학의 가치" Poincaré 단대출판부 19051983

14 강인애, "^문제중심학습또 하나의 구성주의적 교수-학습 모형 구성주의 교육학" 교육과학사 1998

15 Leung, "The Relation of Mathematical Knowledge and Creative Thinking to the Mathematical Problem Posing of Prospective Elementary School Teachers on Tasks Differing in Numerical Information Content University of Pittsburgh The Development of Fifth-grade Children's Problem-posing Abilities Educational Studies in Mathematics" Unpublished Doctoral Dissertation 34 : 19931997

16 A, "The Psychology of Mathematical Abilities in School Children" The Univ of Chicago Press 1976

17 Hadamard,J, "The Psychology of Invention in the Mathematical Field" Dover Publications 1954

18 Brugman,G.M, "The Discovery and Formulation of Problems" 27 : 1995

19 Hoffman, "The Dialectics of Fiftedness" -95, 1995

20 Sheffield,L.J, "The Development of Gifted and Talented Mathematics Students and National Council of Teachers of Mathematics Standard" the national research center on the gifted and talented : 1994

21 English,L.D, "The Development of Fifth-grade Children's Problem-posing Abilities" 34 : 1997

22 Harcourt Brace, "The Art of Thought" 19621994

23 Wakefield, "Some Implications for Art Education" 1985

24 Haylock,D.E, "Recognizing Mathematical Creativity in Schoolchildren" no : 1997

25 Simon,M.A, "Prospective Elementary Teachers' Knowledge of Division" 24 : 1993

26 On Analyzing Problem Posing, "Proceedings of the Seventeenth Annual Meeting of the International Group for the Psychology of Mathematics Education" (hda) : 1993

27 Dillon,J.T, "Problem Finding and Solving" 16 : 1982

28 김용진, "PBL의 이론과 실제" 12 (12): 2000

29 Silver,E.A, "On Mathematical Problem Posing" 14 : 1994

30 "National Council of Teachers Mathematics Principles and Standards for School Mathematics" 2000

31 Silver, "Mathematics Problem Posing and Problem Solving by Middle School Students Paper Presented at the Annual Meeting of the American Educational Research Association The Development of Fifth-grade Children's Problem-posing Abilities Educational Studies in Mathematics" 19931997

32 2nd ed, "How to Solve It A New Aspect of Mathematical Method" 19571994

33 Silver,E.A, "Fostering Creative through Instruction Rich in Mathematical Problem Solving and Problem Posing" 29 (29): 1997

34 Ramirez,V.E, "Finding the Right Problem" 3 : 2002

35 Schoenfeld, "Episodes and Executive Decisions in Mathematical Problem Solving Acquisition of Mathematics Concepts and Processes" 1980

36 Van den Heuvel-Panhuizen, "Easy and Difficult Problems on Percentage For the Learning of Mathematics" 15 (15): 1995

37 "Discovery-oriented Behavior and Originality of Creative Products A Study with Artists Journal of Personality and Social Psychology" 1971

38 Okuda, "Creativity and the Finding and Solving of Real-world Problems Journal of Psychoeducational Assesment" 1991

39 Silver,E.A, "Children's Problem Posing within Formal and Informal Contexts" 29 (29): 1998

40 English, "Children's Problem Posing and Problem-solving Preferences' in J Research in Early Number Learning Australian Association of Mathematics Teachers" 1996

41 Larkin, "A Research Methodology for Studying How People Think" 1984

42 "A New Perspective on Talented Mathematicians Educational Studies in Mathematics" 1986

43 John Wiley, "A Longitudinal Study of Problem-finding in Art" 1976

44 A, "A Key to Creative Productivity Investigating Creativity in Youth" Hampton Press 1999

45 Haylock,D.E, "A Framework for Assessing Mathematical Creativity in Schoolchildren" 18 : 1987