창의성 신장을 위한 초등수학 과제의 유형 = Mathematical Task Types to Enhance Creativity

다국어 초록 (Multilingual Abstract)

The purpose of this research was to analyze mathematical task types to enhance creativity. Creativity is increasingly important in every field of disciplines and industries. To be excel in the 21st century, students need to have habits to think creatively in mathematics learning. The method of the research was to collect the previous research and papers concerning creativity and mathematics. To search the materials, the researcher used the search engines such as the GIL and the KISTI. The mathematical task types to enhance creativity were categorized 16 different types according to their forms and characteristics. The types of tasks include (1) requiring various strategies, (2) requiring preferences on strategies, (3) making word problems, (4) making parallel problems, (5) requiring transforming problems, (6) finding patterns and making generalization, (7) using open-ended problems, (8) asking intuition for final answers, (9) asking patterns and generalization (10) requiring role plays, (11) using literature, (12) using mathematical puzzles and games, (13) using various materials, (14) breaking patterned thinking, (15) integrating among disciplines, and (16) encouraging to change our lives. To enhance students` creativity in mathematics teaching and learning, the researcher recommended the followings: reshaping perspectives toward teaching and learning, developing and providing creativity-rich tasks, applying every day life, using open-ended tasks, using various types of tasks, having assessment ability, changing assessment system, and showing and doing creative thinking and behaviors of teachers and parents.

참고문헌 (Reference)

1 남승인, "초등학교에서 창의성 신장을 위한 교수학습 방안" 교학사 2010

2 교육과학기술부, "초등학교수학교과서(6-1)" 두산동아 2011

3 강완, "초등수학교육론" 경문사 2009

4 송정환, "초등수학 게임 자료. 한국초등수학교육연구회 2008년 연수자료집" 한국초등수학교육연구회 2008

5 한헌조, "초등 창의사고력 수학 팩토" 매스티안 2007

6 우종옥, "창의적 문제해결을 키워라" 대교출판사 2008

7 삼성수학연구소, "창의영재 수학퍼즐" 삼성출판사 2008

8 박배훈, "창의성 신장을 위한 새로운 수학교육 평가 방안에 관한 연구" 대한수학교육학회 5 (5): 1-15, 2003

9 조석희, "창의성 계발을 위한 수학영재 교육방안" 1-21, 2003

10 박만구, "참여수학을 통한 수학교육 활성화를 위한 모델 개발" 한국학교수학회 10 (10): 557-571, 2007

11 황농문, "인생을 바꾸는 몰입" 랜덤하우스 2008

12 김영세, "이노베이터:트렌드를 창조하는 자" 랜덤하우스코리아 2005

13 홍하상, "이건희,세계 인재를 구하다" 북폴리오 2006

14 박교식, "우리나라 초등학교 수학 교수학습에서 볼 수 있는 몇 가지 특징" 6 (6): 99-113, 1996

15 Polya.G, "어떻게 문제를 풀 것인가" 천재교육 1986

16 김부윤, "수학적 창의성에 대한 관점 연구" 한국수학교육학회 46 (46): 293-302, 2007

17 박성선, "수학적 창의성 신장을 위한 탐구학습에 관한 소고" 6 (6): 65-74, 2002

18 한정민, "수학적 창의성 관점에서 본 교사의 발문 분석" 한국초등수학교육학회 14 (14): 865-884, 2010

19 박만구, "수학교육에서 창의성의 개념 및 신장 방안" 한국수학교육학회 23 (23): 803-822, 2009

20 황우형, "수학교육과 수학적 창의성" 20 (20): 561-574, 2006

21 남승인, "수학 창의성 어떻게 기를 것인가? 경북창의성교육연구회 발표 원고"

22 배종수, "수학 영재선발 문항분석 및 문항개발의 개선 방안" 38 : 51-66, 2007

23 김영관, "성냥개비 퍼즐"

24 Csikszentmihalyi,M, "몰입의 즐거움" 해냄 1999

25 정경혜, "드라마 활동이 분수의 개념 이해에 미치는 영향" 서울교육대학교 2010

26 김연수, "내 아이의 창의력을 깨워 주는 종이접기" 교학사 2005

27 Poincare, H, "과학의 방법" 단국대학교 출판부 1982

28 이상범, "과학영재교육센터 학생선발문항 분석 및 선발 방법에 대한 제언" 19 (19): 604-621, 1999

29 교육과학기술부, "개정 2007 수학과 교육과정" 교육과학기술부 2007

30 베르베르, 베르나르, "개미2" 열린책들 1993

31 Cropley, A, "Using assessment to foster creativity, In Creativity: A handbook for teachers" World Scientific 209-230, 2007

32 Jensen,L,R, "The relationships among mathematical creativity, numerical aptitude and mathematical achievement" University of Texas at Austin 1973

33 Becker, J, "The open-ended approach" NCTM 1997

34 Bragg,L.A, "The impact of mathematical games on learning, attitudes, and behaviours" La Trobe University 2006

35 Balka,D.S, "The development of an instrument to measure creative ability in mathematics" University of Missouri. 1974

36 Tharp,T, "The creative habit: Learn it and use it for life" Simon & Schuster 2005

37 Sriraman, B, "The characteristics of mathematical creativity, In Creativity, giftedness, and talented development in mathematics" Informa- tion Age Publishing 1-31, 2008

38 Kneller,G, "The art and science of creativity" International Thomson Publishing 1965

39 Torrance,E.P, "The Torrance tests of creative thinking: Technical-norms manual" Scholastic Testing Services 1973

40 Dulama, M. E, "Studying the degree of creativity of preschool children drawings" 3 (3): 85-96, 2010

41 Van Hieles,P.M, "Structure and insight: A theory of mathematics education" Academic Inc 1986

42 Robinson, K, "Schools kill creativity" TED Video Series 2006

43 Krulik, S, "Reasoning and problem solving: A handbook for elementary school teachers" Allyn and Bacon 1993

44 Posamentier, A. S., "Problem solving in mathematics grades 3-6: Powerful strategies to deepen understanding" Corwin 2009

45 Fouche, K. K, "Problem solving and creativity: Multiple solution methods in a cross-cultural study in middle level mathematics" University of Florida. 1993

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

47 Bolden, D. S, "Pre-service primary teachers’ conceptions of creativity in mathematics" 73 (73): 143-157, 2010

48 Hwang, W.-Y, "Multiple representation skills and creativity effects on mathematical problem solving using a multimedia whiteboard system" 10 (10): 191-212, 2007

49 Olson, A. T, "Mathematics through paper folding"

50 Duda, J, "Mathematical creative activity and the graphic calculator" 18 (18): 3-14, 2011

51 Kruteskii,V.A, "Mathematical aptitude, In Soviet studies in the psychology of learning and teaching mathematics Vol. II" University of Chicago Press 113-128, 1969

52 Atliere,J.L, "Literacy+Math=Creative connections in the elementary classroom" International Reading Association 2010

53 Schoenfeld,A, "Learning to think mathematically: Problem solving, metacognition, and making sense in mathematics, In Handbook of research in mathematics teaching and learning" Macmillan 334-370, 1992

54 Chen, Y, "Integrating computer-supported cooperative learning and creative problem solving into a single teaching strategy" 37 (37): 1283-1296, 2009

55 Krulik, S, "Innovative tasks to improve critical and creative thinking skills, In Developing mathematical reasoning in grade k-12" National Council of Teachers of Mathematics 138-145, 1999

56 Cho, S., "Influence of family processes, motivation, and beliefs about intelligence on creative problem" 33 (33): 46-58, 2011

57 Williams,G, "Identifying tasks that promote creative thinking in mathematics: A tool" 2002

58 Brookhart,S.M, "How to assess higher-order thinking skills in your classroom" ASCD 2010

59 Piirto,J, "How parents and teachers can enhance creativity in children, In Fostering creativity in children, K-8: Theory and practice" Allyn and Bacon 187-192, 2001

60 Schwartz,D.M, "How much is a million" Scholastic 1985

61 Small,M, "Good questions: Great ways to differentiate mathematics introduction" Teachers Collage Press 2009

62 Griffiths, R, "Games: A context and a medium for learning, In Celebrating mathematics learning" The Mathematical Association of Victoria 191-195, 1995

63 Silver,E.A, "Fostering creativity through instruction rich in mathematical problem solving and problem posing" 29 (29): 75-80, 1997

64 Harris, C. R, "Fostering creativity in the Asian-Pacific child K-8: Identification, strategies, implications, In Fostering creativity in children, K-8: Theory and practice" Allyn and Bacon 101-112, 2001

65 Gliner,G.S, "Factors contributing to success in mathematical estimation in preservice teachers: Types of problems and previous mathematical experience" 22 (22): 595-606, 1991

66 Sullivan, P, "Exploring open-ended tasks as teacher learning.Australian Primary Mathematics" 14 (14): 4-9, 2009

67 Artistico, D, "Everyday challenges in context: The influence of contextual factors on everyday problem solving among young, middle-aged, and older adults" 36 (36): 230-247, 2010

68 Landan,E, "Education toward the future: Asking question, In Creativity: A handbook for teachers" World Scientific 187-192, 2007

69 Torrance,E.P, "Education and the creative potential" Univ. of Minnesota Press 1963

70 Sak, U, "Divergence and convergence of mental forces of children in open and closed mathematical problems" 6 (6): 252-260, 2005

71 Sheffield,L.J, "Developing mathematical promise and creativity" 1-7, 2006

72 Hennessey, B. A, "Developing creativity in gifted children: The central importance of motivation and classroom climate" University of Connecticut 2004

73 National Council of Teachers of Mathematics, "Curriculum and evaluation standards for school mathematics" 1989

74 박정숙, "Cultivating divergent thinking in mathematics through an open-ended approach" INST ASIA PACIFIC EDUCATION DEVELOPMENT 7 (7): 51-61, 2006

75 Sternberg,R.J, "Creativity is a habit" 25 (25): 47-64, 2006

76 Starko,A.J, "Creativity in the classroom: School curious delight" Longman Publishers USA 1995

77 Kaufman, J, "Creativity in the classroom coda: Twenty key points and other insights, In Nurturing creativity in the classroom" Cambridge University Press 415-424, 2010

78 McCain, T. C, "Creativity and the elementary school teacher, In Teaching in the elementary school" Macmillan Publishing 283-304, 1977

79 Van Harpen, X. Y, "Creativity and mathematical problem posing: An analysis of high school students' mathematical problem posing in china and the united states"

80 Reiter-Palmon, R, "Creativity and domain specificity: The effect of task type on multiple indexes of creative problem-solving" 3 (3): 73-80, 2009

81 Briggs, M, "Creative teaching mathematics" Routledge 2008

82 Laycock,M, "Creative mathematics at Nueva" 17 : 325-328, 1970

83 Keun, L, "Creative dance:Singapore children's creative thinking and problem-solving responses.Research in Dance" 7 (7): 35-65, 2006

84 Casakin, H, "Creative Thinking as a Predictor of Creative Problem Solving in Architectural Design Students" 4 (4): 31-35, 2010

85 Hudson,L, "Contrary imaginations: A psychological study of the English schoolboy" Penguin 1967

86 Hudson,L, "Contrary imaginations.Methuen"

87 McNulty,R.C, "Children, mathematics and creativity" University of Exeter 1969

88 Eberle, B, "CPS for kids: A resource book for teaching creative problem- solving to children" Prufrock Press 1996

89 Urban,K.K, "Assessing creativity: A componential model, In Creativity: A handbook for teachers" World Scientific 167-184, 2007

90 Chiu,M.S, "Approaches to the teaching of creative and non-creative mathematical problems" 7 (7): 55-79, 2009

91 Shaughnessy,M.F, "An interview with E. Paul Torrance: About creativity" 10 (10): 441-452, 1998

92 Aiken,L.R, "Ability and creativity in mathematics.ERIC Document Reproduction Service No"

93 Spraker,H.S, "A study of the comparative emergence of creative behavior during the process of group and individual study of mathematics" University of Michigan. 1960

94 Teo, L. K. C, "A rasch measure of fostering creativity" 22 (22): 206-218, 2010

95 Haylock,D.W, "A framework for assessing mathematical creativity in schoolchildren" 18 : 59-74, 1987

96 Lee, G. S, "A development of the test for mathematical creative problem solving ability" 7 (7): 163-189, 2003

97 Brophy,D.R, "A comparison of individual and group efforts to creatively solve contrasting types of problems" 18 (18): 293-315, 2006