DOI QR코드

DOI QR Code

초등 수학 영재를 위한 Renzulli의 삼부심화모델 도입 개방형 수학 문제 만들기 프로그램 개발 및 적용

The Development and Application of Posing Open-Ended Problems Program with Renzulli's Enrichment Triad Model for Mathematics-Gifted Elementary Students

  • 투고 : 2016.03.11
  • 심사 : 2016.04.21
  • 발행 : 2016.05.31

초록

This study analyzed the process of steps in a program introducing Renzulli's enrichment triad model and various levels of posing open-ended problems of those who participated in the program for mathematics-gifted elementary students. As results, participants showed their abilities of problem posing related to real life in a program introducing Renzulli's enrichment triad model. From eighteen mathematical responses, gifted students were generally outstanding in terms of producing problems that demonstrated high quality completion, communication, and solvability. Amongst these responses from fifteen open-ended problems, all of which showed that the level of students' ability to devise questions was varied in terms of the problems' openness (varied possible outcomes), complexity, and relevance. Meanwhile, some of them didn't show their ability of composing problem with concepts, principle and rules in complex level. In addition, there are high or very high correlations among factors of mathematical problems themselves as well as open-ended problems themselves, and between mathematical problems and open-ended problems. In particular, factors of mathematical problems such as completion, communication, and solvability showed very high correlation with relevance of the problems' openness perspectives.

키워드

참고문헌

  1. 고상숙, 노지연 (2007). 중학교 기하단원의 개방형문제에서 학생의 문제해결과정의 사고 특성에 관한 연구, 한국학교수학연구회논문집 10(3), 303-322. (Choi-Koh, S.S. & Noh, J.Y. (2007). A study on student's processes of problem solving using open-ended geometric problems in the middle school, Journal of the Korea School Mathematics Society 10(3), 303-322.)
  2. 교육부 (2013). 제3차 영재교육 진흥 종합계획 (2013-2017), 교육부. (Ministry of Education. (2013). The 3rd gifted education development plan (2013-2017), Seoul: The Ministry of Education.)
  3. 교육부 (2015). 교육과정 총론, 교육부. (Ministry of Education. (2015). The general guideline of the national curriculum, Seoul: The Ministry of Education.)
  4. 권오남, 박정숙, 박지현, 조영미 (2005). 개방형 문제 중심의 프로그램이 수학적 창의력에 미치는 효과, 수학교육 44(2), 307-323. (Kwon, O.N., Park, J.S., Park, J.H., & Cho, Y.M. (2005). Cultivating mathematical creativity through open-ended approaches: development of a program and effectiveness analysis, The Mathematical Education 44(2), 307-323.)
  5. 김경탁, 류성림 (2013). 5, 6학년 수학교재의 문제만들기 내용 및 6학년 학생들의 문제만들기에서의 오류 분석, 한국초등수학교육학회지 17(2), 321-350. (Kim, G.T. & Ryu, S.R. (2013). An analysis of problem posing in the 5th and 6th grade mathematics textbook and error in problem posing of 6th graders, Journal of Elementary Mathematics Education in Korea 17(2), 321-350.)
  6. 김민경, 이지영, 홍지연, 김은경 (2011). 초등학교 수학 교과서에서 나타난 '문제'의 비구조성(ill-structured)에 관한 연구, 학습자중심교과교육연구 11(2), 1-21. (KIm, M.K., Lee, J.Y., Hong, J.Y., & Kim, E.K. (2011). A study of 'ill-structured' status from mathematics problems in elementary school textbooks, The Journal of Learner-Centered Curriculum and Instruction 11(2), 1-21.)
  7. 김보경, 권성룡 (2010). 개방형 문제를 활용한 수준별 학습이 학업성취도에 미치는 영향, 한국초등수학교육학회지 14(3), 907-935. (Kim, B.K. & Kwon, S.Y. (2010). An influence of using open-ended problems in ability-level activities on academic achievement of mathematics, Journal of Elementary Mathematics Education in Korea 14(3), 907-935.)
  8. 김은혜, 박만구 (2011). 수학 영재교육 대상 학생과 일반 학생의 개방형 문제 해결 전략 및 행동 특성 분석, 한국초등수학교육학회지 15(1), 19-38. (Kim, E.H. & Park, M.G. (2011). An analysis on the responses and the behavioral characteristics between mathematically promising students and normal students in solving open-ended mathematical problems, Journal of Elementary Mathematics Education in Korea 15(1), 19-38.)
  9. 김판수 (2003). 수학 영재의 문제 설정 단계와 사고과정 분석: 성냥개비 과제에 대한 사례분석을 중심으로, 초등교육연구 18(2), 303-334. (Kim, P.S. (2003). Analysis of think process and step in problem posing of the mathematically gifted children, The Journal of Elementary Education 18(2). 303-334.)
  10. 도종훈 (2007). 개방형 문제를 어떻게 만들 것인가?: 두개의 개방형 문제 제작 사례를 중심으로, 한국학교수학회논문집 10(2), 221-235. (Do, J.H. (2007). How to pose am open problem? : two cases of posing an open-ended problem by reorganizing given closes problems. Journal of the Korean School Mathematics Society 10(2), 221-235.)
  11. 박우자, 전평국 (2003). 개방형 문제 해결과정에서 나타난 소집단 구성원의 합의 패턴 분석, 초등수학교육 7(2), 117-129. (Park, U.J. & Jeon, P.G. (2003). An analysis of small-group children's consensus patterns in open-ended problem solving, Education of Primary School Mathematics 7(2), 117-129.)
  12. 박한홍 (1995). 아동의 문제 설정 유형과 문제 특성에 관한 연구. 석사학위논문, 한국교원대학교. (Park, H.H. (1995). An analysis of the types and the characteristics of problems poses by the children, Unpublished master's thesis, Korea National University of Education.)
  13. 박혜정, 조영미 (2012). Girih 타일링을 이용한 초등수학 영재 프로그램 개발 및 적용 연구, 영재교육연구 22(3), 619-637. (Park, H.J. & Cho, Y.M. (2012). The development and application of Girih tiling program for the math-gifted student in elementary school, Journal of Gifted/Talented Education 22(3), 619-637.) https://doi.org/10.9722/JGTE.2012.22.3.619
  14. 배종수, 오은영 (2005). 개방형 문제를 이용한 학습에 대한 아동의 태도 연구, 한국초등수학교육학회지 9(1), 39-64 (Bae, J.S. & Oh, E.Y. (2005). A study of children's attitudes towards learning mathematics with open-ended problems, Journal of Elementary Mathematics Education in Korea 9(1), 39-64.)
  15. 백대현, 이진희 (2010). Problem posing by mathematically gifted middle school students, 학교수학 12(3), 259-271. (Paek, D.H. & Yi, J.H. (2010). Problem posing by mathematically gifted middle school students. Journal of Korea Society of Educational Studies in Mathematics School Mathematics 12(3), 259-271.)
  16. 송민정, 박종서 (2005). 문제 만들기 프로그램 개발.적용이 수학 학업 성취도 및 태도.흥미도에 미치는 영향, 한국초등수학교육학회지 9(1), 1-18. (Song, M.J. & Park, J.S. (2005). The effects of development and application of problem posing program on mathematics learning achievements, attitude and interest, Journal of Elementary Mathematics Education in Korea 9(1), 1-18.)
  17. 송상헌, 정영옥, 임재훈, 신은주, 이향훈 (2007). 수학영재들이 NIM 게임 과제에서 만든 문제 만들기 사례 분석, 수학교육학연구 17(1), 51-66. (Song, S.H., Chong, Y.O., Yim, J.H., Shin, E.J., & Lee, H.H. (2007). A study on the cases of the problem posing which the mathematically gifted students are made in the nim game, Journal of Educational Research in Mathematics 17(1), 51-66.)
  18. 신마리아, 나귀수 (2012). 학생들의 문제 만들기의 특징에 대한 연구, 한국초등수학교육학회지 16(2), 269-293. (Shin, M. & Na, G.S. (2012). Understanding the characteristics if students' problem posing, Journal of Elementary Mathematics Education in Korea 16(2), 269-293.)
  19. 이강섭, 황동주 (2007). 수학 영재학생과 일반학생의 수학 창의성과 문제 설정과의 상관 연구, 수학교육46(4), 503-519. (Lee, K.S. & Hwang, D.J. (2007). Correlation between gifted and regular students in mathematical problem posing and mathematical creativity ability, The Mathematical Education 46(4), 503-519.)
  20. 이경미, 이광호, 이근철 (2012). 초등학교 5학년 학생들의 문제 만들기, 학교수학 14(4), 431-443. (Lee, K.M., Lee, K.H., & Lee, K.C. The analysis of the 5th graders' responses on problem posing, Journal of Korea Society Educational Studies in Mathematics School Mathematics 14(4), 431-443)
  21. 이경숙, 유미현 (2014). 초등 수학영재 수준을 고려한 무게중심에 대한 교수 학습 프로그램의 개발 및 적용, 과학영재교육 6(1), 15-34. (Lee, K.S. & Yu, M.H. (2014). Development and application of program on the center of mass considering the level of the mathematically gifted elementary students, Journal of Science Education for gifted 6(1), 15-34.)
  22. 이대현 (2008). 초등 수학 평가를 위한 개방형 문제의 활용 결과 분석, 수학교육 47(4), 421-436. (Lee, D.H. (2008). A study on the results of use of open-ended problems for evaluation in elementary mathematics, The Mathematical Education 47(4), 421-436.)
  23. 이영희 (2003). 웹기반 원격 수학영재교육 학습자료 개발, 영재교육연구 13(1), 81-95. (Lee, Y.H. (2003). Development of web-based education program for the gifted in mathematics, Journal of Gifted/Talented Education 13(1), 81-95.)
  24. 이윤영, 송상헌 (2013). 디피(Diffy) 게임을 활용한 원격교육용 초등수학영재 프로그램 개발, 학교수학 15(1), 121-136. (Lee, Y.Y. & Song, S.H. (2013). Development of distance education programs utilizing Diffy game for the math gifted students in elementary school, Journal of Korea Society Educational Studies in Mathematics School Mathematics 15(1), 121-136.)
  25. 이애리 (2013). 저소득층 학생들의 창의적 음악활동 경험에 대한 사례 연구: 지역 아동센터 초등학교 3학년 학생들을 중심으로. 석사학위논문, 이화여자대학교. (Lee, A.R. (2013). A case study on experiences of creative music activities of students from low-income families: A study of 3rd grade elementary school students at a local children's center, Unpublished master's thesis, Ewha Womans University.)
  26. 이종영 (2012). 개방형 문제를 통한 초등학교 수학 수업 개선 방안 연구, 교육종합연구 10(3), 307-322. (Lee, C.Y. (2012). A study for improving mathematics instruction through open problems in the elementary school, The Journal of Educational Research 10(3), 307-322.)
  27. 임근광 (2010). 종이접기 프로그램에서 수학영재학생들의 문제 만들기 전략 분석, 영재교육연구 20(2), 461-486. (Yim, G.G. (2010). Analysis of problem posing strategy of mathematics gifted students in an orgami program, Journal of Gifted/Talented Education 20(2), 461-486.)
  28. 임문규 (1996). 수학교육에서 열린 교수 학습의 실천적 방법 연구, 한국초등수학교육학회지 1, 17-32. (Lim, M.K. (1996). A study on the practical methods of open teaching and learning in mathematics education, Journal of Elementary Mathematics Education in Korea 1, 17-32.)
  29. 임문규 (2001). 7차 교육과정에 따른 초등학교 1, 2학년 수학 교재의 문제 만들기 내용 분석 및 학생들의 실태 조사, 학교수학 3(2), 295-324. (Lim, M.K. (2001). A study on the analysis for problem-posing contents of elementary school first and second grade mathematics textbooks by the 7th curriculum and investigation for children's disposition to mathematical problem-posing, Journal of Korea Society of Educational Studies in Mathematics School Mathematics 3(2), 295-324.)
  30. 최왕균 (2011). 수 퍼즐 문제 만들기 과제에서 나타나는 추등수학 영재들의 수학적 사고 특성 분석-문제설정과 일반화 사고를 중심으로. 석사학위논문, 아주대학교. (Choi, W.G. (2011). Analysis of 'mathematical thinking' process on puzzle problem posing for the mathematically gifted elementary students-focus on the problem posing and generalization, Unpublished master's thesis, Ajou University.)
  31. 최혜진, 김상룡 (2011). 생활소재를 활용한 수학 문제 만들기 활동, 한국초등수학교육학회지 15(1), 121-139. (Choi, H.J. & Kim, S.L. (2011). Activities of mathematical problem posing using real-life materials, Journal of Elementary Mathematics Education in Korea 15(1), 121-139.)
  32. 한국교육개발원 (2013). 통계자료 SM 2013-01 2012 영재교육 통계 연보, 서울: 한국교육개발원. (Korean educational development institute (2013). Gifted education statistical year book, Seoul: Korean educational development institute.)
  33. 한기순 (2006). 국내 영재교육 프로그램의 현황과 과제, 영재와 영재교육 5(1), 109-129. (Han, K.S. (2006). Current status and future prospect of gifted education programs, The Journal of the Korean Society for the Gifted and Talented 5(1), 109-129.)
  34. 황동주 (2006). 중학교 1학년 수학 영재 학생과 일반 학생의 수학 문제해결과 문제 설정 능력의 차이 비교, 한국학교수학회논문집 9(3), 287-308. (Hwang, D.J. (2006). Difference between gifted and regular students in mathematical problem solving ability, Journal of the Korean School Mathematics Society 9(3), 287-308.)
  35. Becker. J.P. & 島田茂(2004). 수학지도를 위한 새로운 제안 개방형 교수법 (구광조, 전평국, 박성선, 문성길 역), 서울: 경문사. (원저 1995년 출판)
  36. Brauner, A., Carey, J., Henriksson, M., Sunnerhagen, M., & Ehrenborg, E. (2007). Open-ended assignment and student responsibility, Biochemistry and Molecular Biology Education 35(3), 187-192. https://doi.org/10.1002/bmb.49
  37. Brown, S.I. & Walter, M.I. (1990). The art of problem posing, PA: Franklin institute press.
  38. Brugman, G.M. (1995). The discovery and formulation of problems, European Education 27(1), 38-57. https://doi.org/10.2753/EUE1056-4934270138
  39. Chen, L., Van Dooren, W., & Verschaffel, L. (2013). The relationship between students' problem posing and problem solving abilities and beliefs: a small-scale study with chinese elementary school children, Front Education China 8(1), 147-161. https://doi.org/10.1007/BF03396966
  40. Cognition and Technology Group at Vanderbuilt (1997). The Jasper project: Lesson in curriculum, instruction, assessment, and professional development, NJ: Lawrence Eribaum Associates.
  41. Davis, G.A. & Rimm, S.B. (2005). 영재교육 (이경화, 최병연, 박숙희 역), 서울: 박학사. (원저 1985년 출판)
  42. Gardner, H. (1993). 마음의 틀 (이경희 역), 서울: 문음사. (원저 1993년 출판)
  43. Grace, S. & Langout, R.D. (2014). Questioning our questions: assessing question asking practices to evaluate a yPAR program, Urban Rev 46, 703-724. https://doi.org/10.1007/s11256-014-0279-4
  44. Veletsianos, G. & Doering, A. (2010). Long-term student experiences in hybrid, open-ended and problem based adventure learning program, Australasian Journal of Educational Technology 26(2), 208-296.
  45. Hertzog, G. (1995). Investigating the nature of open-ended activities, Doctoral dissertation, University of Illinois, Champaign-Urbana.
  46. Koichu, B. & Kontorovich, I. (2013). Dissecting success stories on mathematical problem posing: a case of the billiard task, Educational Studies in Mathematics 83(1), 71-86. https://doi.org/10.1007/s10649-012-9431-9
  47. Landis, J.R. & Koch, G.G. (1977). The measurement of observer agreement for categorical data, Biometrics 33, 159-174. https://doi.org/10.2307/2529310
  48. Leatham, K.R., Lawrence, K., & Mewborn, D.S. (2005). Getting started with open ended assessment, Teaching children mathematics.
  49. Markham, T., Larmer, J., & Ravitz, J. (2003). A guide to standards-focused project based learning for middle and high school teachers, Back institute for education.
  50. Olenchak, F.R. & Renzulli, J.S. (1989). The effectiveness of the schoolwide enrichment model on selected aspects of elementary school change, Gifted Child Quarterly 33(1), 36-46. https://doi.org/10.1177/001698628903300106
  51. Pehkonen, E. (1995). Use open-ended problems in mathematics, Zentralblatt fur Didaktik der Mathematik 27(2), 67-71.
  52. Renzulli, J.S. (1997). The enrichment triad model: A guide for developing defensible program for the gifted and talented, CT: Creative Learning Press.
  53. Renzulli, J.S. & Reis, S.M. (1997). The schoolwide enrichment model: A how-to guide for educational excellence, CT: Creative Learning Press.
  54. Silver, E.A. (1994). On mathematical problem posing, For The Learning of Mathematics 14(1), 19-28.
  55. Silver, E.A. (2007). Teaching and learning mathematical problem solving: Multiple research perspectives, NJ: Lawrence Erlbaum Associates.
  56. Silver. E.A. & Cai. J. (1996). An analysis of arithmetic problem posing by middle school students, Journal for Research in Mathematics Education 27(5), 521-539. https://doi.org/10.2307/749846
  57. VanTassel-Baska, J. & Brown, E.F. (2007). Toward best practice: An analysis of the efficacy of curriculum models in gifted education, Gifted Child Quarterly 51(4), 342-358. https://doi.org/10.1177/0016986207306323

피인용 문헌

  1. Analysis of Abduction in Mathematics Problem Posing and Solving vol.30, pp.0, 2020, https://doi.org/10.29275/jerm.2020.02.30.1.89