Application of '圓容三方互求' as a Mathematically Challenging Problem for Mathematically Gifted Elementary Students

초등 수학영재의 도전적 문제 상황을 위한 원용삼방호구(圓容三方互求)의 활용

  • Chang, Hyewon (Dept. of Math. Edu., Seoul National Univ. of Edu.)
  • Received : 2015.12.15
  • Accepted : 2016.02.15
  • Published : 2016.02.29


This study focused on the selection and application of mathematical problems to provide mathematically challenging tasks for the gifted elementary students. For the selection, a mathematical problem from <算術管見> of Joseon dynasty, '圓容三方互求', was selected, considering the participants' experiences of problem solving and the variety of approaches to the problem. For the application, teaching strategies such as individual problem solving and sharing of the solving methods were used. The problem was provided for 13 mathematically gifted elementary students. They not only solved it individually but also shared their approaches by presentations. Their solving and sharing processes were observed and their results were analyzed. Based on this, some didactical considerations were suggested.


  1. CHANG Hyewon, Diversity of Problem Solving Methods about a Problem of Area from the History of Mathematics by High Achieving Elementary School Students, The Korean Journal for history of mathematics 21(4) (2006), 153-168. 장혜원, 수학사의 한 넓이 문제에 대한 초등 수학 우수아의 풀이 다양성 탐색, 한국수학사학회지 21(4) (2006), 153-168.
  2. N. DAVIDSON, D. L. KROLL, An Overview of Research on Cooperative Learning Related to Mathematics, Journal for Research in Mathematics Education 22(5) (1991), 362-365.
  3. Gifted Education Database (GED), Statistics-mathematically gifted students, 2015, 영재교육종합데이터베이스, 2015, 통계-영재교육대상자,
  4. P. HELLER, R. KEITH, S. ANDERSON, Teaching Problem Solving through Cooperative Grouping (Part 1): Group versus Individual Problem Solving, American Association of Physics Teachers 60(7) (1992), 627-636.
  5. D. HOLTON et al., Teacher development and mathematical challenge, In E. J. BARBEAU, P. J. TAYLOR (Eds.), Challenging Mathematics in and beyond the Classroom: the 16th ICMI Study (Vol. 12), Springer Science & Business Media, 2009.
  6. KIM Hyejung, An Analysis of Collaborative Problem Solving of Mathematically Gifted Students in Elementary School : Focused on the Mathematics-Based STEAM Instruction, Master's thesis of Korea National University of Education, 2015. 김혜정, 초등 수학 영재들의 협력적 문제해결력 분석-수학 기반의 STEAM 수업을 중심으로, 한국교원대학교 석사학위논문, 2015.
  7. LEE SangHyuk, 算術管見, HER Min, KIM Sangmi (trans. 2006), 算術管見, Kyowoo Publisher, 1855. 이상혁, 산술관견, 1855, 허민, 김상미 (역, 2006), 산술관견, 교우사.
  8. LEE ShinDong, WON JaeGourn, KIM KiMyoung, The Comparison of General Students, and the Mathematics Gifted, and the Science Gifted in Learning Style and Preference of Instructional Methods, The Journal of the Korean Society for the Gifted and Talented 6(2) (2007), 107-128. 이신동, 원재권, 김기명, 초등학교 수학영재, 과학영재, 일반 학생의 학습유형 및 교수방법 선호도 비교, 영재와 영재교육 6(2) (2007), 107-128.
  9. LEE YounYoung, SONG SangHun, Development of Distance Education Programs Utilizing Diffy Game for the Math Gifted Students in Elementary School, School Mathematics 15(1) (2013), 121-136. 이윤영, 송상헌, 디피 (Diffy) 게임을 활용한 원격교육용 초등수학영재 프로그램 개발, 대한수학교육학회지 학교수학 15(1) (2013), 121-136.
  10. LIM Munkyu, A Study on Analysing of Various Number Formulas Posed by the Mathematically Talent 4th Grade Children in Elementary School, Journal of Elementary Mathematics Education in Korea 14(2) (2010), 263-285. 임문규, 초등학교 4학년 수학 영재학생들이 만든 다양한 계산식에 관한 분석 연구, 한국초등수학교육학회지 14(2) (2010), 263-285.
  11. LIM Munkyu, A Study on Investigating and Analyzing the Mathematical Problems Posed by the Mathematically Gifted 5th Grade Students in Elementary School, School Mathematics 15(4) (2014), 701-721. 임문규, 초등 5학년 수학영재 학생이 만든 수학문제에 관한 조사 분석, 대한수학교육학회지 학교수학 15(4) (2014), 701-721.
  12. D. K. MEYER, J. C. TURNER, C. A. SPENCER, Challenge in a Mathematics Classroom: Students' Motivation and Strategies in Project-Based Learning, The Elementary School Journal 97(5) (1997), 501-521.
  13. Ministry of Education and Science Technology, Mathematics Curriculum No. 2011-361, 2011. 교육과학기술부, 수학과 교육과정, 교육과학기술부 고시, 제 2011-361호 [별책 8], 2011.
  14. Ministry of Education, Mathematics Curriculum, No. 2015-74, 2015. 교육부, 수학과 교육 과정, 교육부 고시 제 2015-74호 [별책 8], 2015.
  15. A. B. POWELL et al, Challenging Tasks and Mathematics Learning, In E. J. BARBEAU, P. J. TAYLOR (Eds.), Challenging Mathematics in and beyond the Classroom: the 16th ICMI Study 12, 133-170, Springer Springer Science & Business Media, 2009.
  16. S. M. REIS, J. S. RENZULLI, Key Features of Successful Programs for the Gifted and Talented, Educational Leadership, April (1984), 28-34.
  17. J. S. RENZULLI, A Comprehensive Plan for the Development of Creative/Productive Giftedness, International Conference on Gifted Education in Science, 2015, 35-53.
  18. A. H. SCHOENFELD, Learning to Think Mathematically: Problem Solving, Metacognition and Sense-Making in Mathematics, In D. GROUWS (Ed.), Handbook for Research on Mathematics Teaching and Learning, New York: MacMillan, 1992, 334-370.
  19. A. H. SCHOENFELD, Reflections on Problem Solving Theory and Practice, The Mathematics Enthusiast 10(1 & 2) (2013), 9-34.
  20. G. STILLMAN et al., Classroom Practice: Challenging Mathematics, Children 4(3) (2007).
  21. I. VALE, T. PIMENTEI, Mathematical Challenging Tasks in Elementary Grades, In M. PYTLAK, T. ROWLAND, E. SWOBODA (Eds), Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education, 2011, 1154-1164.
  22. YANG SeongHyun, Utilizing 'Wonyongsambanghogu' in Mathematics Education, Journal for History of Mathematics 27(5) (2014), 313-327. 양성현, 원용삼방호구의 수학교육적 활용, Journal for History of Mathematics 27(5) (2014), 313-327.