Communications of Mathematical Education (한국수학교육학회지시리즈E:수학교육논문집)

Korean Society of Mathematical Education (한국수학교육학회)
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Exploration of the educational possibilities of one-stroke drawing problems of complex figure using programming

프로그래밍을 이용한 복잡한 도형의 한붓그리기 문제의 교육적 가능성 탐색

  • Received : 2024.02.29
  • Accepted : 2024.06.10
  • Published : 2024.06.30
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Abstract

This study propose the educational potential of an activity that solves the task of one-stroke drawing of complex figures using a drag-and-drop type educational programming language such as Scratch. The problem of determining whether a given shape is capable of one-stroke drawing is a separate problem from actually finding the path of one-stroke drawing and implementing it through programming. In particular, finding a path that allows one-stroke drawing of complex shapes with regularity and implementing it through programming requires problem-solving capabilities based on the convergence of various mathematical knowledge. Accordingly, in this study, problems related to one-stroke drawing concerning polygon-related shapes, tessellation-related shapes, and fractal shapes were presented, and the results of one-stroke drawing programming of the shapes were exemplified. In addition, the mathematical knowledge and computational thinking elements necessary for the solution of the illustrated problem were analyzed. This study is significant as a new example of the mathematics education that combines mathematics and information.

본 연구는 스크래치 같은 드래그 앤 드롭 방식 교육용 프로그래밍 언어를 활용하여 복잡한 도형의 한붓그리기 과제를 해결하는 활동의 교육적 활용가능성을 논의하고자 한다. 주어진 도형이 한붓그리기가 가능한지를 판별하는 문제와 실제로 한붓그리기의 경로를 찾아서, 프로그래밍으로 구현하는 것은 별개의 문제가 된다. 특히 규칙성을 가지는 복잡한 도형에 대해 한붓그리기가 가능한 규칙적인 경로를 찾고, 이를 프로그래밍으로 구현하는 것은 다양한 수학지식의 융합을 바탕으로 하는 문제해결 역량을 요구한다. 이에 본 연구에서는 다각형 관련 도형들, 테셀레이션 관련 도형들, 프랙탈 도형들 중에 한붓그리기와 관련된 문제를 제시하고, 해당 도형의 한붓그리기 프로그래밍 결과를 예시하였다. 또 예시된 문제의 해결과정을 위해 필요한 수학지식과 계산적 사고 요소들을 분석하였다. 본 연구는 수학과 정보가 융합하는 수학교육에 대한 새로운 예시라는 의미를 갖는다.

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References

  1. Kang, S. J, Rim, H, & Joo, J. (2019). Secondary mathematics with Scratch: Geometry. Emotion Books. 
  2. Kang, S. J, Rim, H, Kim J, Joo J., & Jang M., (2020). Secondary mathematics with Entry: Algebra. Emotion Books. 
  3. Kang, H. R. , Lim, C. L., & Cho., H. H. (2021). A study on coding mathematics curriculum and teaching methods that converges school mathematics and school informatics. The Mathematical Education, 60(4), 457-491. 
  4. Ministry of Education (2022). Mathematics curriculum. Ministry of Education Notice No. 2022-33 [Appendix 8]. 
  5. Kwon, M. (2024) Analysis of Japanese elementary school mathematics textbooks and digital contents on programming education. Education of Primary School Mathematics, 27(1), 57-74.  https://doi.org/10.7468/JKSMEC.2024.27.1.57
  6. Kim, S. M. (2009). A case study of constructions on fractals of the mathematically gifted. Journal of Educational Research in Mathematics, 19(2), 341-354.. 
  7. Park, J. (2021). Discrete mathematics for developing computational thinking. Hanbit Academy. 
  8. Park, J. Y. (2023). A study on inductive reasoning and visualization of elementary school students in congruence and symmetry lessons with exploratory software. Communications of Mathematical Education, 37(2), 299-327.  https://doi.org/10.7468/JKSMEE.2023.37.2.299
  9. Shin, D. & Koh, S. (2019). A study on investigation about the meaning and the research trend of computational thinking(CT) in mathematics education. The Mathematical Education, 58(4), 483-505.  https://doi.org/10.7468/MATHEDU.2019.58.4.483
  10. Lee, S. W. (2020). An analysis of the middle school mathematics curriculum in France: Focusing on 'Algorithms and Programming'. School Mathematics, 22(1), 125-159. 
  11. Rim, H, & Park, E. Y. (2002). Development and utilization of tessellation teaching and learning materials using computer software. Communications of Mathematical Education, 13(2), 563-589. 
  12. Rim, H., Choi, I., & Noh, S. (2014). A study on the application of robotic programming to promote logical and critical thinking in mathematics education. The Mathematical Education, 53(3), 413-434. https://doi.org/10.7468/mathedu.2014.53.3.413
  13. Chang, K. Y. (2017). A feasibility study on integrating computational thinking into school mathematics. School Mathematics, 19(3), 553~570. 
  14. Jeong, J. & Cho, h. (2020). Mathematising of coding education command: Focusing on algebra education, Journal of Educational Research in Mathematics, 30(1), 131-151. 
  15. Choi, K. B. (2005) A study on discrete mathematics subjects focused on the network problem for the mathematically gifted students in the elementary school. School Mathematics, 7(4), 353-373. 
  16. Korea Foundation for the Advancement of Science & Creativity (2019). Final report on The development of a guide to teaching mathematical tasks. Retrieved from https://www.kofac.re.kr/brd/board/457/L/menu/244?brdType=R&thisPage=1&bbIdx=24164&searchField=title&searchText=%EC%A2%8B%EC%9D%80%20%EC%88%98%ED%9599%EA%B3%BC%EC%A0%9C%20%EC%A7%80%EB%8F%84
  17. Wing, J. M. (2006). Computational thinking. Communications of the ACM, 49(3), 33-35. https://doi.org/10.1145/1118178.1118215
  18. Xavier, D. A., Rosary, M., & Arokiaraj, A. (2014). Topological properties of Sierpinski gasket rhombus graphs. International Journal of Mathematics and Soft Computing, 4(2), 95-104. https://doi.org/10.26708/IJMSC.2014.2.4.10