Theoretical Mathematics and Pedagogical Mathematics (한국수학교육학회지시리즈B:이론수학과 교직수학)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

DEDUCTIVE PROBLEM MAKING FOR A DISTRIBUTION TYPE PROBLEM ON COMBINATION WITH REPETITION

배치형 중복조합 문제에 대한 연역적 문제만들기

  • Received : 2025.04.12
  • Accepted : 2025.05.01
  • Published : 2025.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

Problem-making has been continuously studied in mathematics education and problem-solving. In particular, the deductive problem-making method has potential applicability to various mathematical topics. By analyzing the problem-solving process into several substructures and creating problems backward by altering elements within those substructures, this method becomes meaningfully relevant to the reflection phase of problem-solving. This study utilizes the deductive problem-making method for a problem on combination with repetition and examines several pedagogical characteristics.

Keywords

References

  1. Cho, H. (2018). Analysis of characteristics presented in poblem posing based on Permutations and Combinations of high school students [Master's thesis, Ewha Womans University].
  2. Choi, I., Cho, H. (2016). Eye Movements in Understanding Combinatorial Problems. Journal of Eucational Research in Mathematics, 26 (4), 635-662.
  3. Choi, Y. (2011). A Study on combinations with repetition via occupancy problems [Master's thesis, Seoul National University].
  4. Han, I. (2009). An Analysis of Geometrical Differentiated Teaching and Learning Materials Using Inner Structure of Mathematics Problems. Communications of Mathematical Education, 23(2), 175-196.
  5. Han, I. (2020). Learning Polynomials and Knowing Mathematics. Seoul: Kyowoo.
  6. Han, I. (2024). A Making Triangle Construction Problems Using Deductive Problem Making Method. Communications of Mathematical Education, 38(4), 609-630. https://doi.org/10.7468/jksmee.2024.38.4.609
  7. Han, I., Huh, E., & Seo, E. (2023). A Concretization and Application of Deductive Problem Making Method. Communications of Mathematical Education, 37(4), 653-674. https://doi.org/10.7468/jksmee.2023.37.4.653
  8. Han, I., Lee, J. (2009). A Study on Solving Triangle Construction Problems Given by a Midpoint of Side and Other Tow Points. Journal of the Korean school mathematics society, 12(4), 365-388.
  9. Hong, G. (2011). The Effects of Permutation-Combination Instruction Using StructuralMapping on 2nd graders in Highschool [Master's thesis, Korea National University of Education].
  10. Huh, E. (2024). A Study on Constructing the System of Combination with Repetition Problems based on the Didactical Analysis [Doctoral dissertation, Gyeongsang National University].
  11. Joo, H., Han, H. (2016). The anlaysis of middle school students' problem posing types and strategies. The Mathematical Education, 55(1), 73-89. https://doi.org/10.7468/mathedu.2016.55.1.73
  12. Kim, B., Kim, Y., Kang, H., Kim, S., Do, J., Park, J., Song, C., Lim, H., Choi, I., Han, S., & Han, I. (2024). Mathematics Education and Problem Solving: Theory, Trends, and Prospects. Seoul: Kyungmun publ.
  13. Kim, Y. (2017). An analysis of thinking process on converting problem types in combinatorial problem solving [Master's thesis, Korea National University of Education].
  14. Lee, J. (2004). Students' understanding and problem-solving strategy for combinatorial problems based on the types of combinatorial problem [Master's thesis, Seoul National University].
  15. Lee, J. (2006). A Structural Isomorphism between Problems Counting the Number of Combinations [Master's thesis, Seoul National University].
  16. Ministry of Education (2022). Mathematics Currirulum. Sejong: MOE.
  17. Park, M. (2015). Teaching Relational Structure via Mathematical Problem Analogy [Doctoral dissertation, Seoul National University].
  18. Roberts, F. S. (1984). Applied Combinatorics. Prentice-Hall, Inc., Englewood Cliffs, New Jersey.
  19. Shin, D. (2021). Pre-Service Teacher's Noticing in Peer Evaluation of Mathematical Problem Posing: Focusing on permutation and combination. Journal of the Korean School Mathematics, 24(1), 19-38. https://doi.org/10.30807/ksms.2021.24.1.002