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[국내논문] 중·고등학생의 평행사변형과 마름모의 유사성과 차이에 대한 인식 분석
An analysis on the perception of resemblance and difference between parallelogram and rhombus in middle and high school students

韓國學校數學會論文集 = Journal of the Korean school mathematics society, v.27 no.1, 2024년, pp.1 - 22  

장현석 (울산대학교) ,  김명창 (경산 여자중학교)

초록
AI-Helper 아이콘AI-Helper

이 연구에서는 중·고등학생의 평행사변형과 마름모의 유사성과 차이에 대한 인식을 분석하였다. 이를 위해 검사 도구를 개발하고 중·고등학생 총 191명을 대상으로 검사하고, 일부의 학생을 면담하였다. 연구 결과는 다음과 같다. 유사점과 차이점에서 공통으로 평행사변형과 마름모의 종류에 대한 응답 비율이 가장 높았고, 길이와 같은 양적인 응답 비율이 가장 낮았다. 유사점의 경우 첫째, 평행사변형과 마름모의 정의, 변과 각 그리고 대각선의 내림차순으로 응답 비율이 높았다. 둘째, 변환 관점의 응답 비율은 다른 범주와 비교해서 상대적으로 가장 낮았다. 셋째, 대체로 여학생은 도형의 형태에 기반 한 양적인 정보를 토대로 응답하고 남학생은 평행사변형과 마름모의 정의에 기반 해서 응답하였다. 넷째, 조작의 경우 빈도와 비율에서 남학생과 여학생의 차이는 없었지만 학년이 올라감에 따라 증가하였다. 차이점의 경우는 전체적인 길이에 대한 응답에 비해 대각선의 길이에 대한 응답 비율이 높았다. 그러나 대각선을 평행사변형과 마름모의 성질과 관련 지은 응답은 없었다. 마지막으로 개념 정의와 개념 이미지의 관점에서 중·고등학생은 평행사변형과 마름모의 개념 정의에 대한 기억 또는 이름을 이용하거나 개념 이미지 및 각 등을 부분적으로 주목하고 이를 시각적으로 변환하거나 넓이와 같은 양적인 정보를 이용하여 평행사변형과 마름모의 유사성과 차이에 대해 응답하였다.

Abstract ▼ AI-Helper 아이콘AI-Helper

In this study, the perception of the resemblance and difference between the parallelogram and rhombus of middle and high school students was analyzed. To this end, a test tool was developed, a total of 191 middle and high school students were tested, and some students were interviewed. The results o...

Keyword

#사각형   #유사성   #개념 정의   #개념 이미지   #중   #고등학생  

참고문헌 (51)

  1. Ministry of Education (2022). Mathematics curriculum？(# 2022-33 supplement 8). Ministry of Education. 

  2. Kim, D. G. (2012).？Comparison of the development and composition of the [Property of Square] unit in the second year of middle school.？Master's thesis, Ajou university. 

  3. Kim,？H-J., & Kang, W. (2008). An analysis on the teaching quadrilaterals in the elementary school mathematics？textbooks. Education of Primary School Mathematics, 11(2), 141-159. 

  4. Noh, Y-A., & Ahn, B-G. (2007). An analysis on error of fourth grade student in geometric？domain. Journal of Elementary Mathematics Education in Korea, 11(2), 199-216. 

  5. Noh, J. W., Lee, K-H., & Moon, S-J. (2019). Case study on the learning？of the properties of quadrilaterals through semiotic mediation: Focusing on reasoning about the relationships？between the properties. School Mathematics, 21(1), 197-214. https://doi.org/10.29275/sm.2019.03.21.1.197 

    상세보기 crossref

  6. Moon, K. Y. (2016). An analysis？of elementary students' concept image. Master's thesis, Seoul National University of Education. 

  7. Park, J. H. (2017). An analysis on conjecturing tasks in elementary school mathematics textbook:？Focusing on definitions and properties of quadrilaterals. The Journal of Educational Research in Mathematics,？27(3), 491-510. 

  8. Shin, Y. J.？(2017). An analysis of concept images of quadrilaterals of second-year elementary students. Master's thesis, Gyeongin？National University of Education. 

  9. Lim,？J. Y. (2017). An analysis of the examples of triangles and quadrangles generated by elementary school mathematics？textbooks, teachers, and students. Master's thesis, Seoul National University of Education. 

  10. Yoon, M. J. (2012). An？action research on rectangle teaching for 8th grade students. Master's thesis, Korea National University of Education？Chung-Buk. 

  11. Yi, G., & Choi,？Y. (2016). A Study on the word 'is' in a sentence "A parallelogram is trapezoid." School Mathematics, 18(3),？527-539. 

  12. Lee, C. H., & Whang, W. Y. (2010). A Study of the syllabus based on van Hiele theory？using GSP in middle school geometry: Focused on the 2st grade middle school students. The mathematical？Education, 49(1), 85-109. 

  13. Chang, H. S., Kim, M. C., & Lee, B-J. (2022). An analysis on concept definition and concept image？on quadrangle of middle and high school students. The Mathematical Education, 61(2), 323-338. http://doi.org/10.7468/mathedu.2022.61.2.323 

    원문보기 상세보기 crossref

  14. Choi, K. (2017). A design of teaching units for experiencing mathematising of elementary gifted students:？Inquiry into the isoperimetric problem of triangle and quadrilateral. The Mathematical Education, 31(2), 223-239.？https://doi.org/10.7468/jksmee.2017.31.2.223 

    원문보기 상세보기 crossref

  15. Choi, S. I., & Kim, S. J. (2012). A study on defining and naming of the figures in？the elementary mathematics - Focusing to 4th grade geometric domains. Journal of the Korean School Mathematics？Society, 15(4), 719-745. 

  16. Atanasova-Pachemska, T., Gunova, V., Koceva Lazarova, L., & Pachemska, S. (2016). Visualization of the geometry？problems in primary math education: needs and changes. Istrazivanje Matematickog Obrazovanja, 8(15), 33-37.？https://bit.ly/3rR3BnQ 

  17. Clements, D., & Battista, M. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook on mathematics？teaching and learning (pp. 420-464), New York: Macmillan. 

  18. Clements, D., Swaminathan, S., Hannibal, M., & Sarama, J. (1999). Young children's concepts of shape. Journal for？Research in Mathematics Education, 30(2), 192-212. 

    상세보기

  19. Davey, G., & Pegg, J. (1988). Research in geometry and measurement. In Research in mathematical education in？Australasia, 1991, pp. 231-247. 

  20. Denis, M. (1989). Les images mentales (Terauchi, R. Trans.). Tokyo: Keisosyobo (In Japanese). 

  21. Fischbein, E. (2001). Tacit models and infinity. Educational Studies in Mathematics, 48, 309-329. https://doi.org/10.1023/A:1016088708705 

    crossref

  22. Fujita, T. (2012). Learners' level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon.？The Journal of Mathematical Behavior, 31, 60-72. https://doi.org/10.1016/j.jmathb.2011.08.003 

    상세보기 crossref

  23. Gutierrez, A., Jaime, A., & Fortuny, J. M. (1991). An alternative paradigm to evaluate the acquisition of the van？Hiele levels. Journal for Research in Mathematics Education, 22(3), 237-251. 

    상세보기

  24. Guven, B., & Okumus, S. (2011). 8th grade Turkish students' van Hiele levels and classification of quadrilaterals.？In Proceedings of the 35th conference of the international group for the psychology of mathematics education (Vol.？2, pp. 473-480). Ankara, Turkey: PME. 

  25. Hershkowitz, R. (1989). Visualization in geometry: Two sides of the coin. Focus on Learning Problems in Mathematics,？11(1), 61-76. 

  26. Lehrer, R., Jenkins, M., & Osana, H. (1998). Longitudinal study in children's reasoning about space and geometry.？In R. Lehrer, & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and？space (pp. 351-67), Mahwah, NJ: Lawrence Erlbaum Associates. 

  27. Lipovec, A., & Podgorsek, M. (2016). Risba kot orodje za vpogled v matematicno razumevanje [Drawing as a tool？for 25, mathematical understanding]. Psiholoska Obzorja, 25, 156-166. https://doi.org/10.20419/2016.25.452 

    상세보기 crossref

  28. Lowrie, T., & Clements, M. A. (2001). Visual and non-visual processes in grade 6 students' mathematical problem？solving. Journal of Research in Childhood Education, 16, 77-93. https://doi.org/10.1080/02568540109594976 

    상세보기 crossref

  29. Matsuo, N. (1999). Understanding relations among concepts of geometric figures: Identifing states of understanding. Journal of Science Education in Japan, 23(4), 271-282. https://doi.org/10.14935/jssej.23.271 

    crossref

  30. Matsuo, N. (2000). States of understanding relations among concepts of geometric figures: Considered from the aspect？of concept image and concept definition. In T. Nakahara, & M. Koyama (Eds.), Proceedings of the 24th conference？of the international group for the psychology of mathematics education (Vol. 3, pp. 271-278). Hiroshima, Japan:？PME. 

  31. Matsuo, N. (2007). Differences of students' understanding of geometric figures based on their definitions. In Proceedings？of the 24th conference of the international group for the psychology of mathematics education (Vol. 1, p. 264). PME. 

  32. National Council of Teachers of Mathematics (2007). 학교 수학의 원리와 규준(류희찬, 조완영, 이경화, 나귀수, 김남균,？방정숙 역). 서울: 경문사 (원저 2000년 출판). 

  33. Okazaki, M., & Fujita, T. (2007). Prototype phenomena and common cognitive paths in the understanding of the？inclusion relations between quadrilaterals in Japan and Scotland. In Proceedings of the 31st conference of the？international group for the psychology of mathematics education (Vol. 4, pp. 41-48). PME. 

  34. Okazaki, M. (2009). Process and means of reinterpreting tacit properties in understanding the inclusion relations？between quadrilaterals. In Proceedings of the 33th conference of the international group for the psychology of？mathematics education (Vol. 4, pp. 249-236). PME. 

  35. Pegg, J., & Baker, P. (1999). An exploration of the interface between van Hiele's level 1 and 2. In O. Zaslaysky (Ed.),？Proceedings of the 23rd international group for the psychology of mathematics education (Vol. 4, pp. 25-32). Haifa:？PME. 

  36. Presmeg, N. C. (1997). Generalization using imagery. In L. D. English (Ed.), Mathematical reasoning: Analogies, metaphors,？and images (pp. 299-312). Mahwah, NJ: Lawrence Erlbaum Associates. 

  37. Presmeg, N. (2014). Contemplating visualization as an epistemological learning tool in mathematics. ZDM, 46, 151-157. 

    상세보기

  38. Rosch, E., & Mervis, C. (1975). Family resemblances: studies in the internal structures of categories. Cognitive Psychology,？7, 573-605. https://doi.org/10.1016/0010-0285(75)90024-9 

    상세보기 crossref

  39. Shimonaka, H. (1983). The encyclopedia of philosophy. Tokyo: Heibonsya. (In Japanese) 

  40. Silfverberg, H., & Matsuo, N. (2008). Comparing Japanese and Finnish 6th and 8th graders' ways to apply and construct？definitions. In Proceedings of the 32nd conference of international group for the psychology of mathematics education？(Vol. 4, pp. 257-264). PME. 

  41. Sinclair, N., & Yurita, V. (2008). To be or to become: How dynamic geometry changes discourse. Research in Mathematics？Education, 10(2), 135-150. https://doi.org/10.1080/14794800802233670 

    상세보기 crossref

  42. Sinclair, N., & Moss, J. (2012). The more it changes, the more it becomes the same: the development of the routine？of shape identification in dynamic geometry environment. International Journal of Educational Research, 51-52,？28-44. http://dx.doi.org/10.1016/j.ijer.2011.12.009 

    상세보기 crossref

  43. Sinclair, N., Bartolini Bussi, M. G., de Villiers, M. et al. (2016). Recent research on geometry education: An ICME-13？survey team report. ZDM Mathematics Education 48, 691-719. https://doi.org/10.1007/s11858-016-0796-6 

    상세보기 crossref

  44. Van Hiele, P. M. (1985). The child's thought and geometry. In D. Geddes, & R. Tischler (Eds.), English translation？of selected writings of Dina van Hiele-Geldof and Pierre M. van Hiele (pp. 243-252). Brooklyn: Brooklyn College,？School of Education (Original work published 1959). 

  45. Vinner, S., & Hershkowitz, R. (1980). Concept images and common cognitive paths in the development of some？simple geometrical concepts. In R. Karplu (Ed.), Proceedings of the fourth international conference for the psychology？of mathematics education (pp. 177-184), Berkeley, CA: Lawrence Hall of Science, University of California. 

  46. Vinner, S., & Dreyfus, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics？Education, 20(4), 356-366. 

    상세보기

  47. Walcott, C., Mohr, D., & Kastberg, S. E. (2009). Making sense of shape: An analysis of children's written responses.？The Journal of Mathematical Behavior, 28(1), 30-40. https://doi.org/10.1016/j.jmathb.2009.04.001 

    상세보기 crossref

  48. Wang, S., & Kinzel, M. (2014). How do they know it is a parallelogram? Analysing geometric discourse at van Hiele？Level 3. Research in Mathematics Education, 16(3), 288-305. https://doi.org/10.1080/14794802.2014.933711 

    상세보기 crossref

  49. Wheatley, G. H. (1997). Reasoning with images in mathematical activity. In L. D. English (Ed.), Mathematical reasoning:？Analogies, metaphors, and images (pp. 281-298). Mahwah, NJ: Lawrence Erlbaum Associates. 

  50. Wilson, P. S. (1990). Inconsistent ideas related to definitions and examples. Focus on Learning Problems in Mathematics,？12(3-4), 31-47. 

  51. Zakelj, A., & Klancar, A. (2022). The role of visual representations in geometry learning. European Journal of Educational？Research, 11(3), 1393-1411. https://doi.org/10.12973/eu-jer.11.3.1393 

    상세보기 crossref

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