Education of Primary School Mathematics (한국수학교육학회지시리즈C:초등수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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The Fourth Graders' Visual Representation in Mathematics Problem Solving Process

초등학교 4학년 학생들의 수학 문제해결과정에서의 시각적 표현

  • Kim, So Hee (Graduate School of Korea National University of Education) ;
  • Lee, Kwangho (Korea National University of Education) ;
  • Ku, Mi Young (Graduate School of Korea National University of Education)
  • Received : 2013.11.20
  • Accepted : 2013.12.16
  • Published : 2013.12.31
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Abstract

The purpose of the study is to analyze the 4th graders' visual representation in mathematics problem solving process and to find out how to teach the visual representation in mathematics problem solving process. on the basis of the results, this study gives several pedagogical implication related to the mathematics problem solving. The following were the conclusions drawn from the results obtained in this study. First, The achievement level of students and using visual representation in the mathematics problem solving are closely connected. High achieving students used visual representation in the mathematics problem solving process more frequently. Second, high achieving students realize the usefulness of visual representation in the mathematics problem solving process and use visual representation to solve mathematical problem. But low achieving students have no conception that visual representation is one of the method to solve mathematical problem. Third, students tend to especially focus on 'setting up an equation' when they solve a mathematical problem. Because they mostly experienced mathematical problems presented by the type of 'word problem-equation-answer'. Fourth even through students tried visual representation to solve a mathematical problem, they could not solve the problem successfully in numerous instances. Because students who face a difficulty in solving a problem try to construct perfect drawing immediately. But generating visual representation 2)to represent mathematical problem cannot be constructed at one swoop.

본 연구는 초등학교 4학년 학생들의 수학 문제해결 과정에서 나타나는 시각적 표현이 어떠한지를 알아보고, 이를 바탕으로 수학 문제해결에 유용한 시각적 표현을 효과적으로 지도하기 위한 방안을 모색한 것이다. 연구문제 해결을 위해 서울D초등학교 4학년 1개 학급을 대상으로 학생들의 문제해결 과정에서의 시각적 표현이 어떠한지에 관한 검사를 실시하고 분석하였으며, 문제해결과정에서의 시각적 표현에 특징을 보이는 학생 4명을 선정 심층면담을 실시한 후 그 결과를 분석하였다. 학생들의 문제해결에 있어서 성취도와 문제해결과정에서의 시각적 표현의 활용사이에 깊은 관계가 있는 것으로 나타났다. 또한, 학생들이 문제해결과정에서 시각적 표현을 이용해 성공적인 문제를 해결하는 경험을 갖도록 함으로써 문제해결과정에서의 시각적 표현의 유용성을 인식할 수 있게 되었다.

Keywords

References

  1. 교육과학기술부 (2008). 초등학교 교육과정 해설(IV)-수학, 과학, 실과-. 광주: 한솔사 Ministry of Education (2008). Elementary curriculum commentary (IV) - Mathematics, science, and practical course-. Kwangju:Hansolsa.
  2. 김민경.권혁진 (2010). 수학 문제 해결에서 학업성취도에 따를 표상 활용 능력과 특징 분석. 한국수학교육학회지 시리즈 E <수학교육 논문집>, 24(2), 475-502. Kim, M. & Kown, H. (2010). An analysis of representation usage ability and characteristics in solving math problems according to students' academic achievement. Journal of the Korean Society of Mathematical Education. Series E, 24(2), 475-502.
  3. 김영국 (2008). 수학적 표현의 교수학적 의의. 한국수학교육학회 <전국수학교육 연구대회 프로시딩>, 제 41회, (pp. 21-32.) Kim, Y. (2008). On the pedagogical significance of mathematical representations. Proceedings of the 41st National Mathematics Education Research Conference, Korea, (pp. 21-32.)
  4. 김유정.백석윤 (2004). 초등 수학 문제해결 과정에 사용되는 표현 방법에 대한 연구. 한국초등수학교육학회지, 9(2), 85-110. Kim, Y. & Beak, S. (2004). A study of the representation in the elementary mathematical problem-solving process. Journal of Elementary Mathematics Education in Korea, 9(2), 85-110.
  5. 김종백.이성원 (2011). 시각적 스키마 프로그램이 문장제 표상과 문제해결력에 미치는 효과. 대한수학교육학회지 <학교수학>, 13(1), 155-173. Kim, J. & Lee, S. (2011). Effects of the schema-based instructional program on word problem representation and solving ability. Journal of Korea Society of Educational Studies in Mathematics School Mathematics, 13(1), 155-173.
  6. 나일주.성은모.박소영 (2010). 초등학생의 시각화 경향성이 문제해결력에 미치는 효과. 초등교육연구, 23(4), 509-534. Rha, I., Sung, E. & Park, S. (2010). Relationships between elementary students` visualization tendency and problem-solving ability. Research of Elementary Education, 23(4), 509-534.
  7. 박애란.김애화 (2010). 도식을 활용한 표상전략이 수학학습부진학생의 곱셈과 나눗셈 문장제 문제해결에 미치는 효과. 학습장애연구, 7(3), 105-122. Park, E. & Kim, E. (2010). The effects of schema-based representation strategy in multiplication and division For students with mathematical difficulties. Learning Disabilities, 7(3), 105-122.
  8. 윤여주.강신포.김성준 (2010). 시각화가 초등기하문제해결에 미치는 영향. 한국학교수학회논문집, 13(4), 655-677. Yoon, Y., Gang, S. & Kim, S. (2010) An influence of visualization on geometric problem solving in the elementary mathematics. Journal of the Korea Society of Mathematical Education, 13(4), 655-677.
  9. 이양미.전평국 (2005). 초등학교 3학년 학생의 수학적 문제 해결에서의 표상과 표상의 정교화 과정 분석. 한국수학교육학회지 시리즈 A <수학교육>, 44(4), 627-651. Lee, Y. & Jeon, P. (2005). 3rd grade students' representation in mathematical problem solving and analysis of the refinement the process of representation. Journal of the Korea Society of Mathematical Education. Series A, 44(4), 627-651.
  10. 이태수.유재연 (2006). 의미구조에 따른 표상기법이 수학학습부지 및 수학학습 장애아동의 문장제 문제 해결능력에 미치는 효과. 특수교육저널 : 이론과 실천, 7(2), 1-21. Lee, T. & You, J. (2006). Effects of semantics-based-representation instruction on the arithmetic word problem solving performance of students with low achievement and mathematics learning disabilities. Journal of Special Education : Theory and Practice, 7(2), 1-21.
  11. 장혜원 (1997). 수학학습에서의 표현 및 표상에 관한 연구 -표상 모델 개발을 중심으로. 서울대학교 박사학위 논문. Jang, H. (1997). A study on the representations in mathematics learning : Focused on the development of a representation model. Unpublished doctoral dissertation, Seoul National University, Seoul.
  12. 황현미.방정숙 (2009). 수학 문제 해결과정에서 초등학교 6학년 학생들의 시각적 표현에 관한 연구. 한국수학교육학회 시리즈 C <초등수학교육>, 12(2), 81-97. Hwang, H. & Pang, J. (2009). A study on the 6th graders` use of visual representations in mathematical problem solving. Journal of the Korea Society of Mathematical Education. Series C, 12(2), 81-97.
  13. 황혜정.나귀수.최승현.박경미.임재훈.서동엽(2004). 수학교육학 신론. 서울: 문음사. Hwang, H., Rha, G., Choe, S., Park, K., Yim, J. & Seo, D. (2004). Theology of mathematics education. Seoul: Muneumsa.
  14. Diezmann, C. M. (2002). Enhancing students' problem solving through diagram use. Australian Primary Mathematics Classroom, 7(3), 4-8.
  15. George, E. A. (1999). Male and female calculus students; use of visual representation. In O. Zaslavsky (Ed). Proceedings of the 23rd annual meeting of the international group for the psychology of mathematics education 1, (pp. 17-25.) Haifa, Israel: PME.
  16. Hayes, J. R. (1989). The complete problem solver (2nd ed.) Hillsdale, NJ: Lawrence Erlbaum Associates.
  17. Hegarty, M. & Kozhevnikov, M. (1999). Types of visual-spatial representations and mathematical problem solving. Journal of Educational Psychology, 91(4), 684-689. https://doi.org/10.1037/0022-0663.91.4.684
  18. Jitendra, A. K., Star, J. R., Rodriguze, M., Lindell, M & Someki, F. (2011). Improving students' proportional thinking using scheme-based instruction. Learnig and Instruction, 21, (pp. 731-745.) https://doi.org/10.1016/j.learninstruc.2011.04.002
  19. Kell, R. R., Gaustad, M., Porter, J. & Fonzi, J. (2007). Visual-Spatial representation in mathematical problem solving by deaf and hearing students. NY: Oxford University Press Inc.
  20. Kozhevnikov, M., Hegarty, M., & Mayer, R. E. (2002). Revising the visualizer/verbalizer dimension: Evidence for two types of visualizers. Cognition & Instruction, 20, 47-77. https://doi.org/10.1207/S1532690XCI2001_3
  21. National Council of Teachers of Mathematics (2000). Principle and standards for school mathematics. Reston, VA: The Author.
  22. 류희찬.조완영.이경화.나귀수.김남균.방정숙 공역(2007). 학교수학을 위한 원리와 규준, 서울: 경문사.
  23. Nunokawa, K. (1994). Solver's structures of a problem situation and their global restructuring, Journal of Mathematical Behavior 13, 275-297. https://doi.org/10.1016/0732-3123(94)90009-4
  24. Nunokawa, K. (2006). Using drawings and generating information in mathematical problem solving process. Eurasia Journal of Mathematical, Science & Technology Education 2(3), 33-54.
  25. Patton, M. Q. (2002). Qualitative research & evaluation method. Thousand Oaks, CA: Sage Publications.
  26. Polya, G. (1957). How to solve it. 우정호 역 (2002). 어떻게 문제를 풀 것인가. 서울: 교우사.
  27. Stylianous, D. A. & Silver, E. A. (2004). The role of visual representations in advanced mathematical problem solving: an examination of expert-novice similarities and difference. Mathematical Thinking and Learning 6(4), (pp. 353-387.) https://doi.org/10.1207/s15327833mtl0604_1
  28. van Garderen, D. (2007). Teaching students with LD to use diagrams to solve mathematical word problems. Journal of Learning Disabilities, 40(6), 540-553. https://doi.org/10.1177/00222194070400060501
  29. van Garderen, D. & Montague, M. (2003). Visual-spatial representation, mathematical problem solving, and students of varying abilities. Learning Disabilities Research & Practice, 18(4), (pp. 246-254.) https://doi.org/10.1111/1540-5826.00079
  30. Zhaner, D. & Corter, J. E. (2010). The process of probability problem solving: Use of external visual representations. Mathematical Thinking and Learning, 12, (pp. 177-204.) https://doi.org/10.1080/10986061003654240