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An analysis of 6th graders' cognitive structure about division of fraction - Application of Word Association Test(WAT) -

분수의 나눗셈과 관련된 초등학교 6학년 학생들의 인지구조 분석 - 단어연상검사(Word Association Test) 적용 -

  • Received : 2014.03.18
  • Accepted : 2014.08.12
  • Published : 2014.08.31

Abstract

The purpose of this study is to understand the difference of cognitive structure depending on the level of the 6th graders' problem-solving abilities about the division of fraction and to propose a method for improving the 6th graders' understanding about the division of fraction through the word association test. The following is the findings from this study. 1)The lower level students' is, the lower the step that the chunk appeared in cognitive structure is. 2)The basic level students' association frequency between any two concepts was less than the excellent level students and the ordinary level students' it. 3)The basic level students' connection number between concepts was far less than the excellent level students and the ordinary level students' it. 4)The connection between natural number and unit fractions, subtraction of fraction and division of fraction, division of fraction and reduction to common denominator, and division of fraction and common multiple that expected in this study did not appear in the three groups.

Keywords

References

  1. 권점례 (2012). 우수학력과 기초학력 미달 학생들의 수학과 학업성취도 특성 분석, 수학교육 논문집 26(1), 29-50. (Kwon, J. R. (2012). Comparison on proficient level and below basic level students' mathematical achievement in the National Achievement Evaluation and Assessment, Communications of mathematical education 26(1), 29-50.)
  2. 김경미, 강완 (2008). 초등학생들이 분수의 나눗셈에서 보이는 반복적 오류 분석, 한국초등수학교육학회지11(1), 1-19. (Kim, K. M. & Kang, W. (2008). An Analysis on the Repeated Error Patterns in Division of Fraction by Elementary Students. Education of primary school mathematics 11(1), 1-19.)
  3. 김경미, 황우형 (2011). 분수의 곱셈과 나눗셈에 대한 학생의 이해와 문장제 해결의 관련성 분석, 수학교육 50(3), 337-354. (Kim, K. M. & Whang, W. H. (2011). An Analysis of the Relationship between Students' Understanding and their Word Problem Solving Strategies of Multiplication and Division of Fractions, The Mathematical Education 50(3), 337-354.) https://doi.org/10.7468/mathedu.2011.50.3.337
  4. 김경미, 황우형 (2012). 자연수와 분수 연산에 대한 학생들의 이해 분석, 수학교육 51(1), 21-45. (Kim, K. M. & Whang, W. H. (2012). An analysis of students' understanding of operations with whole numbers and fractions, The Mathematical Education 51(1), 21-45.) https://doi.org/10.7468/mathedu.2012.51.1.021
  5. 김명운, 장경윤 (2009). 맥락화를 통한 분수의 곱셈과 나눗셈 지도, 학교수학 11(4), 685-706. (Kim, M. W. & Chang, K. Y. (2009). Teaching Multiplication & Division of Fractions through Contextualization, School Mathematics 11(4), 685-706.)
  6. 김민경 (2003). 나눗셈 개념에 대한 초등예비교사의 이해도 분석, 학교수학 5(2), 223-240. (Kim, M. K. (2003). Knowledge of Preservice Elementary Teachers with Respect to Division. School Mathematics 5(2), 223-240.)
  7. 김민경 (2009). 초등학생의 분수 이해 분석-6학년의 분수 개념 및 분수 나눗셈을 중심으로-, 한국학교수학회논문집 12(2), 151-170. (Kim, M. K. (2009). A Study of the Sixth Graders' Knowledge of Concepts and Operations about Faction, Journal of the Korean School Mathematics 12(2), 151-170.)
  8. 김성훈 (2005). 인지구조모형에 근거한 학생의 지식상태의 진단, 교육학연구 43(1), 81-107. (Kim, S. H. (2005). Diagnosis of students' knowledge states based on a cognitive model: An application of Rule-space theory, Korean journal of educational research 43(1), 81-107.)
  9. 박교식, 권석일 (2011). 예비초등교사들이 분수 포함제의 몫과 나머지 구하기에서 범하는 오류에 대한 분석, 초등수학교육 14(3), 317-328. (Park, K. S. & Kwon, S. I. (2011). A study on errors committed by Korean prospective elementary teachers in finding and interpreting quotient and remainder within measurement division of fraction, Education of primary school mathematics 14(3), 317-328.)
  10. 박교식, 송상헌, 임재훈 (2004). 우리나라 예비 초등 교사들의 분수 나눗셈의 의미 이해에 대한 연구, 학교수학 6(3), 235-249. (Park, K. S., Song, S. H., & Yim, J. H. (2004). A Study on Understanding of the Elementary Teachers in Pre-service with respect to Fractional Division, School Mathematics 6(3), 235-249.)
  11. 방정숙, Ye Ping Li (2008). 예비 초등 교사들의 분수 나눗셈에 대한 지식 분석, 수학교육 47(3), 291-310. (Pang, J. S. & Ye Ping Li (2008). An Analysis on the Prospective Elemenary Teachers' Knowledge, The Mathematical Education 47(3), 291-310.)
  12. 방정숙, 이지영 (2009a). 사례 연구를 통한 분수 나눗셈의 연산 감각 분석, 학교수학 11(1), 71-91. (Pang, J. S. & Lee, J. Y. (2009a). An Analysis of Operation Sense in Division of Fraction Based on Case Study, School Mathematics 11(1), 71-91.)
  13. 방정숙, 이지영 (2009b). 분수의 곱셈과 나눗셈에 관한 초등학교 수학과 교과용 도서 분석, 학교수학 11(4), 723-743. (Pang, J. S. & Lee, J. Y. (2009b). An Analysis of the Multiplication and Division of Fractions in Elementary Mathematics Instructional Materials, School Mathematics 11(4), 723-743.)
  14. 백선수 (2004). 비형식적 지식을 이용한 대안적인 분수나눗셈의 형식화 방안에 관한 연구, 초등수학교육 8(2), 97-113. (Baek, S. S. (2004). A Study on Alternative Formalization of Division of Fractions Using Informal Knowledge, Education of primary school mathematics 8(2), 97-113.)
  15. 송미영, 이영선, 박윤수 (2011). 인지진단모형을 통한 국가수준 학업성취도 평가 결과 분석 및 성적 보고 방법 탐색. 서울: 한국교육과정평가원. (Song, M. Y., Lee. Y. S., & Park. Y. S. (2011). Analysis and score reporting based in cognitive diagnostic models using tne National Assessment of Educational Archievement. Seoul: Korea Institute of Curriculum and Evaluation.)
  16. 신재홍 (2010). 분수나눗셈을 해결하기 위한 학생들의 자기-생성 알고리듬 구성에 관한 연구, 학교수학 12(3), 439-454. (Shin, J. H. (2010). Construction of a Student-Generated Algorithm for Fraction Measurement Division, School Mathematics 12(3), 439-454.)
  17. 신준식 (1996). 실제적 접근 방법에 의한 분수 교수-학습에 대한 연구. 한국교원대학교대학원 박사학위 논문. (Shin, J. S. (1996). A study on the teaching and learning of fraction based on the realistic approach. Doctoral dissertation, Korea National University of Education.)
  18. 이영주, 이광호, 이효진 (2012). 분수의 나눗셈에 대한 학습자의 인지구조, 한국초등수학교육학회지 16(2), 295-320. (Lee, Y. J., Lee, K. H., & Lee, H. J. (2012). A Study on Learner's Cognitive Structure in Division of Fraction, Elementary Mathematics Education 16(2), 295-320.)
  19. 임재훈 (2007). 카테시안 곱의 역 맥락에서 분수의 나눗셈, 학교수학 9(1), 13-28. (Yim, J. H. (2007). Division of Fractions in the Contexts of the Inverse of a Cartesian Product, School Mathematics 9(1), 13-28.)
  20. 임재훈, 김수미, 박교식 (2005). 분수 나눗셈 알고리즘 도입 방법 연구, 학교수학 7(2), 103-121. (Yim, J. H., Kim, S. M., & Park, K. S. (2005). Different Approaches of Introducing the Division Algorithm of Fractions: Comparison of Mathematics Textbooks of North Korea, South Korea, China, and Japan, School Mathematics 7(2), 103-121.)
  21. 임규혁, 임웅 (2007). (학교학습 효과를 위한) 교육심리학. 서울: 학지사. (Lim, K. H. & Lim. W. (2007). Educational psychology. Seoul: hakjisa.)
  22. 전평국, 박성선 (2009). 수학교육연구방법. 서울: 교우사. (Jeon, P. K. & Park, S. S. (2009). Research methods in mathmatics education. Seoul: kyowoosa.)
  23. 전평국, 박혜경 (2003). 분수 나눗셈의 개념적 이해를 위한 관련 지식의 연결 관계 분석, 수학교육논문집 15, 71-76. (Jeon, P. & Park, H. (2003). The analysis of the relationship about knowledge connection for conceptual understanding of fraction division, Communications of Mathematical Education, 15, 71-76.)
  24. 정현주 (2000). 학습 내용이 어려워지는 이유, 경희대학교 교육문제연구소 논문집 16, 219-233. (Jeung, H. J. (2000). The reason why some material is difficult to understand? Educational research community of Kyonghee University 16, 219-233.)
  25. 한광희 (1997). 인지과학과 인지심리학의 관계 고찰, 인문과학 76-77, 403-424. (Han, K. H. (1997). The Relation of Cognitive Science and Cognitive Psychology, The Liberal Arts 76-77, 403-424.)
  26. Aydin, F., & Tasar, M. F. (2010). An investigation of pre-service science teachers' cognitive structures and ideas about the nature of technology. Journal of Kirsehir Education Faculty, 11(4), 209-221.
  27. Bahar, M., Johnstone, A., & Sutcliffe, R. (1999). Investigation of students' cognitive structure in elementary genetics through word association tests. Journal of Biological Education, 33(3), 134-141. https://doi.org/10.1080/00219266.1999.9655653
  28. Bahar, M., & Tongac, E. (2009). The effect of teaching approaches on the pattern of pupils' cognitive structure: Some evidence from the field. The Asia-Pacific Education Researcher, 18(1), 21-45.
  29. Cachapuz, A., & Maskill, R. (1987). Detecting changes with learning in the organization of knowledge: Use of word association tests to follow the learning of collision theory. International Journal of Science Education, 9(4), 491-504. https://doi.org/10.1080/0950069870090407
  30. Ercan, F., Tasdere, A., & Ercan, N. (2010). Observation of cognitive structure and conceptual changes through word associations tests. Journal of Turkish Science Education, 7(2), 155-158.
  31. Flores, A. (2002). Profound understanding of division of fractions. In B. Litwiller & G. Bright (Eds.), Making Sense of Fractions, Ratios, and Proportions: 2002 Yearbook, 237-246. Reston, VA:NCTM
  32. Garskof, B. E., & Houston, J. P. (1963). Measurement of verbal relatedness: An idiographic approach. Psychological Review, 70(3), 277-288. https://doi.org/10.1037/h0041879
  33. Geeslin, W. E., & Shavelson, R. J. (1975). Comparison of content structure and cognitive structure in high school students' learning of probability. Journal for Research in Mathematics Education, 6(2), 109-120. https://doi.org/10.2307/748612
  34. Haylock, D. W. (1982). Understanding in mathematics:Making connections. Mathematics Teaching, 98, 54-56.
  35. Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K.C., Wearne, D., Murray, H. et al. (1997). MakingSense: teaching and learning mathematics withunderstanding. USA: University of Wisconsin Foundation. 김수환, 박영희, 이경화, 한대희 공역.(2004). 어떻게 이해하지?. 서울: 경문사.
  36. Ifenthaler, D., Masduki, I., & Seel, N. M. (2011). The mystery of cognitive structure and how we can detect it: Tracking the development of cognitive structures over time. Instructional Science, 39(1), 41-61. https://doi.org/10.1007/s11251-009-9097-6
  37. Ma, L. (1999). Knowing and teaching elementarymathematics: Teachers' understanding offundamental mathematics in China and the UnitedStates. Mahwah, New Jersey: Lawrence ErlbaumAssociates. 신현용, 승영조 역. (2002). 초등학교 수학이렇게 가르쳐라. 서울: 승산.
  38. Martindale, C. (1991). Cognitive psychology: A neural-network approach. Thomson Brooks/Cole Publishing Co. 신현정 역. (1994). 인지심리학-신경회로망적 접근-. 서울: 교육과학사.
  39. Mervis, C. B., & Rosch, E. (1981). Categorization of natural objects. Annual Review of Psychology, 32(1), 89-115. https://doi.org/10.1146/annurev.ps.32.020181.000513
  40. Novak, J. D., & Canas, A. J. (2006). The theory underlying concept maps and how to construct and use them. Technical Report No. IHMC CmapTools 2006-01. Pensacola, FL: Institute for Human and Machine Cognition.
  41. Novak, J. D., & Gowin, D. B. (1984). Learning how to learn. New York: Cambridge University Press.
  42. Resnick, L. B., & Ford, W. W. (1981). The psychologyof mathematics for instruction L. ErlbaumAssociates. 구광조, 오병승, 전평국 공역. (2007). 수학학습 심리학. 서울: 교우사.
  43. Shavelson, R. J. (1974). Some methods for examining content structure and cognitive structure in instruction 1. Educational Psychologist, 11(2), 110-122. https://doi.org/10.1080/00461527409529132
  44. Sinicrope, R., Mick, H. W., & Kolb, J. R. (2002). Interpretations of fraction division. In B. Litwiller & G. Bright (Eds.), Making Sense of Fractions, Ratios, and Proportions: 2002 Yearbook, 153-161. Reston, VA: NCTM
  45. Wu, Y. T., & Tsai, C. C. (2005). Development of elementary school students' cognitive structures and information processing strategies under longterm constructivist‐oriented science instruction. Science Education, 89(5), 822-846. https://doi.org/10.1002/sce.20068