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http://dx.doi.org/10.7468/jksmee.2015.29.2.215

The Effect of the Fraction Comprehension and Mathematical Attitude in Fraction Learning Centered on Various Representation Activities  

Ahn, Ji Sun (Bondong Elementary School)
Kim, Min Kyeong (Ewha Womans University)
Publication Information
Communications of Mathematical Education / v.29, no.2, 2015 , pp. 215-239 More about this Journal
Abstract
A goal of this study is figuring out how fraction learning centered on various representation activities influences the fraction comprehension and mathematical attitudes. The study focused on 33 4th-grade students of B elementary school in Seoul. In the study, 15 fraction learning classes comprising enactive, iconic, and symbolic representations took place over 6 weeks. After the classes, the ratio of the students who achieved relational understanding increased and the students averagely recorded 90 pt or more on the fraction comprehension test I, II and III. Two-dependent samples t-test was conducted to analyze a significant difference in mathematical attitudes between pre-test and post-test. On the test result, there was the meaningful difference with 0.01 level of significance. To conclude, the fraction learning centered on various representation activities improves students' relational understanding and fraction understanding. In addition, the fraction learning centered on various representation activities gives positive influences on mathematical attitudes since it increases learning orientation, self-control, interests, value cognition, and self-confidence of the students and decreases fears of the students.
Keywords
relational understanding; representation; EIS theory; fraction comprehension;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
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1 추은영 (2003). 이분모 분수의 덧셈과 뺄셈에서 오류와 원인 분석. 춘천교육대학교 교육대학원 석사학위논문.(Chu, E. Y. (2003). An analysis on the errors and their causes in addition and subtraction of fraction with different denominator. Master's Thesis, Chuncheon National University of Education.)
2 최승현.구자옥.김주훈.박상욱.오은순.김재우 (2013). PISA와 TIMSS 결과에 기반한 우리나라 학생의 정의적 특성 함양 방안. 한국교육과정평가원연구보고 RRE 2013-8.(Choi, S. H., Koo, J. O., Kim, J. H., Park, S. W., Oh, E. S., & Kim, J. W. (2013). Improvable way of affective characteristic for Korean student based on the results of PISA and TIMSS. Research report of Korea Institute for Curriculum and Evalution RRE 2013-8.)
3 최창우 (2006). 초등수학교육의 이해. 서울: 경문사.(Choi, C. W. (2006). Understanding of elementary mathematics education. Seoul: Kyungmoon Sa.)
4 현동희 (2000). 초등학교 수학 수업에서 패턴 블록의 활용 방안 연구. 인천교육대학교 교육대학원 석사학위논문.(Hyun, D. H. (2000). A study on the method for using the pattern blocks in the mathematiocs class of elementary school. Master's Thesis, Incheon National University of Education.)
5 홍은숙.강완 (2008). 분수 개념에 관한 초등학생의 비형식적 지식. 한국초등수학교육학회지, 12(1), 59-78.(Hong, E. S., & Kang, W. (2008). The informal knowledge of elementary school students about the concepts of fraction. Journal of Elementary Mathematics Education in Korea, 12(1), 59-78.)
6 황민영 (2009). 중학교 1학년 학생의 관계적 이해와 도구적 이해에 기초한 평면도형의 성질 지도 방안 연구. 아주대학교 대학원 석사학위논문.(Hwang, M. Y. (2009). A study on the plane figure teaching based on relational understanding and instrumental understanding of 1st grade middle school students. Master's Thesis, Ajou University.)
7 Armstrong, B. E., & Bezuk, N. (1995). Multiplication and division of fractions: The search for meaning, In J. T. Sowder & B. P. Schappelle (Eds.), Providing a foundation for teaching mathematics in the middle grades (p. 85-119). New York, NY: State University of New York Press.
8 Behr, M. J., & Post, T. R (1992). Teaching rational number and decimal concepts, In T. R. Post (Ed.), Teaching mathematics in Grades K-8 : Research-based methods (pp. 201-248). Needham Heights, MA: Allyn and Bacon.
9 Bezuk, N., & Bieck, M. (1992). Current research on rational numbers and common fractions: Summary and implications. In D. T. Owens (Ed.), Research ideas for the classroom: Middle grade mathematics (pp. 118-136). NY: Macmillan Publishing Company.
10 Bezuk, N., & Cramer, K. (1989). Teaching about fractions: What, when, and how? In P. Trafton (Ed.), New directions for elementary school mathematics - 1989 yearbook (pp.156-167). Reston, VA: NCTM.
11 Bruner, J. S. (1964). The course of cognitive growth. American Psychologist, 19, 1-15.   DOI
12 Connell, M. L., & Peck, D. M. (1993). Report of a conceptual change intervention in elementary mathematics. Journal of Mathematical Behavior, 12, 329-350.
13 Cramer, K., Post, T., & DelMas, R. (2002). Initial Fraction Learning by Fourth- and Fifth-Grade Students: A Comparison of the Effects of Using Commercial Curricula with the Effects of Using the Rational Number Project Curriculum. Journal for Research in Mathematics Education, 33(2), 111-144.   DOI
14 Freudental, H. (1983). Fractions, didactical phenomenology of mathematical structures. Dordrecht, Netherlands: D. Reidel Publishing Company.
15 Hiebert, J., & Behr, M. (1988). Capturing the major themes. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 1-18). Hillsdale, NJ: Erlbaum.
16 Kouba, V., Zawojewski, J., & Strutchens, M. (1997). What do students know about numbers and operations? In P. A. Kenney & E. A. Silver (Eds.), Results from the sixth mathematics assessment of the National Assessment of Educational Progress (pp. 87-140). Reston, VA: NCTM.
17 Skemp, R. R. (1987). Psychology of learning mathematics. 황우형 역(2000). 수학학습 심리학. 서울: 사이언스북스.
18 Lesh, R., Behr, M., & Post, T. (1987). Rational number relations and proportions. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 41-58). Hillsdale, NJ: Erlbaum.
19 Moore, R. C. (1994). Making transition to formal proof. Educational Studies in Mathematics, 27, 249-266.   DOI
20 Moss, J., & Case, R. (1999). Developing children's understanding of the rational numbers: A new model and an experimental curriculum. Journal for Research in Mathematics Education, 30, 122-147.   DOI
21 Streefland, L. (1982). Subtracting fractions with different denominators. Educational Studies in Mathematics, 13, 233-255.   DOI
22 Post, T., Behr, M., & Lesh, R. (1982). Interpretations of rational number concepts. In L. Silvey & J. Smart (Eds.), Mathematics for Grades 5-9, 1982 NCTM Yearbook (pp. 59-72). Reston, VA: NCTM.
23 Vinner, S. (1991). The role of definition in teaching and learning of mathematics. In D. Tall (Ed.), Advanced mathematical thinking (pp. 65-81). Dordrecht: Kluwer.
24 Watson, J. M., Campbell, K. J., & Collis, K. F. (1993). Multimodal functioning in understanding fractions. Journal of Mathematical Behavior, 12, 45-62.
25 김경희 (2007). 수학교과에서 관계적이해를 위한 소프트웨어활용에 관한연구. 조선대학교 교육대학원 석사학위논문.(Kim, K. H. (2007). A study on software application for relational understanding in mathematics subject. Master's Thesis, Chosun University.)
26 구광조.오병승.전평국 (1995). 수학학습심리학. 서울: 교우사.(Koo, G. J., Oh, B. S., & Jeon, P. K. (1995). The psychology of mathematics for instruction. Seoul: Kyowoo Sa.)
27 구미종 (2002). 패턴 블록을 활용한 분수학습에서 초등학교 4학년 학생의 학업성취도 및 태도에 관한 연구. 이화여자대학교 교육대학원 석사학위논문.(Koo, M. J. (2002). A study on the achievement and attitude of elementary school 4th graders in fraction learning using pattern blocks. Master's Thesis, Ewha Womans University.)
28 권성룡 (1997). 측정활동을 통한 분수학습 프로그램의 효과에 관한 연구. 한국교원대학교 대학원 석사학위논문.(Kwon, S. R. (1997). A study on the effect of the instructional program of fraction based on measuring activities. Master's Thesis, Korea National University of Education.)
29 김선영 (2003). 분수의 덧셈, 뺄셈에 대한 오류 유형 분석 및 효과적인 지도방안 연구. 국민대학교 교육대학원 석사학위논문.(Kim, S. Y. (2003). The error type analysis against the addition and a subtraction of the fountain and effective map plan research. Master's Thesis, Kookmin University.)
30 김미영.백석윤 (2010). 분수 덧셈, 뺄셈에서 나타나는 인지적 장애 현상 분석. 한국초등수학교육학회지, 14(2), 241-262.(Kim, M. Y., & Paik, S. Y. (2010). An analysis on cognitive obstacles using addition and subtraction with fractions. Journal of Elementary Mathematics Education in Korea, 14(2), 241-262.)
31 김영국 (2008). 수학적 표현의 교수학적 의의. 한국수학교육학회지 시리즈 A <수학교육>, 47(2), 155-168.(Kim, Y. K. (2008). On the pedagogical significance of mathematical representations. J. Korea Soc. Math. Ed. Ser. A: The Mathematical Education, 47(2), 155-168.)
32 노지선 (2005). Skemp의 관계적 이해를 도입한 고등학교 함수영역의 지도 방안 연구. 동국대학교 교육대학원 석사학위논문.(Noh, J. S. (2005). A study on the measure to teach the function section of high school with Skemp's relational understanding. Master's Thesis, Dongguk University.)
33 김옥경 (1997). 초등학교 6학년 학생들의 분수 개념 이해 및 분수 수업 방안에 대한 연구. 한국교원대학교 대학원 석사학위논문.(Kim, O, K. (1997). A study on conceptual understanding of fractions for 6th graders and instructional methods for fractions. Master's Thesis, Korea National University of Education.)
34 김용태.신봉숙.최대욱.이순희 (2005). 유추를 통한 분수 연산에 관한 연구. 한국수학교육학회지 시리즈 E <수학교육논문집>, 19(4), 715-731.(Kim, Y. T., Shin, B. S., Choi, D. U., & Lee, S. H. (2005). A study on operations with fractions through analogy, J. Korea Soc. Math. Ed. Ser. E: Communications of Mathematical Education, 19(4), 715-731.)
35 김정식 (2005). 초등학교 수학교과서에 나타난 분수의 덧셈과 뺄셈에 대한 분석. 서울교육대학교 교육대학원 석사학위논문.(Kim, J. S. (2005). An analysis of addition and subtraction of fractions in elementary mathematics textbooks. Master's Thesis, Seoul National University of Education.)
36 명혜경 (2007). 초등학생의 수학적 능력 향상을 위한 과정중심 수학 쓰기 프로그램 개발. 이화여자대학교 교육대학원 석사학위논문.(Myung, H. K. (2007). The development of the progress based mathematics writing program for improving mathematical abilities in elementary school. Master's Thesis, Ewha Womans University.)
37 박성택 (2006). 수학 학습 심리와 교수-학습 전략. 서울: 경문사.(Park, S. T. (2006). The psychology of learning mathematics and teaching and learning strategies. Seoul: Kyungmoon Sa.)
38 박정.정은영.김경희.한경혜.이서영 (2004). 수학, 과학 성취도 추이변화 국제비교 연구 -TIMSS 2003 결과 보고서. 한국교육과정평가원연구보고 RRE 2004-3-2.(Park, J., Jeong, E. Y., Kim, K. H., Han, K. H. & Lee, S. Y. (2004). Trends in International Mathematics and Science Study -TIMSS 2003 result report, Research report of Korea Institute for Curriculum and Evalution RRE 2004-3-2.)
39 방정숙.이지영 (2009). 분수의 덧셈과 뺄셈에 관한 초등학교 수학과 교과용도서 분석. 한국초등수학교육학회지, 13(2), 285-304.(Bang, J. S., & Lee, J. Y. (2009). An analysis of the addition and subtraction of fractions in elementary mathematics instructional materials, Journal of Elementary Mathematics Education in Korea, 13(2), 285-304.)
40 신준식 (1996). 실제적 접근 방법에 의한 분수 교수-학습 지도에 대한 연구. 한국교원대학교 대학원 박사학위논문.(Shin, J. S. (1996). A study on the teaching and learning of fraction based on the realistic approach. Doctorial Dissertation, Korea National University of Education.)
41 염석일 (2001). 현실적 수학교육론에 의한 분수지도에 관한 기초연구. 진주교육대학교 교육대학원 석사학위논문.(Yeom, S. I. (2001). A study on the teaching of fractions based on realistic mathematics education. Master's Thesis, Jinju National University of Education.)
42 유현주 (1995). 분수개념의 교수현상학적 분석과 학습 지도 방향에 관한 연구. 서울대학교 대학원 박사학위논문.(Yoo, H. J. (1995). A study on ways of instructing and a phenomenological analysis on fraction concept. Doctorial Dissertation, Seoul National University.)
43 이종희.김수진 (2010). PISA 2003 결과에서 수학의 정의적 영역에 영향을 주는 변인 분석. 대한수학교육학회지 <학교수학>, 12(2), 219-237.(Lee, C. H., & Kim, S. J. (2010). Analysis of affective factors on mathematics learning according to the results of PISA 2003. Journal of the Korea Society of Educational Studies in Mathematics School Mathematics, 12(2), 219-237.)
44 이종희.김선희.김수진.김기연.김부미.윤수철.김윤민 (2011). 수학 학습에 대한 정의적 성취 검사 도구 개발 및 검증. 한국수학교육학회지 시리즈 A <수학교육>, 50(2), 247-261.(Lee, C. H., Kim, S. H., Kim, S. J., Kim, K. Y., Kim, B. M., Yoon, S. C., & Kim, Y. M. (2011). Development and verification of an affective inventory in Mathematical Learning. J. Korea Soc. Math. Ed. Ser. A: The Mathematical Education, 50(2), 247-261.)
45 조병윤 (1992). 분수계산오류의 효과적인 교정 지도방안. 한국교원대학교 대학원 석사학위논문.(Joh, B. Y. (1992). A study on effective teaching for the remedy of errors in fraction computation. Master's Thesis, Korea National University of Education.)
46 조지민.김수진.김미영.옥현진.임해미.손수경 (2012). 학업성취도 국제 비교 연구 결과에 기초한 우리나라 학생들의 정의적 성취 향상 지원 방안. 한국교육과정평가원 연구보고 CRE 2012-4.(Joh, J. M., Kim, S. J., Kim, M. Y., Ok, H. J. Lim, H. M., & Sohn, S. K. (2012). Supportive way for improving affective achievement of Korean student based on the results of achievement international comparison. Research report of Korea Institute for Curriculum and Evalution CRE 2012-4.)