무리수 단원에 대한 교과서 분석 연구: 과정과 대상의 관점으로
A textbook analysis of irrational numbers unit: focus on the view of process and object
0
조회
0
다운로드
7
인용
0
참고문헌
키워드
초록
The representation of irrational numbers has a key role in the learning of irrational numbers. However, transparent and finite representation of irrational numbers does not exist in school mathematics context. Therefore, many students have difficulties in understanding irrational numbers as an ‘Object’. For this reason, this research explored how mathematics textbooks affected to students’ understanding of irrational numbers in the view of process and object. Specifically we analyzed eight textbooks based on current curriculum and used framework based on previous research. In order to supplement the result derived from textbook analysis, we conducted questionnaires on 42 middle school students. The questions in the questionnaires were related to the representation and calculation of irrational numbers. As a result of this study, we found that mathematics textbooks develop contents in order of process-object, and using ‘non repeating decimal’, ‘numbers cannot be represented as a quotient’, ‘numbers with the radical sign’, ‘number line’ representation for irrational numbers. Students usually used a representation of non-repeating decimal, although, they used a representation of numbers with the radical sign when they operate irrational numbers. Consequently, we found that mathematics textbooks affect students to understand irrational numbers as a non-repeating irrational numbers, but mathematics textbooks have a limitation to conduce understanding of irrational numbers as an object.
Abstract
The representation of irrational numbers has a key role in the learning of irrational numbers. However, transparent and finite representation of irrational numbers does not exist in school mathematics context. Therefore, many students have difficulties in understanding irrational numbers as an ‘Object’. For this reason, this research explored how mathematics textbooks affected to students’ understanding of irrational numbers in the view of process and object. Specifically we analyzed eight textbooks based on current curriculum and used framework based on previous research. In order to supplement the result derived from textbook analysis, we conducted questionnaires on 42 middle school students. The questions in the questionnaires were related to the representation and calculation of irrational numbers. As a result of this study, we found that mathematics textbooks develop contents in order of process-object, and using ‘non repeating decimal’, ‘numbers cannot be represented as a quotient’, ‘numbers with the radical sign’, ‘number line’ representation for irrational numbers. Students usually used a representation of non-repeating decimal, although, they used a representation of numbers with the radical sign when they operate irrational numbers. Consequently, we found that mathematics textbooks affect students to understand irrational numbers as a non-repeating irrational numbers, but mathematics textbooks have a limitation to conduce understanding of irrational numbers as an object.
참고문헌 (27)
- 고호경, "중학교 수학 3" (2013), 교학사
- 김서령, "중학교 수학3" (2013), 천재교육
- 김원경, "중학교 수학 3" (2014), 비상교육
- 김흥기, "중학교에서 순환소수 취급과 무리수도입에 관한 고찰", 수학교육학연구, 14(1), pp.1~17 (2004), 대한수학교육학회
- 류희찬, "중학교 수학 3" (2015), 천재교육
- 박달원, "무한소수에 대한 학생들의 이해", 한국학교수학회논문집, 10(2), pp.237~246 (2007), 한국학교수학회
- 박윤희, "중학교 수학에서 무리수 개념에 관한 학습자의 이해 연구", 한국학교수학회논문집, 7(2), pp.99~116 (2004), 한국학교수학회
- 변희현, "무리수의 개념적 측면을 강조한 교육방안: ‘통약불가능성’을 통한 무리수 고찰", 학교수학, 4(4), pp.8~653 (2002), 대한수학교육학회
- 신보미, "실수로의 수 체계 확장을 위한 유리수의 재해석에 대하여", 한국학교수학회논문집, 11(2), pp.285~298 (2008), 한국학교수학회
- 우정호, "반영적 추상화와 조작적 수학 학습-지도", 수학교육연구, 9(2), pp.383~404 (1999)
- 우정호, "중학교 수학 3" (2013), 두산동아
- 이선비, "예비 중등 교사들의 무리수에 대한 이해", 한국학교수학회논문집, 16(3), pp.499~518 (2013), 한국학교수학회
- 이지현, "무한소수 기호: 불투명성과 투명성", 수학교육학연구, 24(4), pp.595~605 (2014), 대한수학교육학회
- 이지현, "유리수와 무리수의 합집합을 넘어서: 실수가 자명하다는 착각으로부터 어떻게 벗어날 수 있는가?", 수학교육학연구, 25(3), pp.263~279 (2015), 대한수학교육학회
- 정상권, "중학교 수학 3" (2013), 금성출판사
- 허민, "중학교 수학 3" (2015), 대교
- 황선욱, "중학교 수학 3" (2013), 좋은책신사고
- Arnon, I., "APOS theory: A framework for research and curriculum development in mathematics education" (2013), Springer Science & Business Media
- Gray, E. M., "Duality, ambiguity, and flexibility: A" proceptual" view of simple arithmetic", Journal for research in Mathematics Education, 25(2), pp.116~140 (1994)
- Moreira, P. C., "Academic mathematics and mathematical knowledge needed in school teaching practice : Some conflicting elements", Journal of Mathematics Teacher Education, 11(1), pp.23~40 (2008)
- Sfard, A., "On the dual nature of mathematical conceptions : reflections on processes and objects as different sides of the same coin", Educational Studies in Mathematics, 22, pp.1~36 (1991)
- Sirotic, N., "Irrational numbers:The gap between formal and intuitive knowledge", Educational Studies in Mathematics, 65(1), pp.49~76 (2007)
- Sirotic, N., "Irrational numbers on the number line–where are they?", International Journal of Mathematical Education in Science and Technology, 38(4), pp.477~488 (2007)
- Voskoglou, M. G., "An application of the APOS", ACE approach in teaching the irrational numbers, 2013, pp.8(1), 30~47
- Watson, A, "색다른 학교 수학" (2015), 경문사
- Zazkis, R., "Representing numbers: prime and irrational", International journal of mathematical education in science and technology, 36(2-3), pp.207~218 (2005)
- Zazkis, R., "Representing and defining irrational numbers: Exposing the missing link", CBMS Issues in Mathematics Education, 16, pp.1~27 (2010)