1 |
고은성.이경화(2007). 초등학교 6학년 학생의 비례 추론 능력 분석. 수학교육학연구, 17(4), 359-380.
|
2 |
교육과학기술부(2011a). 수학 6-1. 서울: 두산동아(주).
|
3 |
교육과학기술부(2011b). 수학과교육과정. 교육과학기술부 고시 제2011-361호 [별책 8]. 교육과학기술부.
|
4 |
교육과학기술부(2012). 수학 5-2. 서울: 두산동아(주).
|
5 |
교육인적자원부(2007). 수학과교육과정. 교육인적자원부 고시 제 2007-79호 [별책 8]. 교육인적자원부.
|
6 |
김경선.박영희(2007). 초등학생의 비례 추론 지도에 관한 연구. 학교수학, 9(4), 447-466.
|
7 |
김경희.백희수(2010). 비와 비율 영역에 대한 우리나라와 싱가포르 교육과정 및 교과서 비교-TIMSS 평가 목표와 공개문항을 중심으로. 학교수학, 12(4), 473-491.
|
8 |
김수현.나귀수(2008). 비와 비율 지도에 대한 연구. 수학교육학연구, 18(3), 309-333.
|
9 |
나귀수.황혜정.한경혜(2001). 수학과 교육목표 및 내용체계 연구(II). 연구보고 RRC 2001-9. 한국교육과정평가원.
|
10 |
박정숙(2008). 비와 비례 과제에서 가법적 전략을 사용하는 학생의 문제해결 특징. 학교수학, 10(4), 603-623.
|
11 |
안숙현.방정숙(2008). 5, 6, 7학년 학생들의 비례 추론 능력 실태 조사. 수학교육학연구, 18(1), 103-121.
|
12 |
유현주(1995). 유리수 개념의 교수현상학적 분석과 학습-지도 방향에 관한 연구. 서울대학교 대학원 박사학위논문.
|
13 |
이경화.정영옥.나귀수.김성여(2009). 수학 국정교과서 개발 사전 기획연구. 한국과학창의 재단.
|
14 |
정은실(2003a). 비 개념에 대한 교육적 분석. 수학교육학연구, 13(3), 247-265.
|
15 |
정은실(2003b). 비 개념에 대한 역사적, 수학적, 심리적 분석. 학교수학, 5(4), 421-440.
|
16 |
정은실(2013). 초등학교 수학교과서에서의 비례 추론에 대한 연구. 수학교육학연구, 23(4), 505-516.
|
17 |
홍지연.김민경(2013). 초등수학 비구조화된 문제해결 과정에서의 비례적 추론. 학교수학, 15(4), 723-742.
|
18 |
Behr, M. J., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio, and proportion. In D. A. Grouws(Ed), Handbook of Research on Mathematics Teaching and Learning. A Project of the National Council of Teachers of Mathematics (pp. 296-331). New York: Macmillan Publishing Company.
|
19 |
Bell, M., Bell, J., Bretzlauf, J., Dillard, A., Flanders, J., Hartfield, R., Issacs, A., Leslie, D. A., McBride, J., Pitvorec, K., & Saecker, P. (2007). Everyday Mathematics. The University of Chicago School Mathematics Project. Student Reference Book. Chicago: Wright Group/McGrawHill.
|
20 |
Ben-Chaim, D., Keret, Y., & Ilany, B. S. (2012). Ratio and Proportion. Research and Teaching in Mathematics Teachers' Education (Pre-and In-Service Mathematics Teachers of Elementary and Middle School Classes). Rotterdam, AW: Sense Publishers.
|
21 |
Broekman, H., van der Valk, T., & Wijers, M. (2000). Teacher knowledge needed to teach ratio and proportion in secondary school mathematics. Paper presented to the 25th ATEE Conference, Barcelona, Spain.
|
22 |
Cramer, K., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: Research implications. In D. T. Owens(Ed.), Research Ideas for the Classroom: Middle Grades Mathematics (pp. 159-178). New York: Macmillan Publishing Company.
|
23 |
Freudenthal, H. (1983). Didactical Phenomenology of Mathematical Structures. Dordrecht: D. Reidel Publishing Company.
|
24 |
De Bock, D., Verschaffel, L., & Janssens, D. (1998). The predominance of the linear model in secondary school students' solutions of word problems involving length and area of similar figures. Educational Studies in Mathematics, 35(1), 65-83.
DOI
|
25 |
Dwyer, N. K., Causey-Lee, B. J., & Irby, N. M. (2003). Conceptualizing ratios with look-alike polygons. Mathematics Teaching in the Middle School, 8(8), 426-431.
|
26 |
Feijs, E., de Lange, J., van Reeuwijk, M., Spence, M. S., & Brendefur, J. (2004). 어디까지 보이나요? Looking at an Angle. (나온교육연구소 역). 서울: 도서출판 이우. (영어원작은 1998년 출판).
|
27 |
Freudenthal, H., Janssen, G. M., & Sweers, W. J. (1976). Five Years IOWO. Educational Studies in Mathematics, 7(3), 186-367.
|
28 |
Harel, G., Behr, M., Lesh, R., & Post, T. (1994). Invariance of ratio: The case of children's anticipatory scheme for constancy of taste. Journal for Research in Mathematics Education, 25(4), 324-345.
DOI
|
29 |
Heath, T. L. (1956). Euclid The Thirteen Books of the Elements, Vol. 2 (Books III-IX). New York: Dover Publications, Inc.
|
30 |
Howe, C., Nunes, T., Bryant, P. (2011). Rational number and proportional reasoning: Using intensive quantities to promote achievement in mathematics and science. International Journal of Science and Mathematics Education, 9(2), 391-417.
DOI
|
31 |
Karplus, R., Pulos, S., & Stage, E. (1983). Early adolescents' proportional reasoning on 'rate' problems. Educational Studies in Mathematics, 14(3), 219-233.
DOI
|
32 |
Keijer, R., van den Heuvel-Panhuizen, M., Wijers, M., Shew, J., Brinker, L. J., Margaret, A. P., Shafer, M.C., & Brendefur, J. (2003). 늘었다 줄었다. More or Less. (나온교육연구소 역). 서울: 도서출판 이우. (영어원작은 1998년 출판).
|
33 |
Kastberg, S. E., D'Ambrosio, B., & Lynch-Davis, K. (2012). Understanding proportional reasoning for teaching. Australian Mathematics Teacher, 68(3), 32-40.
|
34 |
Keijer, R., Abels, M. Brinker, L. J., Cole, B. R., & Shew, J. A. (2004). 비와 비율. Ratios and Rate. (나온교육연구소 역). 서울: 도서출판 이우. (영어원작은 1998년 출판).
|
35 |
Keijer, R., Abels, M. Brinker, L. J., Cole, B. R., & Shew, J. A. (1998). Ratios and Rate. Teacher Guide. In T. A. Romberg (Ed.), Mathematics in Contexts: A Connected Curriculum for Grades 5-8. Chicago: Encyclopedia Britannica Educational Corporation.
|
36 |
Lamon, S. J. (1993). Ratio and proportion: Children's cognitive and metacognitive processes. In T. P. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Rational Numbers An Integration of Research(pp. 131-156). New Jersey, Hillsdale: Lawrence Erlbaum Associates, Publishers.
|
37 |
Lamon, S. J. (2005). Teaching Fractions and Ratios for Understanding. New Jersey: Lawrence Erbaum Associates, Inc., Publishers.
|
38 |
Langrall, C. W., & Swafford, J. (2000). Three balloons for two dollars: Developing proportional reasoning. Mathematics Teaching in the Middle School, 6(4), 254-261.
|
39 |
Lanius, C. A., & Williams, S. E. (2003). Proportionality: A unifying theme for the middle grades. Mathematics Teaching in the Middle School, 8(8), 392-396.
|
40 |
Lesh, R., Post, T., & Behr, M. (1988). Proportional reasoning. In J. Hiebert & M. Behr (Eds.), Number Concepts and Operations in the Middle Grades(pp. 93-118). Reston, VA: National Council of Teachers of Mathematics, INC.
|
41 |
Post, T., Behr, M., & Lesh, R. (1988). Proportionality and the development of pre-algebra understandings. In A. Coxford & A. Shulte (Eds.), The Idea of Algebra K-12 (1988 Yearbook, pp. 78-90). Reston, VA: National Council of Teachers of Mathematics.
|
42 |
National Council of Teachers of Mathematics (2007). 학교수학을 위한 원리와 규준. (류희찬.조완영.이경화.나귀수.김남균.방정숙 옮김). 서울: 경문사 (영어 원작은 2000년 출판).
|
43 |
Norton, S. J. (2005). The construction of proportional reasoning. In H. L. Chick, & J. L. Vincent (Eds.), Proceedings of the 29th Conference International Group for the Psychology of Mathematics Education (Vol 4, pp. 17-24). Melbourne: PME.
|
44 |
Ozgun-Koca, S. A., Altay, M. K. (2009). An investigation of proportional reasoning skills of middle school students. Investigations in Mathematics Learning, 2(1), 26-48.
DOI
|
45 |
Reys, R. E., Lindquist, M. M., Lamdin, D. V., & Smith, N. L. (2012). 초등교사를 위한 수학과 교수법. 박성선.김민경.방정숙.권점례 역. 서울; 경문사. (영어 원작은 2009년 출판).
|
46 |
Schwarz, J. L. (1988). Intensive quantity and referent transforming arithmetic operations. In J. Hiebert, & M. Behr (Eds.), Number Concepts and Operations in the Middle Grades, Vol. 2 (pp. 41-52). Reston, VA: National Council of Teachers of Mathematics.
|
47 |
Shield, M., & Dole, S. (2013). Assessing the potential of mathematics textbooks to promote deep learning. Educational Studies in Mathematics, 82(2), 183-199.
DOI
|
48 |
Streefland, L. (1984). Search for the roots of ratio: Some thoughts on the long term learning process. Part I. Educational Studies in Mathematics 15, 327-347.
DOI
|
49 |
Streefland, L. (1985). Search for the roots of ratio: Some thoughts on the long term learning process. Part II. Educational Studies in Mathematics 16, 75-94.
DOI
|
50 |
Streefland, L., Simon, A., Burrill, G., & Middleton, J. A. (1997). Grasping Sizes. Teacher Guide. In T. A. Romberg (Ed.), Mathematics in Contexts: A Connected Curriculum for Grades 5-8. Chicago: Encyclopedia Britannica Educational Corporation.
|
51 |
Streefland, L., Simon, A., Burrill, G., & Middleton, J. A. (2004). 달은 얼마나 높이 있을까? Grasping Sizes. (나온교육연구소 역). 서울: 도서출판 이우. (영어원작은 1997년 출판).
|
52 |
Sylvana, N. S. (2014). Design Research On Mathematics Education: Ratio Table In Developing The Students' Proportional Reasoning. Unpublished master dissertation, Sriwijaya University(In Collaboration between Sriwijaya University and Utrecht University), Palembang.
|
53 |
The School Mathematics Project(2003a). SMP Interact Practice for Book 7T. Cambridge University Press.
|
54 |
The School Mathematics Project(2003b). SMP Interact Practice for Book 8T. Cambridge University Press.
|
55 |
The School Mathematics Project(2003c). SMP Interact Practice for Book 9T. Cambridge University Press.
|
56 |
The School Mathematics Project(2003d). SMP Interact Practice for Book 7S. Cambridge University Press.
|
57 |
The School Mathematics Project(2003e). SMP Interact Practice for Book 8S. Cambridge University Press.
|
58 |
The School Mathematics Project(2003f). SMP Interact Practice for Book 9S. Cambridge University Press.
|
59 |
The School Mathematics Project(2003g). SMP Interact Practice for Book 9C. Cambridge University Press.
|
60 |
Thompson, P. W., & Thompson, A. G. (1994). Talking about rates conceptually, Part I: A teacher's struggle. Journal for Research in Mathematics Education, 25(3), 279-303.
DOI
|
61 |
Van den Heuvel-Panhuizen, M., Streefland, L., Middleton, J. A., & Meyer, M. R. (2004). 백 분율은 백을 좋아해. Per Sense. (나온교육연구소 역). 서울: 도서출판 이우. (영어원작은 1997년 출판).
|
62 |
Tourniaire, F., & Pulos, S. (1985). Proportional reasoning: A review of the literature. Educational Studies in Mathematics, 16(2), 181-204.
DOI
|
63 |
Treffers, A. (1987). Three Dimensions. A Model of Goal and Theory Description in Mathematics Instruction-The Wiskobas Project. Dordrecht: D. Reidel Publishing Company.
|
64 |
Van den Heuvel Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics 54, 9-35.
DOI
|
65 |
Van de Walle, J. A. (2008). 수학을 어떻게 가르칠 것인가. (남승인 외 역). 서울: 경문사. (영어 원작은 2004년 출판).
|
66 |
Van Dooren, W., De Bock, D., Hessels, A., Janssens, D., & Verschaffel, L. (2005). Not everything is proportional: Effects of age and problem type on properties of overgeneralization. Cognition and Instruction, 23(1), 57-86.
DOI
|
67 |
Van Dooren, W., De Bock, D., Janssens, D., & Verschaffel, L. (2008). The linear imperative: An inventory and conceptual analysis of students' overuse of linearity. Journal for Research in Mathematics Education, 39(3), 311-342.
|
68 |
Van Galen, F., Wijers, M., Burrill, G., & Spence, M. S. (2004). 똑같이 나누어요. Some of the Parts. (나온교육연구소 역). 서울: 도서출판 이우. (영어원작은 1997년 출판).
|
69 |
Vergnaud, G. (1988). Multiplicative structures. In J. Hiebert, & M. Behr (Eds.), Number Concepts and Operations in the Middle Grades, Vol. 2 (pp. 141-161). Reston, VA: National Council of Teachers of Mathematics.
|
70 |
Webb, D. C., Boswinkel, N., & Dekker, T. (2008). Beneath the tip of the iceberg: Using representations to support student understanding. Mathematics Teaching in the Middle School, 14(2), 110-113.
|
71 |
WSOY(2012a). 핀란드 초등 수학교과서 Laskutaito 4-2. 양재욱.도영 역. 서울: 솔빛길출판사.
|
72 |
WSOY(2012b). 핀란드 초등 수학교과서 Laskutaito 5-1. 문보람.도영 역. 서울: 솔빛길출판사.
|
73 |
WSOY(2012c). 핀란드 초등 수학교과서 Laskutaito 5-2. 문보람.도영 역. 서울: 솔빛길출판사.
|
74 |
WSOY(2012d). 핀란드 초등 수학교과서 Laskutaito 6-1. 오수현.도영 역. 서울: 솔빛길출판사.
|
75 |
WSOY(2012e). 핀란드 초등 수학교과서 Laskutaito 6-2. 이영석.도영 역. 서울: 솔빛길출판사.
|