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A Semiotic Analysis of Opportunity to Learn about Plane Figures in Grade 1 and 2 Mathematics Textbooks  

Cho, Jinwoo (경인교육대학교)
Publication Information
Journal of Elementary Mathematics Education in Korea / v.24, no.1, 2020 , pp. 129-149 More about this Journal
Abstract
This study reports the results of analyzing the learning opportunities about the plane figures provided by the first and second grade mathematics textbooks. The plane figures that students learn during this period are important in that it serves as the basis for the later geometric education. With assumptions that mathematics learning is related to the problem of meaning and that meaning-related activity can be viewed as a symbolic activity, it adopts and uses the perspectives and tools of semiotics to analyze the learning opportunities provided by the mathematics textbook. The analysis of the semiotic process of the textbook activities revealed the significance of learning opportunities and helped to distinguish the seemingly similar learning opportunities. Based on the results of the analysis, I discussed the link between learning opportunities provided by grade 1 and grade 2 mathematics textbooks. Finally, the paper concludes with suggestions and conclusions and suggestions for further research.
Keywords
plane figures; mathematics textbooks; opportunity to learn; semiotic process;
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1 강문봉, 김정하 (2015). 평면도형의 넓이 지도 방법에 대한 고찰: 귀납적 방법 대 문제해결식 방법. 수학교육학연구, 25(3), 461-472.
2 교육부 (2015). 수학과 교육과정. 교육부 고시 제215-74호(별책8)
3 교육부 (2017a). 수학 1-2. 서울: 천재교육.
4 교육부 (2017b). 수학 2-1. 서울: 천재교육
5 교육부 (2017c). 수학 교사용 지도서 1-2. 서울: 천재교육.
6 교육부 (2017d). 수학 교사용 지도서 2-1. 서울: 천재교육.
7 권석일, 박교식 (2011). 우리나라 초등학교 수학 교과서에서의 입체도형 관련 지도 내용에 대한 분석과 비판. 수학교육학연구, 21(3), 221-237.
8 권유미, 안병곤 (2005). 초등 수학 교과서에 사용되고 있는 수학 용어에 대한 학생들의 이해도 분석-도형 영역을 중심으로. 한국초등수학교육학회지, 9(2), 137-159.
9 김구연, 전미현 (2017). 중학교 수학교과서가 학생에게 제공하는 함수 학습기회 탐색. 학교수학, 19(2), 289-317.
10 김선희, 이종희 (2003). 통계 자료의 정리와 표현에서 중학생들의 기호화와 해석화 과정 분석. 수학교육학연구, 13(4), 463-483.
11 김수미, 정은숙 (2005). 범례 제시를 통한 도형 개념 지도 방안. 수학교육학연구, 15(4), 401-417.
12 김수민, 김선희 (2018). 수학 문제 해결 과정의 의사소통에 대한 기호학적 분석. 학교수학, 20(1), 131-147.
13 우정호 (2017). 학교수학의 교육적 기초 (중). 서울: 서울대학교출판문화원.
14 김지원 (2016). 초등학교 2 학년 학생들의 삼각형에 대한 개념 이미지 분석. 학교수학, 18(2), 425-440.
15 박정일 (2013). 전기 비트겐슈타인의 프레게 의미이론 비판. 논리연구, 16(3), 347-380.   DOI
16 박진형, 이경화 (2013). 수학적 모델링 과정에서 수학화의 기호학적 분석. 수학교육학연구, 23(2), 95-116.
17 최병훈, 방정숙, 송근영, 황현미, 구미진, 이성미 (2006). 한국과 싱가포르의 초등 수학 교과서 비교 분석: 도형과 측정 영역을 중심으로. 학교수학, 8(1), 45-68.
18 최병철 (2017). 개념 형성 과정에 관여하는 표현의 기호학적 분석. 수학교육학연구, 27(4), 663-678.
19 최수임, 김성준 (2012). 정의하기와 이름짓기를 통한 도형의 이해 고찰-초등학교 4 학년 도형 영역을 중심으로. 한국학교수학회논문집, 15(4), 719-745.
20 Banicky, L. (2000). Opportunity to learn (Education Policy Brief, vol. 7). College of Human Resources, Education, and Public Policy, University of Delaware. http://udspace.udel.edu/bitstream/handle/19716/2446/opp%20to?sequence=1 에서 2020년 1월 15일 인출.
21 Begle, E. G. (1973). Some lessons learned by SMSG. Mathematics Teacher, 66(3), 207-14.   DOI
22 Charalambous, C. Y., Delaney, S., Hsu, H. Y., & Mesa, V. (2010). A comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical Thinking and Learning, 12(2), 117-151.   DOI
23 Cohen, D. K., Raudenbush, S. W. & Ball, D. L. (2003). Resources, instruction, and research. Educational Evaluation and Policy Analysis 25(2), 119-142.   DOI
24 Ding, M., & Li, Xiaobao. (2010). A comparative analysis of the distributive property in U.S. and Chinese elementary mathematics textbooks. Cognition and Instruction, 28(2), 146-180.   DOI
25 Duval, R. (1995). Semiosis et pensee humaine. Berna: Peter Lang.
26 Peirce, C. S. (1998). The essential Peirce: selected philosophical writings. Vol. 2 (1893-1913). (Peirce Edition Project, eds). Bloomington: Indiana University Press.
27 Frege, G. (1948). Sense and reference. The Philosophical Review, 57(3), 209-230.   DOI
28 Grouws, D., Smith, M., & Sztajn, P. (2004). The preparation and teaching practices of United States mathematics teachers: Grades 4 and 8. In P. Kloosterman & F. Lester (Eds.), Results and interpretations of the 1990 through 2000 mathematics assessments of the national assessment of educational progress. Reston, VA: National Council of Teachers of Mathematics.
29 Li, Y. (2000). A comparison of problems that follow selected content presentations in American and Chinese mathematics textbooks. Journal for Research in Mathematics Education, 31(2), 234-241.   DOI
30 McDonnell, L. M. (1995). Opportunity to learn as a research concept and a policy instrument. Educational Evaluation and Policy Analysis, 17(3), 305-322.   DOI
31 Pepin, B., & Haggarty, L. (2001). Mathematics textbooks and their use in English, French and German classrooms. ZDM, 33(5), 158-175.
32 Remillard, J. T. (2005). Examining key concepts in research on teachers' use of mathematics curricula. Review of Educational Research, 75(2), 211-246.   DOI
33 Rezat, S. & Strasser, R. (2012). From the didactical triangle to the socio-didactical tetrahedron. ZDM , 44(5), 641-651.   DOI
34 Schmidt, W. H., McKnight, C. C., Valverde, G. A., Houang, R. T., & Wiley, D. E. (1997). Many visions, many aims: A cross-national investigation of curricular intentions in school mathematics. Dordrecht: Kluwer Academic Publishers.
35 Duval, R. (2008). Eight problems for a semiotic approach in mathematics education. In Semiotics in mathematics education (pp. 39-61). Brill Sense.
36 Tarr, J. E., Chavez, O., Reys, R. E., & Reys, B. J. (2006). From the written to the enacted curricula: The intermediary role of middle school mathematics teachers in shaping students' opportunity to learn. School Science and Mathematics, 106(4), 191-201.   DOI
37 Schimidt, W. H., McKnihgt, C. C., Houang, R. T., Wang, H., Wiley, D. E., Cogan, L. S., & Wolfe, R. G. (2001). Why schools matter: A cross-national comparison of curriculum and learning. San Francisco, CA: Jossey-Bass.
38 Seeger, F. (2008). Intentionality and sign. In L. Radford, G. Schubring, & F. Seeger (Eds.), Semiotics in mathematics education: Epistemology, history, classroom and culture (pp. 1-18). Rotterdam: Sense Publishers.
39 Stein, M. K., Remillard, J., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319-369). Greenwich, CT: Information Age Publishing.
40 Thompson, D. R., Senk, S. L., & Johnson, G. J. (2012). Opportunities to learn reasoning and proof in high school mathematics textbooks. Journal for Research in Mathematics Education, 43(3), 253-295.   DOI
41 Van Dormolen, J., (1986), Textual Analysis, In Christiansen, B and A.G. Howson and M. Otte, Perspectives on mathematical education. Dordrecht: Reidel, 141-171.
42 Thompson, D. R., & Huntley, M. A. (2014). Researching the enacted mathematics curriculum: learning from various perspectives on enactment. ZDM, 46(5), 701-704.   DOI
43 Tornroos, J. (2005). Mathematics textbooks, opportunity to learn and student achievement. Studies in Educational Evaluation, 31(4), 315-327.   DOI
44 Valverde, G. and L. Bianchi and R. Wolfe and W. Schmidt and R. Houang, (2002), According to the book: using TIMSS to investigate the translation of policy into practice through the world of textbooks, London: Kluwer Academic Publishers.
45 Reys, B. J., Reys, R. E., & Chavez, O. (2004). Why Mathematics Textbooks Matter. Educational Leadership, 61(5), 61-66.
46 Vygotsky, L. S. (2011). The dynamics of the schoolchild’s mental development in relation to teaching and learning. Journal of Cognitive Education and Psychology, 10(2), 198-211.   DOI