Browse > Article

An Analysis on Conjecturing Tasks in Elementary School Mathematics Textbook: Focusing on Definitions and Properties of Quadrilaterals  

Park, JinHyeong (Myongji University)
Publication Information
Journal of Educational Research in Mathematics / v.27, no.3, 2017 , pp. 491-510 More about this Journal
Abstract
This study analyzes on conjecturing tasks in elementary mathematics textbook. We adopted Peircean semiotic perspective and variation theory to analyze conjecturing tasks in elementary mathematics textbook. We specifically analyzed mathematical tasks designed to support students' inquiries into definitions and properties of quardrilaterals. As a result, we found that conjecturing tasks in textbooks do not focus on supporting students' diagrammatic reasoning and inductive verification on provisional abductions. These tasks were mainly designed to support students' conjecturing on commonalities of mathematical objects rather than differences between objects.
Keywords
mathematics textbook; mathematical tasks;
Citations & Related Records
연도 인용수 순위
  • Reference
1 교육과학기술부(2010). 초등학교 수학 4-2. 서울: 두산동아.
2 교육부 (2015a). 2015개정 수학과교육과정. 교육부고시 제 2015-74호 [별책 8].
3 교육부 (2015b). 초등학교 교사용 지도서 수학 4-2. 서울: 천재교육.
4 교육부 (2015c). 초등학교 수학 4-2. 서울: 천재교육.
5 김현정, 강완(2008). 초등학교 수학 교과서에 나타난 사각형 지도 방법에 대한 분석. 초등수학교육, 11(2), 141-159.
6 노영아, 안병곤(2007). 도형 영역의 오류 유형과 원인 분석에 관한 연구 - 초등학교 4학년을 중심으로. 한국초등수학교육학회지, 11(2), 199-216.
7 강문봉(1995). 귀납적인 교수 방법의 재고. 수학교육학연구, 5(1), 65-72.
8 강문봉, 김정하(2015). 평면도형의 넓이 지도 방법에 대한 고찰 - 귀납적 방법 대 문제해결식 방법. 수학교육학연구, 25(3), 461-472.
9 문성재, 이경화(2017). 수학 교수-학습에서 기호와 주의의 역할. 학교수학, 19(1), 189-208.
10 방정숙, 김승민(2017). 수학 교과서 연구 동향 분석: 최근 5년 동안 게재된 국내 학술지 논문을 중심으로. 학교수학, 19(2), 249-265.
11 서동엽(2003). 초등 수학 교재에서 활용되는 추론 분석. 수학교육학연구, 13(2), 159-178.
12 이윤경, 조정수(2015). '큰 수의 법칙' 탐구 활동에서 나타난 가추법의 유형 분석. 수학교육학연구, 25(3), 323-345.
13 최수임, 김성준(2012). 정의하기와 이름짓기를 통한 도형의 이해 고찰. 한국학교수학회논문집, 15(4), 719-745.
14 Arzarello, F. & Sabena, C. (2008) Semiotic and theoretic control in argumentation and proof activities. Educational Studies in Mathematics, 70, 97-109.
15 Hoffmann, M. H. G. (2004). How to get it. Diagrammatic reasoning as a tool of knowledge development and its pragmatic dimension. Foundation of Science, 9, 285-305.
16 Lenhard, J. (2005). Deduction, perception and modeling: The two Peirces on the essence of mathematics. In M. H. G. Hoffinann, J. Lenhard & F. Seeger (Eds.) Activity and sign - Grounding mathematics education (pp. 313-324). New York: Springer.
17 Marton, F. (2006). Sameness and difference in transfer. The Journal of the Learning Sciences, 15(4), 499-535.   DOI
18 Otte, M. (2006). Mathematical epistemology from a Peircean semiotic point of view. Educational Studies in Mathematics, 61, 11-38.   DOI
19 Park, J., Park, M.-S., Park, M., Cho, J. & Lee, K.-H. (2013). Mathematical modelling as a facilitator to conceptualization of the derivative and the integral in a spreadsheet environment. Teaching Mathematics and Its Applications, 32, 123-139.   DOI
20 Pedemonte, B. & Reid, D. (2011). The role of abduction in proving processes. Educational Studies in Mathematics, 76, 281-303.   DOI
21 Peirce, C. S. (C.P.) (1931-1935, 1958) Collected papers of Charles Sanders Peirce. Cambridge, MA: Harvard University Press.
22 Peirce, C. S. (NEM) (1976). The new elements of mathematics by Charles S. Peirce (Vol. I - IV). Hague: Mouton.
23 Peng, Y. & Reggia, J. A. (1990). Abductive inference models for diagnostic problem- solving. New York: Springer.
24 Stein, M. K., Grover, B. W. & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455-488.   DOI
25 Prawat, R. S. (1999). Dewey, Peirce, and the learning paradox. American Educational Research Journal, 36(1), 47-76.   DOI
26 Presmeg, N. (2005). Metaphor and metonymy in processes of semiosis in mathematics education. In M. H. G. Hoffinann, J. Lenhard & F. Seeger (Eds.) Activity and sign - Grounding Mathematics Education (pp. 105-116). New York: Springer.
27 Radford, L. (2010). Layers of generality and types of generalization in pattern activities. PNA-Pensamiento Numerico Avanzado, 4(2), 37-62.
28 Watson, A. & Mason, J. (2005). 색다른 학교수학. (이경화 역). 서울: 경문사.