References
- 강영란․조정수 (2015). CBR을 활용한 초등 영재 학생의 그래프 활동에 관한 연구. 학교수학, 17(1), 65-78. Kang young ran, Cho cheong soo (2015). The study of the graph activity of gifted elementary students using CBR. School Mathematics, 17(1), 65-78.
- 김남균 (2002). 초등학교 수학 교수-학습에서의 수학적 상징화에 관한 연구. 한국교원대학교 대학원 박사학위논문. Kim nam gyun (2002). Study on the mathematical symbolizing in elementary school. Unpublished doctoral dissertation, Korea National University of Education, Chungju.
- 심은영 (2006). 다면적 표상 기반 전략훈련이 수학 문장제 해결에 미치는 영향. 국민대학교 대학원 박사학위논문. Sim eun young (2006). The effects of strategy training based on multiple representations on the mathematical word-problem solving. Unpublished doctoral dissertation, Kookmin University of Education, Chungju.
- Andrew, I. (2003). We want a statement that is always true: Criteria for good algebraic representations and the development of modeling knowledge. Journal for Research in Mathematics Education, 34(3), 164-187.
- Cobb, P. (2000). From representations to symbolizing: Comments on semiotics and mathematical learning. In P. Cobb, K. McClain, & E. Yackel (Eds.), Symbolizing and communicating in mathematics classrooms (pp. 17-36). Mahwah, NJ: Lawrence Erlbaum Associates.
- Despina, A. S. (2011). An examination of middel school students' representation practices in mathematical problem solving through the lens of expert work: Towards an organizing scheme. Educational Studies in Mathematics, 76, 265-280. https://doi.org/10.1007/s10649-010-9273-2
- Dufour-Janvier, B., Bednarz, N., & Belanger, N. (1987). Pedagogical considerations concerning the problem of representation. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 109-122). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
- Duval, R. (1993). Registers of semiotic representation and cognitive functioning of thought. Annales de Didactique et de Sciences Cognitives, 5, 37-65.
- Engestrom, Y. (2001). Expansive learning at work: Toward an activity theoretical reconceptualization. Journal of Education and Work, 14(1), 133-156. https://doi.org/10.1080/13639080020028747
- Goldin, G. A., & Shteingold, N. (2001). System of representations and the development of mathematical concepts. In A. A. Cuoco (Ed.), The roles of representation in school mathematics (pp. 1-23). Reston, VA: National Council of Teachers of Mathematics, Inc.
- Goldin, G. A. (2008). Perspectives on representation in mathematical learning and problem solving, In L. D. English (Ed.) Handbook of international research in mathematics education. Routledge, NY: New York.
- Gonzalez-Martin, A. S., Hitt, F., & Morasse, C.(2008). The introduction of the graphicrepresentation of functions through the conceptof covariation and spontaneous representations.In O. Figueras & A. Sepúlveda (Eds.),Proceedings of the 32nd conference of theInternational Group for the Psychology ofMathematics Education and the 30th PME-NA(pp. 89-97). Morelia Mexico: PME.
- Hillel, J. (1993). Computer algebra systems as cognitive technologies: Implication for the practice of mathematics education. In C. Keitel, & K. Ruthven (Eds.), Learning from computers:Mathematics education and technology (pp. 18-48). Springer Verlag.
- Hitt, F. (2003). The functional nature of the representations. Annales de Didactique et des Sciences Cognitives, 8, 255-271.
- Hitt F. (2007). Use of CAS in a method of collaborative learning, scientific debateand self reflection. In M. Baron, D. Guin, & L. Trouche (Eds.), Environments informatises et ressources numEriques pour l'apprentissage (pp. 65-88). Editorial Hermes.
- Hitt, F., & Morasse, C. (2009). Developing the concept of covariation and function in 3rd year of secondary school in the context of mathematical modelling and problem solving situations.http://math.unipa.it/-grim/cieaem/quaderno19_suppl_2.htm
- Kamii, C., Kirkland, L., & Lewis, B. A. (2001). Representation and abstraction in young children's numerical reasoning. In A. A. Cuoco (Ed.), The roles of representation in school mathematics (pp.24-34). Reston, VA: National Council of Teachers of Mathematics, Inc.
- National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics, Inc.
- Pugalee, D. K. (2004). A comparison of verbal and written descriptions of students' problem solving process. Educational Studies in Mathematics, 55, 27-47. https://doi.org/10.1023/B:EDUC.0000017666.11367.c7
- Seeger, F. (1997). Representations in the mathematics classroom: Reflections and constructions. In J. Voigt (Ed.), The culture of the mathematics classroom (pp. 308-343). NY:Cambridge University Press.
- Slavit, D. (1997). An alternate route to the reification of function. Educational Studies in Mathematics, 33, 259-281.
- Swafford, J. O., & Langrall, C. W. (2000). Grade 6 students' preinstructional use of equations to describe and represent problem situations. Journal for Research in Mathematics Education, 31(1) , 89-112. https://doi.org/10.2307/749821
- Zawojewski, J. S., Lesh, R., & English, L. (2003). A models and modeling perspective on the role of small group learning activities. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism (pp. 317-336). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
- Zou, X. (2000). The use of introductory physics: An example for work and energy. Unpublished doctoral dissertation, The Ohio State University, Mansfield.