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Semiotic Micro-world for Mathematical Visualization

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Part of the book series: Advances in Creativity and Giftedness ((ACAG,volume 1))

Abstract

With the advent of a knowledge-based society, social demand for nurturing creative talents has increased. Gifted education has also been strengthened in relation to creativity education. The present selection system mainly relies on tests to assess students’ abilities. However, gifted education features multi-dimensional considerations such as observation and performance assessment to evaluate the students’ abilities, and a teacher training program for the purpose of giving guidance for the selection process of gifted students is also offered. This transformation from teachers’ instruction-directed learning to students’ self-directed learning highlights constructionism, which allows students to explore and gain knowledge by themselves. Thus, an environment in which students obtain knowledge and develop creativity needs to be provided.

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References

  • Biggs, J. B., & Collis, K. F. (1982). Evaluating the quality of learning: The SOLO taxonomy (Structure of the Observed Learning outcome). New York: Academic Press.

    Google Scholar 

  • Casey, B. M., Andrews, N., Schindler, H., Kersh, J. E., Samper, A., & Copley, J. (2008). The development of spatial skills through interventions involving block building activities, Cognition and Instruction, 26, 269–309.

    Article  Google Scholar 

  • Clements, D. H. (1989). Computers in elementary mathematics education. New Jersey: Prentice-Hall, Inc. A Division of Simon & Schuster Englewood Cloffs.

    Google Scholar 

  • De Jong, T., & Monica, G. F. (1996). Types and qualities of knowledge, Educational Psychologist, 31(2), 105–113.

    Article  Google Scholar 

  • Dreyfus, T. (1993). Didactic design of computer-based learning environments. In C. Keitel & K. Ruthven (Eds.), Learning from computers: Mathematics education and technology, NATO ASI Series (Vol. F 121, pp. 101–130). Berlin: Springer-Verlag, 1993.

    Google Scholar 

  • Freudenthal Institute. (2010-present). “WisWeb”, Freudenthal Institute and APS-wiskunde. Retrieved from http://www.fi.uu.nl/wisweb/

  • Hall, M. (2000). Bridging the gap between everyday and classroom mathematics: An investigation of two teachers’ intentional use of semiotic chains. Unpublished Ph.D. Dissertation, The Florida State University.

    Google Scholar 

  • Healy, L., & Hoyles, C. (1996). Seeing, doing and expressing: An evaluation of task sequences for supporting algebraic thinking. In L. Puig & A. Gutierrez (Eds.), Proceedings of the 20th PME international conference (Vol. 3, pp. 67–74).

    Google Scholar 

  • Hoyles, C., & Noss, R. (2003). What can digital technologies take from and bring to research in mathematics education?. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second International Handbook of Mathematics Education (pp. 323–349). Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Kynigos, C. & Latsi, M. (2007). Turtle’s navigation and manipulation of geometrical figures constructed by variable processes in a 3d simulated space, EuroLOGO, 2007.

    Google Scholar 

  • Morgan, C., & Alshwaikh, J. (2008) Imag(in)ing three-dimensional movement with gesture: ‘Playingturtle’ orpointing? Proceedings of the British Society for Research into Learning Mathematics, 28(3).

    Google Scholar 

  • NCTM (2010-present). Isometric drawing tool. National Council of Teachers of Mathematics. Retrieved form http://illuminations.nctm.org/activitydetail.aspx?id=125

  • Nemirovsky, R., & Noble, T. (1997). On mathematical visualization and the place where we live. Educational Studies in Mathematics, 33, 99–131.

    Article  Google Scholar 

  • Noss, R., Hoyles, C., & Pozzi, S. (2002). Abstraction in expertise: A study of nurses’ conceptions of concentration, Journal for Research in Mathematics Education, 33(3), 204–229.

    Article  Google Scholar 

  • Olive, J. (1991). Logo programming and geometric understanding: An in-depth study. Journal for Research in Mathematics Education, 22(2), 90–111.

    Article  Google Scholar 

  • Presmeg, N. (2006a). Research on visualization in learning and teaching mathematics. In A. Gutierrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: past, present and future.

    Google Scholar 

  • Presmeg, N. (2006b). Semiotics and the “Connections” standard: Significance of semiotics for teachers of mathematics. Educational Studies in Mathematics, 61, 163–182.

    Article  Google Scholar 

  • Uden, L., Liu, K., & Shank, G. (2001). Linking radical constructivism and semiotics to design a constructivist learning environment, Journal of Computing in Higher Education, 12(2), 34–51.

    Article  Google Scholar 

  • Vandenberg, S. G., & Kuse, A. R. (1978) Mental rotations, a group test of three dimensional spatial visualisation. Perceptual and Motor Skills, 60, 343–350.

    Google Scholar 

  • Van der Meij, J., & de Jong, T. (2006). Supporting students’ learning with multiple representations in a dynamic simulation-based learning environment. Learning and Instruction, 16, 199–212.

    Article  Google Scholar 

  • Wechsler, D. (2003). Technical and interpretive manual of the Wechsler intelligence scale for children- IV. New York: Psychological Corporation.

    Google Scholar 

  • Yeh, A., & Nason, R. (2004). Toward a semiotic framework for using technology in mathematics education: The case of learning 3D geometry. International Conference on Computers in Education, Melbourne, Australia.

    Google Scholar 

  • Zazkis, R., Dubinsky, E. & Dautermann, J. (1996). Using visual and analytic strategies: A study of students’ understanding of permutation and symmetry groups. Journal of Research in Mathematics Education, 27(4), 435–457.

    Article  Google Scholar 

  • Zazkis, R., & Liljedahl, P. (2004). Understanding primes: The role of representation. Journal for Research in Mahtematics Education, 35(3), 164–186.

    Article  Google Scholar 

  • Zimmermann, W., & Cunningham, S. (1991). Editors’ introduction: What is mathematical visualization? In W. Zimmermann & S. Cunningham (Eds.), Visualization in teaching and learning mathematics, (pp. 1–7).

    Google Scholar 

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© 2011 Sense Publishers

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Cho, H.H., Song, M.H., Lee, J.Y. (2011). Semiotic Micro-world for Mathematical Visualization. In: Sriraman, B., Lee, K.H. (eds) The Elements of Creativity and Giftedness in Mathematics. Advances in Creativity and Giftedness, vol 1. SensePublishers. https://doi.org/10.1007/978-94-6091-439-3_10

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