Learning geometric translations in a dynamic geometry environment

Dinamik öğrenme ortamları, matematiksel kavramların keşfedilmesi ve incelenmesi açısından öğrencilere birçok fırsatlar tanımaktadır. Bu çalışmanın amacı, GeoGebra dinamik programının eğitimsel bir araç olarak kullanıldığı bir ortamda 4 ilköğretim matematik öğretmen adayının öteleme kavramının gelişiminin incelenmesidir. Bireysel öğretim deneyi metodu kullanılarak öğretmen adaylarının öteleme dönüşümü üzerine gelişimleri incelenmiştir. Çalışma üç bölümden oluşmuştur: (1) yarı-yapılandırılmış klinik görüşmeler; (2) öğretim deneyleri ve (3) geriye dönük yarı-yapılandırılmış klinik görüşmelerin ve öğretim deneylerinin analizi. Çalışmanın bulguları, dinamik geometri programının öğretmen adaylarının öteleme kavramının gelişimini desteklediğini göstermiştir. Özellikle, programın sürükleme ve ölçme özelliklerinin öğretmen adaylarının öteleme kavramının özelliklerini keşfetmelerine, matematiksel varsayımlarda bulunmalarına, çeşitli yöntemler kullanmalarına ve yeni bilgiler oluşturmalarına yardımcı olduğu gözlemlenmiştir.

Öteleme dönüşümünün dinamik geometri ortamında öğrenimi

Dynamic learning environments provide a variety of opportunities for learners to explore mathematical concepts. The purpose of this study was to explore the nature of the growth of 4 prospective middle school mathematics teachers understanding of geometric translations in a technology mediated environment using GeoGebra as a pedagogical medium. Individual teaching experiment methods were used to examine the progress of prospective teachersunderstanding of geometric translations. The study design included three phases: (1) semistructured clinical interviews; (2) teaching episodes; and (3) a retrospective analysis of the semistructured clinical interviews and teaching episodes. The findings of the study indicated that the availability of the dynamic geometry software supported the teacher candidates understanding of geometric translations. Specifically, the dragging and measurement features of the program enabled teacher candidates to explore the properties of geometric translations, make conjectures, employ various strategies, and construct new understandings.

___

  • Ada, T., & Kurtulus, A. (2010). Students’ misconceptions and errors in transformation geometry. International Journal of Mathematical Education in Science and Technology, 41(7), 901– 909.
  • Aguirre, J. M. (1988). Student preconceptions about vector kinematics. Physics Teacher, 26(4), 212– 216.
  • Brown, T. (1994). Towards a hermeneutical understanding of mathematics and mathematical learning. In P. Ernest (Ed.), Studies in mathematics education (pp. 141–150). London: The Falmer Press.
  • Calder, N., Brown, T., Hanley, U., & Darby, S. (2006). Forming conjectures within a spreadsheet environment. Mathematics Education Research Journal, 18(3), 100-116.
  • Desmond, N. S. (1997). The geometric content knowledge of prospective elementary teachers. Unpublished doctoral dissertation, University of Minnesota.
  • Edwards, L. (2003). The nature of mathematics as viewed from cognitive science. Paper presented at the Third Congress of the European Society for Research in Mathematics, Bellaria, Italy.
  • Falcade, R., Laborde, C., & Mariotti M. A. (2007). Approaching functions: Cabri tools as instruments of semiotic mediation. Educational Studies in Mathematics, 66(3), 317-333.
  • Flanagan, K. (2001). High school students’ understandings of geometric transformations in the context of a technological environment. Unpublished doctoral dissertation, Pennsylvania State University.
  • Gawlick, Th. (2002). On dynamic geometry software in the regular classroom. Zentralblatt für Didaktik der Mathematik, 34(3), 85-92.
  • Gawlick, Th. (2005). Connecting arguments to actions - Dynamic geometry as means for the attainment of higher van hiele levels. Zentralblatt für Didaktik der Mathematik, 37(5), 361- 370.
  • Glass, B. J. (2001). Students’ reification of geometric transformations in the presence of multiple dynamically linked representations. Unpublished doctoral dissertation, The University of Iowa.
  • Hadas, N. & Hershkowitz, R. (1998). Proof in geometry as an explanatory and convincing tool.
  • In A. Olivier & K. Newstead, (Eds.), Proceedings of the 22nd PME Conference (Vol, 3, pp. 25–32). Stellenbosch, South Africa.
  • Harper, S. (2003). Enhancing elementary pre-service teachers’ knowledge of geometric transformations through the use of dynamic geometry computer software. In C. Crawford et al. (Eds.), Proceedings of Society for Information Technology & Teacher Education International Conference (pp. 2909–2916). Chesapeake: AACE.
  • Hollebrands, K. F. (2003). High school students’ understandings of geometric transformations in the context of a technological environment. Journal of Mathematical Behavior, 22(1), 55-72.
  • Hollebrands, K. F. (2007). The role of a dynamic software program for geometry in the strategies high school mathematics students employ. Journal for Research in Mathematics Education, 38(2), 164-192.
  • Jung, I. (2002). Student representation and understanding of geometric transformations with technology experience. Unpublished doctoral dissertation, The University of Georgia.
  • Kazu, İ. Y., & Yavuzalp, N. (2008). Teachers’ opinions about using instructional software. Education and Science, 33(150), 110-126.
  • Laborde, C. (2001). Integration of technology in the design of geometry tasks with cabri-geometry. International Journal of Computers for Mathematical Learning, 6(3), 283-317.
  • Mehdiyev, R. (2009). Exploring students’ learning experiences when using a Dynamic Geometry Software (DGS) tool in a geometry class at a secondary school in Azerbaijan. Unpublished doctoral dissertation, Universiteit van Amsterdam.
  • Miera. L (1995). The microevolution of mathematical representations in children’s activities. Cognition and Instruction, 13, 269-313.
  • Molina, D. D. (1990). The applicability of the van Hiele theory to transformational geometry. Unpublished doctoral dissertation, The University of Texas at Austin.
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • Portnoy, N., Grundmeier, T., & Graham, K. J. (2006). Students’ understanding of mathematical objects in the context of transformational geometry: Implications for constructing and understanding proofs. Journal of Mathematical Behavior, 25, 196–207.
  • Ruthven, K., Hennessy, S., & Deaney, R. (2008). Constructions of dynamic geometry: A study of the interpretative flexibility of educational software in classroom practice. Computers and Education, 51(1), 297-317.
  • Simon, M. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114–145.
  • Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In A. E. Kelly, & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 267–306). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Thaqi, X., Gimenez, J., & Rosich, N. (2011). Geometrical transformations as viewed by prospective teachers. Seventh Congress of the European Society for Research in Mathematics Education. Retrieved January 5, 2011, from https://www.cerme7.univ.rzeszow.pl/WG/4/ WG4_Xhevdet.pdf
  • Watson, A. Spyrou, P., & Tall, D. (2002). The relationship between physical embodiment and mathematical symbolism: The concept of vector. The Mediterranean Journal of Mathematics Education, 1(2), 73–97. Retrieved from http://www.warwick.ac.uk/staff/David.Tall/pdfs/ dot2003c-watsonspirou.pdf
  • Williford, H. J. (1972). A Study of transformational geometry instruction in the primary grades. Journal for Research in Mathematics Education, 3(4), 260–271.
  • Yanik, H.B., & Flores, A. (2009). Understanding rigid geometric transformations: Jeff’s learning path for translation. The Journal of Mathematical Behavior, 28(1), 41–57.
  • Yanik, H. B. (2011). Prospective middle school mathematics teachers’ preconceptions of geometric translations. Educational Studies in Mathematics,78(2), 231-260.