İlköğretim 5. Sınıf Öğrencileri Geometrik Şekillerdeki Simetri Doğrularını Cabri Geometri Yazılımı Yardımıyla Nasıl Belirliyorlar?

Year 2009, Volume: 8 Issue: 1, 159 - 175, 26.06.2009

Nilüfer Yavuzsoy Köse , Aynur Özdaş

Abstract

Bu araştırmada, ilköğretim beşinci sınıf öğrencilerinin Cabri Geometri yazılımı ele çeşitli geometrik şekillerdeki simetri doğrusu / doğrularını nasıl belirlediklerinin devamını amaçlamış. Araştırma eylemi araştırmanın yanında desenlenmiş ve altı ilköğretim beşinci sınıf öğrencilerinin katılımı ile gerçekleştirilmiştir. Veriler için video kayıtları, klinik görüşmeler, çalışma ve günlükler açısından toplanmıştır. Cabri Geometri içeren belirlerken, doğru düzlemsel şekillerdeki simetri doğrularını, simetri doğrusunun yani oluşturduğu parçaların eşliğine, oluşturmaya, doğru katlandığında parçaların çakışmasına ve verilen şekillerin kenar uzunluklarının/açı ölçümlerinin eşit olmasına odaklandıkları görülmüştür.

Keywords

Matematik e itimi, Dinamik geometri ortamlarM, Cabri Geometri, Simetri, lkö retim

How do the fifth grade primary school students determine the line of symmetry in various geometrical shapes using Cabri Geometry software?

Abstract

The aim of this study was to investigate the way that the fifth grade students define line of
symmetry in various geometrical shapes using Cabri Geometry software. The study was designed as an action
research and six fifth grade primary school students participated. The data was collected through video
recordings of weekly teaching periods, clinical interviews, worksheets and diaries. Consequently, it was
observed that when the shapes were fold visually by students along the line and the equality of the edge length/
angle measurements of the given shapes by using Cabri software the students mostly focused on the equality of
pieces shaped by lines of symmetry, its reflection, the collision of the pieces.

Keywords

Mathematics education, Dynamic geometry environments, Cabri Geometry, Symmetry, Primary school

References

• Arcavi, A., & Hadas, N. (2000). Computer mediated learning: An example of an approach. International Journal of Computers for Mathematical Learning, 5, 25-45. Baki, A. (2001). BiliKim teknolojisi MKM M altMnda matematik e itiminin de erlendirilmesi. Milli Eitim Dergisi,149, 26-31. Baki, A. (2004). Problem solving experiences of student mathematics teachers through Cabri: A case study. Teaching Mathematics and Its Applications, 23 (4), 172-180. BintaK, J., Altun, M., & Arslan, K. (2003). Gerçekçi Matematik E itimi le Simetri Ö retimi. MATDER, [Online]: http://www.matder.org.tr/Default.asp?id=107 adresinden 10.12.1006 tarihinde indirilmiKtir. Clement, J. (2000). Analysis of clinical interviews: Foundations and model viability. In A. E. Kelly and R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp.547-590). London: Lawrence Erlbaum Asssociates. De Villiers, M. (1998). An alternative approach to proof in dynamic geometry. In R. Lehrer and D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp.369-393). London: Lawrence Erlbaum Asssociates. Doerr, H., & Tinto, P. (2000). Paradigms for teacher-centered, classroom-based research. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education(pp. 403-427). London: Lawrence Erlbaum Associates Publishers. Duatepe, A. (2000). An investigation of the relationship between van Hiele geometric level of thinking and demographic variables for pre-service elementary school teachers. YayMnlanmamMK Yüksek Lisans Tezi. Middle East Technical University. Gallou-Dumiel, E. (1989). Reflection, point symmetry and logo. In C. A. Maher, G. A. Goldin & R. B. Davis (Eds.) Proceedings of the Eleventh Annual Meeting,North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 149-157). New Brunswick: Rutgers University. Grenier, D. (1987). Middle School pupils conceptions about reflections according to a task of construction. In R. Hershkowitz & S. Vinner (Eds.), 11th International Conference for the Psychology of Mathematics Education (pp.183-188). Montréal, Canada. Güven, B. (2002). Dinamik geometri yazMlMmM cabri ile keKfederek geometri ö renme. YayMnlanmamMK Yüksek Lisans Tezi, Karadeniz Teknik Üniversitesi. Hazzan,O., & Goldenberg E.P. (1997) An expression of the idea of successive refinement in dynamic geometry environments In E. Pehkonen (Ed.) Proceedings of the Conference of the Psychology of Mathematics Education (pp.49-56), 3, Lahti: Finland. Hoyles, C., & Healy, L. (1997). Unfolding meanings for reflective symmetry. International Journal of Computers for Mathematical Learning, 2, 27-59. Jones, K. (2000). Providing a foundation for deductive reasoning: Students’ interpretations when using dynamic geometry software and their evolving mathematical explanations. Educational Studies in Mathematic, 44(1/2), 55-85. Kuzu, A. (2005). OluKturmacMlM a dayalM çevrimiçi destekli ö retim: Bir eylem araKtMrmasM, YayMnlanmamMK Doktora Tezi. EskiKehir: Anadolu Üniversitesi E itim Bilimleri Enstitüsü. Küchemann, D. (1981). Reflection and rotation. In J. Murray (Ed.), Children’s understanding of mathematics: 11~16 (pp.137-157). Great Britain: Athenoeum Press Ltd. Laborde, C. (2001). Intergration of technology in the design of geometry tasks with Cabri-Geometry. International Journal of Computers for Mathematical Learning, 6, 283-317. Laborde, C., Kynigos, C., Hollebrands, K., & Strasser, R. (2006). Teaching and learning geometry with technoloy. In A. Gutiérrez & P. Boero(Eds.), Handbook of Research on The Psychology of Mathematics Education: Past, Present and Future. (pp. 275-304).Rotterdam: Sense Publishers. Leikin, R., Berman, A., & Zaslavsky, O. (1997). Defining and understanding symmetry. In E. Pehkonen (Ed.), Procedding of PME 21 Vol. 3 (pp. 192-199). Liebeck, P. (1984). How children learn mathematics. A guide for parents and teachers. England: Penguin Books. MEB. (2005). -lköretim Matematik Dersi (1-5. Snflar) Öretim Program. Ankara: Devlet KitaplarM Müdürlü ü BasMmevi. Mills, G. E. (2003). Action research a guide for the teacher researcher (2nd. Ed.). New Jersey: Pearson Education. Miles M., & Huberman, M. (1994). An expanded sourcebook qualitative data analysis (2nd. Ed.). CA: Sage Publications. Orton, J. (1999). Children’s perception of pattern in relation to shape. In A. Orton (Ed.), Pattern in the teaching and learning of maths. (pp. 149-167). London: Cassell. Olkun, S. (2006). Yeni Ö retim ProgramlarMnM nceleme ve De erlendirme Raporu: Matematik Ö retim ProgramM nceleme Raporu. -lköretim-Online, 96-111, [Online]:http://ilkogretimonline.org.tr adresinden 14.06.2007 tarihinde indirilmiKtir. Sinclair, N., & Crespo, S. (2006). Learning mathematics in dynamic computer environments. Teaching Children Mathematics, 9(12), 437-444. Stewart, C., & Chance, L. (1995). Making connections: Journal writing and the professional teaching standards. The Mathematics Teacher, 88(2), 92–95. Tripp, D. H. (1990). Socially critical action research. Theory Into Practice, Vol XXIX, (3), 158-166. YMldMrMm, A., & 6imKek, H. (2005). Sosyal Bilimlerde Nitel Aratrma Yöntemleri (5. Basm). Ankara: Seçkin YayMncMlMk. Zembat, . Ö. (2007). YansMma DönüKümü, Do rudan Ö retim ve YapMlandMrmacMlM Mn Temel BileKenleri. Gazi Eitim Fakültesi Dergisi, 27(1), 195-213, [Online]: http://www.gefad.gazi.edu.tr//window/dosyapdf/2007/1/2007-1-195-213-11- ismailczgcrzembat.pdf adresinden 14 Ocak 2008 tarihinde indirilmiKtir.