İlköğretim 5. Sınıf Öğrencileri Geometrik Şekillerdeki Simetri Doğrularını Cabri Geometri Yazılımı Yardımıyla Nasıl Belirliyorlar?
Yıl 2009,
Cilt: 8 Sayı: 1, 159 - 175, 26.06.2009
Nilüfer Yavuzsoy Köse
,
Aynur Özdaş
Öz
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.
Kaynakça
- 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.
How do the fifth grade primary school students determine the line of symmetry in various geometrical shapes using Cabri Geometry software?
Yıl 2009,
Cilt: 8 Sayı: 1, 159 - 175, 26.06.2009
Nilüfer Yavuzsoy Köse
,
Aynur Özdaş
Öz
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.
Kaynakça
- 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.