Öteleme Dönüşümünün Wingeom-tr Ortamında Vektörler Yardımıyla Öğretimi

Öz

Bu çalışma ilköğretim seviyesinde geometrik dönüşümlerden öteleme dönüşümünün kavramsal olarak yapılandırılmasında gerekli olan algı biçimlerini incelemektedir. Bu amaçla Wingeom-tr isimli dinamik geometri yazılımıyla desteklenen bir müfredat parçası geliştirilmiş ve öğretim deneyi metodu kullanılarak dört ilköğretim 6. Sınıf öğrencisi üzerinde uygulanmıştır. Uygulama sonunda öğrencilerin öteleme dönüşümünü ve dönüşümü anlamlandırmada gerekli olan bileşenleri nasıl anlamlandırdıkları, ne gibi zorluklar çektikleri, yazılımın öğretimde kullanımının (dez)avantajları ve müfredat geliştirme ile ilgili edinilen deneyimler Parsyzz ve Labord’un figür-çizim ayrımına dair ürettiği teorik çatı dikkate alınarak analiz edilmiştir. Sonuçta öteleme’nin öğretiminde vektör kavramının öğrenilmesinin gerekliliği ve Wingeom-tr (içerdiği dinamiklikten dolayı) ve ardından statik (kağıt) ortam kullanımının öğretim sürecini olumlu etkilediği görülmüştür

Anahtar Kelimeler

• Öteleme, vektör, müfredat geliştirme, anlayış, dinamik geometri yazılımı, Wingeom-tr

Teaching of Translations through use of Vectors in Wingeom-tr Environment

Abstract

This study investigated the kinds of understandings required to conceptually develop the meaning of translations at the elementary school level. For this purpose, a curriculum piece supported by the use of a geometry software, called Wingeom-tr, was developed and applied to four sixth graders via teaching experiment methodology. As a result, how participants made sense of translations and the constructs necessary to understand translations, the kinds of difficulties participants experienced, the (dis)advantages of using Wingeom-tr in teaching translations, and the kind of experience gained from the curriculum development were analyzed. Such analyses were guided by the use of drawing-figure theoretical framework offered by Parsyzz and Laborde. Results indicate that understanding vectors is necessary in abstracting the meaning of translations. Additionally, use of a dynamic environment such as Wingeom-tr followed by static environment (paper-pencil environment) fosters the learning process.

Keywords

• Translations,vectors,curriculum development,understanding,dynamic geometry environment,Wingeom-tr

Kaynakça

1. Baki, A. (1996). Matematik ögretiminde bilgisayar herşey midir? Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 12, 135-143
2. Faydacı, S. (2008). İlkögretim 6. sınıf ögrencilerine geometrik dönüsümlerden öteleme kavramının bilgisayar destekli ortamda ögretiminin incelenmesi. Yayınlanmamış yüksek lisans tezi, Gazi Üniversitesi Gazi Eğitim Enstitüsü, Ankara, Türkiye.
3. Flanagan, K. (2001). High school student’ understandings of geometric transformations in the context of a technological environment. Unpublished Ph.D. Dissertation, The Pennsylvania State University, University Park, USA.
4. Glass, B. (2004). Transformations and technology: What path to follow? Mathematics Teaching in the Middle School, 9(7), 392-397.
5. Güven, B., ve Karataş, İ. (2003). Dinamik geometri yazılımı Cabri ile geometri öğrenme: Öğrenci görüşleri. The Turkish Online Journal of Educational Technology – TOJET, 2(2), 67-78.
6. Hollebrands, K. F. (2003). High school student’ understandings of geometric transformations in the context of a technological environment. Journal of Mathematical Behavior, 22, 55-72.
7. Hollebrands, K. F., & Smith, R. C. (2009). Using interactive geometry software to teach secondary school geometry: Implications from research. In T. V. Craine, & R. Rubenstein (Eds.), Understanding geometry for a changing world: Seventy first yearbook (pp.221-232). Reston, VA: National Council of Teachers of Mathematics.
8. Labord, C. (1993). Learning from Computers: Mathematics Education and Technology. In C. Keitel, & K. Ruthven (Eds.), The computer as part of the learning environment: The case of geometry (p. 48-67). Berlin: Springer.

9. Martin, G. (1982). Transformation geometry: An introduction to symmetry. New York: Springer-Verlag.
10. McClain, K., Cobb, P., & Gravemeijer, K. (2000). Supporting students’ ways of reasoning about data. In M. Burke and R. Curcio, (Eds.), Learning mathematics for a new century, 2000 yearbook (pp.174-187). Reston, VA: National Council of Teachers of Mathematics.
11. Parris, R. (2011). Wingeom (trans. to Turkish, I. O. Zembat). Exeter, NH: Peanut Software.
12. Parzysz, B. (1988). "Knowing vs seeing": Problems of the plane representation of space geometry . figuresEducational Studies in Mathematics, 19, 79-92.
13. Piaget, J. (2001). Studies in reflecting abstraction (Trans. R. L. Campbell). Sussex, England: Psychology Press.
14. Portnoy, N., Grundmeier, T. A., & 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.
15. Simon, M. A., Saldanha, L., McClintock, E., Akar, G. K., Watanabe, T., & Zembat, I. O. (2010). A developing approach to studying students’ learning through their mathematical activity. Cognition and Instruction, 28(1), 70-112.
16. Steffe, L. P. (1991). The constructivist teaching experiment: Illustrations and implications. In E. von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 177-194). Dordrecth, The Netherlands: Kluwer Academic Publishers.
17. Steffe, L. P., & Thompson, P. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh & A. E. Kelly (Eds.), Research design in mathematics and science education (pp.267–307). Hillsdale, NJ: Erlbaum.
18. T.C. Milli Eğitim Bakanlığı (MEB). (2009). İlköğretim matematik dersi 6–8. Sınıflar öğretim programı. Milli Eğitim Bakanlığı Yayınları: Ankara.
19. Tzur, R. (1999). An integrated study of children’s construction of improper fractions and the teacher’s role in promoting that learning. Journal for Research in Mathematics Education, 30(4), 390-416.
20. van de Walle, J. A. (2007). Elementary and middle school mathematics: Teaching developmentally (Sixth Edition – International Edition). Boston: Pearson Education, Inc.
21. Yanık, H. B. (2006). Prospective elementary teachers’ growth in knowledge and understanding of rigid geometric transformations. Unpublished Ph.D. Dissertation, Arizona State University, USA.
22. Yanık, H. B., & Flores, A. (2009). Understanding rigid geometric transformations:Jeff’s learning path for translation. The Journal of Mathematical Behavior, 28(1), 41-57.
23. Yanık, H. B. (2011). Prospective middle school mathematics teachers’ preconceptions of geometric translations. Educational Studies in Mathematics, 78(2), 231-260.
24. Zembat, I. O. (2007). Asimilasyon prensibinin anlamının öğretmen adaylarınca kavranması ve takdir edilmesi. Hacettepe Universitesi Eğitim Fakültesi Dergisi, 32, 306-318.
25. Zembat, I. O. (2010). A micro-curricular analysis of unified mathematics curricula in Turkey. ZDM - The International Journal on Mathematics Education, 42(5), 443-455. doi: 10.1007/s11858-010- 0236-y