Abstract
Bu çalışmanın amacı, bir devlet üniversitesinin eğitim fakültesi matematik öğretmenliği programında yer alan geometri öğretimi dersinde kullanılan öğretim materyallerini Geometrik Çalışma Düzlemleri (GÇD) modeli ile incelemektir. Bu model geometri dersinde gerçekleştirilen çalışmaları incelemek için geliştirilmiş ve Türkçe alan yazında henüz çalışılmamıştır. Bu amaç doğrultusunda geometri dersinde verilen sınıf içi etkinlikler, modelde tanımlanan dikey düzlemlere ve geometri paradigmalarına göre içerik analizi yapılarak sınıflandırılmıştır. Etkinliklerin çoğunun Geometri II paradigması bağlamında olduğu ve neredeyse tamamında öğretmen adaylarından beklenen geometri çalışmalarının göstergebilimsel-söylemsel ve araçsal-söylemsel düzlemlere dayandığı ortaya çıkmıştır. Bu sonuç, tümdengelimli akıl yürütmeyi ve Öklid geometrisinin aksiyomatik yapısını tanıtmayı hedefleyen dersin amacı ile uyumludur. Ancak Geometri I paradigmasına dayalı ve göstergebilimsel-araçsal düzlemle ilgili etkinliklerin de ders kapsamında ele alınmasının öğretmen adaylarının geometri paradigmaları arasındaki ilişki konusunda farkındalık geliştirmelerine ve etkinliklerin gerektirdiği geometri çalışmalarını daha iyi kavramalarına yardımcı olacağı düşünülmektedir. Çalışmadan elde edilen sonuçların, matematik öğretmenliği programlarında yer alan geometri öğretimi derslerinin içeriği hazırlanırken yol göstereceği düşünülmektedir.
Supporting Institution
Boğaziçi Üniversitesi
Project Number
18762
References
- Çalışkan-Dedeoğlu, N. (2016). Geometrik Paradigmalar. E. Bingölbali, S. Arslan, & İ. Ö. Zembat, Matematik Eğitiminde Teoriler (s. 291-305) içinde. Pegem Akademi.
- Gómez-Chacón, I.M., ve Kuzniak, A. (2015). Spaces for geometric work: figural, instrumental, and discursive geneses of reasoning in a technological environment. International Journal of Science and Mathematics Education, 13(1), 201-226. https://doi.org/10.1007/s10763-013-9462-4
- Gómez-Chacón, I.M., Romero Albaladejo, I.M., ve del Mar García López, M. (2016). Zig-zagging in geometrical reasoning in technological collaborative environments: A Mathematical Working Space-framed study concerning cognition and affect. ZDM Mathematics Education, 48(6), 909–924. https://doi.org/10.1007/s11858-016-0755-2
- Houdement, C. (2007). Geometrical working space, a tool for comparison. D. Pitta-Pantazi ve G. Philippou (Haz.), Proceedings of the Fifth Conference of the European Society for the Research of Mathematics Education (s. 972-981) içinde. University of Cyprus.
- Houdement, C., ve Kuzniak, A. (2003). Elementary geometry split into different geometrical paradigms. Proceedings of CERME 3 içinde, http://www.mathematik.uni-dortmund.de/~erme/CERME3/Groups/TG7/TG7_list.php. Bellaria, Italy: ERME.
- Jacinto, H., ve Carreira, S. (2017). Mathematical problem solving with technology: The techno-mathematical fluency of a student-with-GeoGebra. International Journal of Science and Mathematics Education, 15(6), 1115-1136. https://doi.org/10.1007/s10763-016-9728-8
- Jiménez, L., ve Ärlebäck, JB (2018). Using the Mathematical Working Space model as a lens on geometry in the Swedish mathematics upper secondary curriculum. Perspectives on Professional development of mathematics teachers, Proceedings of MADIF, 11, 201-210.
- Kuzniak, A. (2014). Understanding geometric work through its development and its transformations. S. Rezat, S., M. Hattermann, ve A. Peter-Koop (Haz.), Transformation-A Fundamental Idea of Mathematics Education (s. 311-325) içinde. Springer.
- Kuzniak, A. (2018). Thinking about the teaching of geometry through the lens of the theory of geometric working spaces. P. Herbst vd. (Haz.) International perspectives on the teaching and learning of geometry in secondary schools (s. 5-21) içinde. Springer, Cham.
- Kuzniak, A., ve Nechache, A. (2015). Using the geometric working spaces to plan a coherent teaching of geometry. CERME 9 - Ninth Congress of the European Society for Research in Mathematics Education, Charles University in Prague, Faculty of Education; ERME, Prague, Czech Republic. (s. 543-549).
- Kuzniak, A., ve Nechache, A. (2021). On forms of geometric work: a study with pre-service teachers based on the theory of Mathematical Working Spaces. Educational Studies in Mathematics, 106(2), 271-289. https://doi.org/10.1007/s10649-020-10011-2
- Kuzniak, A., Nechache, A., ve Drouhard, JP (2016). Understanding the development of mathematical work in the context of the classroom. ZDM Mathematics Education, 48(6), 861-874. https://doi.org/10.1007/s11858-016-0773-0
- Kuzniak, A., ve Rauscher, JC (2011). How do teachers' approaches to geometric work relate to geometry students' learning difficulties? Educational Studies in Mathematics, 77(1), 129-147. https://doi.org/10.1007/s10649-011-9304-7
- Kuzniak, A., Tanguay, D. ve Elia, I. (2016). Mathematical Working Spaces in schooling: an introduction. ZDM Mathematics Education, 48(6), 721–737, https://doi.org/10.1007/s11858-016-0812-x
- Radford, L. (2016). The epistemic, the cognitive, the human: a commentary on the mathematical working space approach. ZDM Mathematics Education, 48(6), 925-933. https://doi.org/10.1007/s11858-016-0811-y
Abstract
In this study, materials used in a teaching geometry course were examined using Geometric Working Spaces (GWS) model. The model, developed to examine the activities carried out in geometry lessons, has not yet been studied in Turkish context. In this study, in-class activities were classified by content analysis according to the vertical planes and geometry paradigms defined in the model. Most of the activities were in line with Geometry II paradigm and oriented towards semiotic-discursive and instrumental-discursive planes. This result is in line with the aim of the course, which introduces deductive reasoning and the axiomatic structure of Euclidean geometry. However, including activities based on Geometry I paradigm and related to semiotic-instrumental plane in the course would help pre-service teachers to recognize the relationship between geometry paradigms and better comprehend geometry studies required by the activities. Results are thought to guide the design of teaching geometry courses.
Supporting Institution
Boğaziçi University
Project Number
18762
References
- Çalışkan-Dedeoğlu, N. (2016). Geometrik Paradigmalar. E. Bingölbali, S. Arslan, & İ. Ö. Zembat, Matematik Eğitiminde Teoriler (s. 291-305) içinde. Pegem Akademi.
- Gómez-Chacón, I.M., ve Kuzniak, A. (2015). Spaces for geometric work: figural, instrumental, and discursive geneses of reasoning in a technological environment. International Journal of Science and Mathematics Education, 13(1), 201-226. https://doi.org/10.1007/s10763-013-9462-4
- Gómez-Chacón, I.M., Romero Albaladejo, I.M., ve del Mar García López, M. (2016). Zig-zagging in geometrical reasoning in technological collaborative environments: A Mathematical Working Space-framed study concerning cognition and affect. ZDM Mathematics Education, 48(6), 909–924. https://doi.org/10.1007/s11858-016-0755-2
- Houdement, C. (2007). Geometrical working space, a tool for comparison. D. Pitta-Pantazi ve G. Philippou (Haz.), Proceedings of the Fifth Conference of the European Society for the Research of Mathematics Education (s. 972-981) içinde. University of Cyprus.
- Houdement, C., ve Kuzniak, A. (2003). Elementary geometry split into different geometrical paradigms. Proceedings of CERME 3 içinde, http://www.mathematik.uni-dortmund.de/~erme/CERME3/Groups/TG7/TG7_list.php. Bellaria, Italy: ERME.
- Jacinto, H., ve Carreira, S. (2017). Mathematical problem solving with technology: The techno-mathematical fluency of a student-with-GeoGebra. International Journal of Science and Mathematics Education, 15(6), 1115-1136. https://doi.org/10.1007/s10763-016-9728-8
- Jiménez, L., ve Ärlebäck, JB (2018). Using the Mathematical Working Space model as a lens on geometry in the Swedish mathematics upper secondary curriculum. Perspectives on Professional development of mathematics teachers, Proceedings of MADIF, 11, 201-210.
- Kuzniak, A. (2014). Understanding geometric work through its development and its transformations. S. Rezat, S., M. Hattermann, ve A. Peter-Koop (Haz.), Transformation-A Fundamental Idea of Mathematics Education (s. 311-325) içinde. Springer.
- Kuzniak, A. (2018). Thinking about the teaching of geometry through the lens of the theory of geometric working spaces. P. Herbst vd. (Haz.) International perspectives on the teaching and learning of geometry in secondary schools (s. 5-21) içinde. Springer, Cham.
- Kuzniak, A., ve Nechache, A. (2015). Using the geometric working spaces to plan a coherent teaching of geometry. CERME 9 - Ninth Congress of the European Society for Research in Mathematics Education, Charles University in Prague, Faculty of Education; ERME, Prague, Czech Republic. (s. 543-549).
- Kuzniak, A., ve Nechache, A. (2021). On forms of geometric work: a study with pre-service teachers based on the theory of Mathematical Working Spaces. Educational Studies in Mathematics, 106(2), 271-289. https://doi.org/10.1007/s10649-020-10011-2
- Kuzniak, A., Nechache, A., ve Drouhard, JP (2016). Understanding the development of mathematical work in the context of the classroom. ZDM Mathematics Education, 48(6), 861-874. https://doi.org/10.1007/s11858-016-0773-0
- Kuzniak, A., ve Rauscher, JC (2011). How do teachers' approaches to geometric work relate to geometry students' learning difficulties? Educational Studies in Mathematics, 77(1), 129-147. https://doi.org/10.1007/s10649-011-9304-7
- Kuzniak, A., Tanguay, D. ve Elia, I. (2016). Mathematical Working Spaces in schooling: an introduction. ZDM Mathematics Education, 48(6), 721–737, https://doi.org/10.1007/s11858-016-0812-x
- Radford, L. (2016). The epistemic, the cognitive, the human: a commentary on the mathematical working space approach. ZDM Mathematics Education, 48(6), 925-933. https://doi.org/10.1007/s11858-016-0811-y
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Teacher Education and Professional Development of Educators, Mathematics Education |
| Journal Section | Original Articles |
| Authors | |
| Project Number | 18762 |
| Publication Date | October 15, 2023 |
| Published in Issue | Year 2023 Volume: 40-2 Issue: 2 |
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