An examination of GeoGebra Tasks Designed by Pre-service Mathematics Teachers in Terms of Mathematical Depth and Technological Action
Year 2019,
, 515 - 544, 31.12.2019
Melike Yiğit Koyunkaya
,
Gülay Bozkurt
Abstract
The aim of this study is to examine pre-service mathematics teachers’ technology based tasks using a dynamic mathematics software –GeoGebra– that were designed during a technology based course. The dynamic geometry task analysis framework consisting of mathematical depth and technological action components was chosen as the conceptual framework of the study. In this study, qualitative research paradigm is adopted and data consisted of GeoGebra tasks and the forms including open-ended questions regarding the tasks. The participants of the study were 20 second grade pre-service secondary mathematics teachers who enrolled in teacher education program at a state university in Turkey. The findings of this study indicated that the mathematical depth of designed tasks was mostly at the beginning levels and only one pre-service teacher designed a task with mathematical depth with higher levels. Looking at the type of technological action they targeted, it was observed that almost all the preservice teachers benefited from the drag and slide feature of the software.
References
- Akkoç, H. (2012). Bilgisayar destekli ölçme-değerlendirme araçlarının matematik öğretimine entegrasyonuna yönelik hizmet öncesi eğitim uygulamaları ve matematik öğretmen adaylarının gelişimi. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 3(2), 99-114.Akkoç, H. (2013). Integrating technological pedagogical content knowledge (TPCK) framework into teacher education. Conference of the International Journal of Arts and Science, 6(2), 263-270. Akyüz, D. (2016). Farklı öğretim yöntemleri ve sınıf seviyesine göre öğretmen adaylarının TPAB analizi. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 7(1), 89-111.Arzarello, F., Olivero, F., Paola, D., & Robutti, O. (2002). A cognitive analysis of dragging practises in Cabri environments. ZDM: The International Journal on Mathematics Education, 34(3), 66–72.Baki, A. (2001). Bilişim teknolojisi ışığı altında matematik eğitiminin değerlendirilmesi. Milli Eğitim Dergisi, 149(1), 26-31.Berelson, B. (1952). Content analysis in communication research. New York: The Free Press.Bowers, J. S., & Stephens, B. (2011). Using technology to explore mathematical relationships: A framework for orienting mathematics courses for prospective teachers. Journal of Mathematics Teacher Education, 14(4), 285-304.Christou, C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2004). Proofs through exploration in dynamic geometry environments. International Journal of Science and Mathematics Education, 2(3), 339–352.de Villiers, M. (1998). An alternative approach to proof in dynamic geometry. In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 369–393). Mahwah, NJ: Lawrence Erlbaum.Gonzalez, G., & Herbst, P. G. (2009). Students’ conceptions of congruency through the use of dynamics geometry software. International Journal of Computers for Mathematical Learning, 14, 153-182.Healy, L., & Hoyles, C. (1999). Visual and symbolic reasoning in mathematics: Making connections with computers?. Mathematical Thinking and Learning, 1(1), 59-84.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.Hoyles, C., & Jones, K. (1998). Proof in dynamic geometry contexts. In C. Mammana & V. Villani (Eds.), Perspectives on the teaching of geometry for the 21 st century (pp. 121–128). Dordrecht: Kluwer Academic Publishers.Hölzl, R. (1996). How does ‘dragging’ affect the learning of geometry. International Journal of Computers for Mathematical Learning, 1(2), 169-187.Hölzl, R. (2001). Using dynamic geometry software to add contrast to geometric situations: A case study. International Journal of Computers for Mathematical Learning, 6(1), 63–86.Koehler, M. J., & Mishra, P. (2008). Introducing TPCK. In AACTE Committee on Innovation and Technology (Ed.), Handbook of technological pedagogical content knowledge (TPCK) for educators (pp. 3-29). New York, NY: Routledge. Laborde, C. (2001). Integration of technology in the design of geometry tasks with cabri geometry. International Journal of Computers for Mathematical Learning, 6, 283-317. Mariotti, M. (2012). Proof and proving in the classroom: Dynamic geometry systems as tools of semiotic mediation. Research in Mathematics Education, 14(2), 163–185.Marrades, R., & Gutierrez, Á. (2000). Proofs produced by secondary school students learning geometry in a dynamic computer environment. Educational Studies in Mathematics, 44(1-2), 87-125. Milli Eğitim Bakanlığı. (2013). Ortaöğretim Matematik (9, 10, 11 ve 12. Sınıflar) Dersi Öğretim Programı. Ankara: Yazar. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics. Ozgun-Koca, S. A., Meagher, M., & Edwards, M. T. (2010). Preservice teachers' emerging tpack in a technology-rich methods class. Mathematics Educator, 19(2), 10-20.Sinclair, M. (2003). Some implications of the results of a case study for the design of pre- constructed, dynamic geometry sketches and accompanying materials. Educational Studies in Mathematics, 52(3), 289–317. Sinclair, M. (2004). Working with accurate representations: The case of pre-constructed dynamic geometry sketches. The Journal of Computers in Mathematics and Science Teaching, 23(2), 191–208. Smith, M. S. & Stein, M. K. (1998). Selecting and creating mathematical tasks: from research to practice. Mathematics Teaching in the Middle School, 3(5), 344-350.Swan, M. (2007). The impact of task-based professional development on teachers’ practices and beliefs: A design research study. Journal of Mathematics Education, 10, 217-237. Trocki, A., & Hollebrands, K. (2018). The development of a framework for assessing dynamic geometry task quality, Digital Experiences in Mathematics Education, 4, (2-3), 110-138. Yin, R. (2018). Case study research: Design and methods (6th ed.). London: Sage.
Matematik Öğretmen Adaylarının Tasarladığı GeoGebra Etkinliklerinin Matematiksel Derinlik ve Teknolojik Eylem Açısından İncelenmesi
Year 2019,
, 515 - 544, 31.12.2019
Melike Yiğit Koyunkaya
,
Gülay Bozkurt
Abstract
Bu çalışmanın amacı, matematik öğretmen adaylarının teknoloji temelli bir ders kapsamında, yaygın olarak kullanılan bir dinamik matematik yazılımı olan GeoGebra yazılımını kullanarak geliştirmiş oldukları etkinliklerin incelenmesidir. Geliştirilen matematik öğrenme etkinliklerini incelemek için matematiksel derinlik ve kullanılan teknolojik eylem bileşenlerinden oluşan dinamik geometri etkinliği analiz çerçevesi bu çalışmanın kavramsal çerçevesi olarak seçilmiştir. Araştırmada, nitel araştırma paradigması benimsenmiş olup Türkiye’deki bir devlet üniversitesinin ortaöğretim matematik öğretmenliği programında öğrenim gören 20 matematik öğretmeni adayının hazırladığı etkinlikler ve bu etkinliklere dair formlar çalışmanın veri grubunu oluşturmaktadır. Analizler sonucunda, öğretmen adaylarının hazırladığı etkinliklerde matematiksel derinlik olarak çoğunlukla başlangıç düzeylerinde kaldıkları ve sadece bir öğretmen adayının yüksek düzeyde matematiksel derinliğe sahip bir etkinlik hazırladığı gözlenmiştir. Hedefledikleri teknolojik eylemin çeşidine bakıldığında neredeyse bütün öğretmen adaylarının yazılımın sürükleme ve sürgü özelliğinden faydalandığı göze çarpmıştır.
References
- Akkoç, H. (2012). Bilgisayar destekli ölçme-değerlendirme araçlarının matematik öğretimine entegrasyonuna yönelik hizmet öncesi eğitim uygulamaları ve matematik öğretmen adaylarının gelişimi. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 3(2), 99-114.Akkoç, H. (2013). Integrating technological pedagogical content knowledge (TPCK) framework into teacher education. Conference of the International Journal of Arts and Science, 6(2), 263-270. Akyüz, D. (2016). Farklı öğretim yöntemleri ve sınıf seviyesine göre öğretmen adaylarının TPAB analizi. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 7(1), 89-111.Arzarello, F., Olivero, F., Paola, D., & Robutti, O. (2002). A cognitive analysis of dragging practises in Cabri environments. ZDM: The International Journal on Mathematics Education, 34(3), 66–72.Baki, A. (2001). Bilişim teknolojisi ışığı altında matematik eğitiminin değerlendirilmesi. Milli Eğitim Dergisi, 149(1), 26-31.Berelson, B. (1952). Content analysis in communication research. New York: The Free Press.Bowers, J. S., & Stephens, B. (2011). Using technology to explore mathematical relationships: A framework for orienting mathematics courses for prospective teachers. Journal of Mathematics Teacher Education, 14(4), 285-304.Christou, C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2004). Proofs through exploration in dynamic geometry environments. International Journal of Science and Mathematics Education, 2(3), 339–352.de Villiers, M. (1998). An alternative approach to proof in dynamic geometry. In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 369–393). Mahwah, NJ: Lawrence Erlbaum.Gonzalez, G., & Herbst, P. G. (2009). Students’ conceptions of congruency through the use of dynamics geometry software. International Journal of Computers for Mathematical Learning, 14, 153-182.Healy, L., & Hoyles, C. (1999). Visual and symbolic reasoning in mathematics: Making connections with computers?. Mathematical Thinking and Learning, 1(1), 59-84.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.Hoyles, C., & Jones, K. (1998). Proof in dynamic geometry contexts. In C. Mammana & V. Villani (Eds.), Perspectives on the teaching of geometry for the 21 st century (pp. 121–128). Dordrecht: Kluwer Academic Publishers.Hölzl, R. (1996). How does ‘dragging’ affect the learning of geometry. International Journal of Computers for Mathematical Learning, 1(2), 169-187.Hölzl, R. (2001). Using dynamic geometry software to add contrast to geometric situations: A case study. International Journal of Computers for Mathematical Learning, 6(1), 63–86.Koehler, M. J., & Mishra, P. (2008). Introducing TPCK. In AACTE Committee on Innovation and Technology (Ed.), Handbook of technological pedagogical content knowledge (TPCK) for educators (pp. 3-29). New York, NY: Routledge. Laborde, C. (2001). Integration of technology in the design of geometry tasks with cabri geometry. International Journal of Computers for Mathematical Learning, 6, 283-317. Mariotti, M. (2012). Proof and proving in the classroom: Dynamic geometry systems as tools of semiotic mediation. Research in Mathematics Education, 14(2), 163–185.Marrades, R., & Gutierrez, Á. (2000). Proofs produced by secondary school students learning geometry in a dynamic computer environment. Educational Studies in Mathematics, 44(1-2), 87-125. Milli Eğitim Bakanlığı. (2013). Ortaöğretim Matematik (9, 10, 11 ve 12. Sınıflar) Dersi Öğretim Programı. Ankara: Yazar. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics. Ozgun-Koca, S. A., Meagher, M., & Edwards, M. T. (2010). Preservice teachers' emerging tpack in a technology-rich methods class. Mathematics Educator, 19(2), 10-20.Sinclair, M. (2003). Some implications of the results of a case study for the design of pre- constructed, dynamic geometry sketches and accompanying materials. Educational Studies in Mathematics, 52(3), 289–317. Sinclair, M. (2004). Working with accurate representations: The case of pre-constructed dynamic geometry sketches. The Journal of Computers in Mathematics and Science Teaching, 23(2), 191–208. Smith, M. S. & Stein, M. K. (1998). Selecting and creating mathematical tasks: from research to practice. Mathematics Teaching in the Middle School, 3(5), 344-350.Swan, M. (2007). The impact of task-based professional development on teachers’ practices and beliefs: A design research study. Journal of Mathematics Education, 10, 217-237. Trocki, A., & Hollebrands, K. (2018). The development of a framework for assessing dynamic geometry task quality, Digital Experiences in Mathematics Education, 4, (2-3), 110-138. Yin, R. (2018). Case study research: Design and methods (6th ed.). London: Sage.