# Investigation of pre-service elementary mathematics teachers’ problem posing situations in dynamic geometry environment

### Abstract

This study examined problem posing situations of pre-service elementary mathematics teachers in dynamic geometry environment by using problem posing strategies. The qualitative method of multiple case study was applied and geometric concepts that participants used for each type of problem posing are examined. Eight participants from 3rd grade pre-service mathematics teachers voluntarily participated in the study in 2015-2016 fall semester had previously received Computer Aided Mathematics course in the 2014-2015 spring semester. During six weeks’ data collection period, participants tried to pose new problems via dynamic geometry software by using given problem posing situations and their studies were recorded by screen saving program. The relationship between the problems that given to them and the concepts in the new problems were examined through screen recordings. Findings show new problems are established in parallel with the shape or problem statement in the problem posing situations given to them. Compared with other types of problem posing situations, it is seen the concepts are more diversified in the free problem posing. Participants develop their problem posing skills during the process so it is suggested these topics should be included in mathematics education undergraduate program in order for future students to gain these skills.

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### References

Argün, Z., Arıkan, A., Bulut, S., & Halıcıoğlu, S. (2014). Temel matematik kavramların künyesi. Ankara: Gazi Kitabevi.

Aydın, H. (2014). Matematik öğretmen adaylarının gerçek hayat durumlarından matematiksel problem yazma ve çözme becerilerinin incelenmesi.Unpublished doctorate dissertation, Gazi Üniversitesi Eğitim Bilimleri Enstitüsü, Ankara.

Baki, A. (2004). Problem solving experiences of students’ mathematics teachers through Cabri: A case study. Teaching Mathematics and Its Applications, 23(4), 172-180.

Brown, S., & Walter, M. (1969). What if not? Mathematics Teaching, 46, 38-45.

Brown, S., & Walter, M. (2005). The art of problem posing. Mahwah, New Jersey: Lawrence Erlbaum.

Cai, J., & Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. Journal of Mathematical Behavior, 21, 401-421.

English, L. D. (1997). The development of fifth-grade children’s problem posing abilities. Educational Studies in Mathematics, 34, 183-217.

English, L. D. (1998). Children’s problem posing within formal and informal context. Journal for Research in Mathematics Education, 29(1), 83-106.

Gomes, A. S., & Vergnaud, G. (2004). On the learning of geometric concepts using Dynamic Geometry Software. Novas Technologias na Educaçao, 2(1), 1-20.

Güven, B., & Karataş, İ. (2005). Dinamik geometri yazılımı Cabri ile oluşturmacı öğrenme ortamı tasarımı: Bir model. İlköğretim-Online, 4(1), 62-72.

Hashimoto, Y. (1986). Classroom practice of problem solving in Japanese elementary schools.In J. Becker & T. Miwa (Eds.),Paper presented at the Proceedings of the U.S.-Japan Seminar on Mathematical Problem Solving (pp. 94-119). Carbondale, IL: Southern Illinois University.

Işık, C., Kar, T., Yalçın, T., & Zehir, K. (2011). Prospective teachers’ skills in problem posing with regard to different problem posing models. Procedia Social and Behavioral Sciences, 15, 485-489.

Karadağ, Z. (2009). Analyzing students’ mathematical thinking in technology-supported environments.Unpublished doctorate dissertation, Toronto.

Kırnap Dönmez, S. M. (2014). İlköğretim matematik öğretmen adaylarının problem kurma becerilerinin incelenmesi.Unpublished master’s thesis, Erciyes Üniversitesi Eğitim Bilimleri Enstitüsü, Kayseri.

Leung, S. S., & Silver, E. A. (1997). The role of task format, mathematics knowledge, and creative thinking on the arithmetic problem posing of prospective elementary school teachers. Mathematics Education Research Journal, 9(1), 5-24.

MEB (2005). T.C. Milli eğitim bakanlığı talim ve terbiye kurulu başkanlığı, ilköğretim matematik dersi 6-8. sınıflar öğretim programı. Ankara: Milli Eğitim Bakanlığı.

MEB (2013). T.C. Milli eğitim bakanlığı talim terbiye kurulu başkanlığı, ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı. Ankara: Milli Eğitim Bakanlığı.

MEB (2018). T.C. Milli eğitim bakanlığı talim terbiye kurulu başkanlığı,matematik dersi öğretim programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar). Ankara: Milli Eğitim Bakanlığı.

Patton, M. (1990). Qualitative evaluation and research methods. Beverly Hills, CA: Sage.

Rosli, R., Capraro, M. M., & Capraro, R. M. (2014). The effects of problem posing on student mathematical learning: A meta-analysis. International Educational Studies, 7(13), 227-241.

Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.

Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27(5), 521-539.

Silver, E. A., Mamona-Downs, J., Leung, S. S., & Kenny, P. A. (1996). Posing mathematical problems: An explatory study. Journal for Research in Mathematics Education, 27(3), 293-309.

Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students' problem posing in school mathematics.In P. Clarkson (Ed.),Paper presented at the Proceedings of the 19th Annual Conference of the Mathematics Education Research Group of Australasia (pp.518-525).Melbourne: Mathematics Education Research Group of Australasia.

Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory. New Delhi: SAGE.

Voorst, C. V. (1999). Technology in mathematics teacher education. Retrieved March 24, 2016, from,http://www.cimm.ucr.ac.cr/usodetecnologia/Uso%20de%20tecnologia/PDF,%20Viejos%20y%20Nuevos%20(uso%20de%20tecnologia)/Van%20Voorst,%20C.pdf

Walter, S. I., & Brown, M. I. (2013). Problem posing: Reflections and applications. Retrieved March 24, 2016, from https://books.google.com.tr/books?hl=tr&lr=&id=0GSYAgAAQBAJ& oi=fnd&pg=PP 1&dq=problem+posing+reflections+and+applications&ots=I5bFRvEDd4&sig=F-QPqQIx3m5XfEEGa HWQ9HepH60&redir_esc=y#v=onepage&q=problem%20posing%20reflections%20and%20applications&f=false

Xie, J. (2016). An investigation of us and Chinese prospective elementary teachers’ problem posing when interacting with problem-solving activities.Unpublished doctorate dissertation, Syracuse University.

Yevdokimov, O. (2005). On development of students' abilities in problem posing: A case of plane geometry.In A. Gagatsis, F. Spagnolo, Gr. Makrides, & V. Farmaki (Eds.), Paper presented at the 4th Mediterranean Conference on Mathematics Education (pp. 255-267). Palermo: University of Palermo.

Yıldırım, A., & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin.

Yin, R. K. (2003). Case study research: Design and methods. Thousand Oaks, CA: Sage.

*Pegem Eğitim Ve Öğretim Dergisi*,

*9*(1), 125-148. https://doi.org/10.14527/pegegog.2019.005

Copyright (c) 2018 Birnaz Kanbur Tekerek (Author); Ziya Argün (Advisor)

This work is licensed under a Creative Commons Attribution 4.0 International License.