Matematik Öğretmeni Adaylarının Araç ve Kaynakların Erişilebilirliğine Yanıt Vermeye Yönelik Yaklaşımlarının Dörtlü Bilgi Modeli Bağlamında Kavramsallaştırılması

Year 2024, , 831 - 848, 31.10.2024

Semiha Kula Ünver , Esra Bukova Guzel

https://doi.org/10.30831/akukeg.1475760

Abstract

Bu çalışmanın amacı, matematik öğretmeni adaylarının öğretim sürecinde karşılaştıkları beklenmeyen olaylara yönelik yaklaşımlarını, araç ve kaynakların erişilebilirliğine yanıt verme bağlamında kavramsallaştırmaktır. Araştırmanın katılımcıları dokuz matematik öğretmeni adayıdır. Gömülü teoriye dayalı çalışmanın amacına ulaşabilmesi için katılımcıların dersleri gözlemlenmiş, video kamera kullanılarak kayıt altına alınmış ve yarı-yapılandırılmış görüşmeler yapılmıştır. Kod doygunluğuna ulaşıldığında veri toplama işlemi tamamlanmıştır. Böylece katılımcılar tarafından yürütülen toplam 54 saatlik ders incelenmiştir. Sonuç olarak katılımcıların beklenmeyen olaylara ilişkin yaklaşımları içerisinde araç ve kaynakların erişilebilirliğine yanıt verme bağlamında dört alt kod belirlenmiştir. Katılımcıların gerçek sınıf ortamındaki derslerinde ortaya çıkan önceden planlanmamış durumlara ilişkin yaklaşımlarının kavramsallaştırılmasının öğretmen eğitiminde yarar sağlayacağı düşünülmektedir.

Keywords

araçların ve kaynakların erişilebilirliğine yanıt verme, beklenmeyen olaylar bilgisi, dörtlü bilgi modeli, matematik öğretmeni adayı, gömülü teori

Conceptualizing Mathematics Student Teachers' Approaches towards Responding to Availability of Tools and Resources in the Context of Knowledge Quartet

Abstract

The purpose of this study is to conceptualize the approaches of secondary mathematics student teachers towards contingencies encountered during the teaching process within the context of responding to availability of tools and resources. In order to achieve the goal of the study based on the grounded theory, the nine secondary mathematics student teachers’ lessons were observed, and recorded using a video camera, and semi-structured interviews were performed. The data collection process ended after 54 lesson hours of observation, that is, when code saturation was reached. As a result, four sub-codes in the context of responding to availability of tools and resources were identified within the approaches of participants in relation to contingent moments. It is thought that conceptualizing the approaches of participants towards unplanned situations encountered during lessons in real class environment would prove to be beneficial in teacher training.

Keywords

responding to availability of tools and resources, contingency, knowledge quartet, mathematics student teachers, grounded theory.

References

• Bretscher, N. (2019). Using the knowledge quartet to analyse interviews with teachers manipulating dynamic geometry software. In U. T. Jankvist, M. van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedings of the eleventh congress of the European society for research in mathematics education (pp. 3855-3862). Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
• Bukova-Güzel, E. (2010). An investigation of pre-service mathematics teachers’ pedagogical content knowledge, using solid objects. Scientific Research and Essays, 5(14), 1872-1880.
• Carlsen, M., Erfjord, I., & Hundeland, P. S. (2023). The knowledge quartet as a theoretical lens to explore kindergarten teachers’ teaching of mathematics. In H. Palmér, C. Björklund, E. Reikerås, & J. Elofsson (eds.) Teaching mathematics as to be meaningful–foregrounding play and children’s perspectives: Results from the POEM5 conference (pp. 131-144). Springer International Publishing.
• Charmaz, K. (2006). Constructing grounded theory: A practical guide through qualitative analysis. Sage.
• Cohen, D. K., Raudenbush, S. W., & Ball, D. L. (2003). Resources, instruction, and research. Educational Evaluation and Policy Analysis, 25(2), 119-142. https://doi.org/10.3102/01623737025002119
• Corcoran, D. (2013). Róisín teaching equivalence of fractions. Retrieved from http://www.knowledgequartet.org/326/rci-scenario-2/ on June 25, 2019.
• Fitzmaurice, O., Walsh, R., & Burke, K. (2021). The ‘Mathematics Problem’ and preservice post primary mathematics teachers – analysing 17 years of diagnostic test data. International Journal of Mathematical Education in Science and Technology, 52(2), 259-281. https://doi.org/10.1080/0020739X.2019.1682700
• Glaser, B. (1978) Theoretical sensitivity: Advances in the methodology of grounded theory. Sociology Press.
• Glaser, B., & Strauss, A. (1967). The discovery of grounded theory: Strategies for qualitative research. Sociology Press.
• Johnson, T. L. (2011). Elementary preservice teachers’ mathematical knowledge for teaching: using situated case studies and educative experiences to examine and improve the development of MKT in teacher education (UMI No. 3477561) [Doctoral dissertation, University of North Carolina]. ProQuest Dissertations & Theses Global.
• Kgothego, N., & Westaway, L. (2023). The use of lesson study in developing grade 1 teachers’ pedagogical content knowledge. In A. Stott (Ed.), Proceedings of the 31st annual conference of the Southern African association for research in mathematics, science and technology education (pp. 148-151). Free State University.
• Kula, S. (2011). Examining mathematics pre-service teachers’ subject matter and pedagogical content knowledge by using knowledge quartet: The case of limit [Unpublished master’s thesis]. Dokuz Eylül University.
• Kula, S. (2014). Conceptualizing mathematics pre-service teachers’ approaches towards contingency in teaching process in the context of Knowledge Quartet [Unpublished doctoral dissertation]. Dokuz Eylül University.
• Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. Sage.
• Mutlu, E., & Duatepe Paksu, A. (2022). Changes in middle school pre-service mathematics teachers’ transformation knowledge of fraction division. The Journal of Buca Faculty of Education, 54, 898-930.
• Neill, S. J. (2007). Grounded theory sampling: ‘Whole’ family research. Journal of Research in Nursing, 12(5), 435-443. https://doi.org/10.1177/1744987106078881
• Patton. M. Q. (2002). Qualitative research and evaluation methods (3rd ed.). Thousand Oaks, CA: Sage Publications.
• Petrou, M. (2010). Adapting the knowledge quartet in the Cypriot mathematics classroom. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the sixth congress of the European society for research in mathematics education (pp. 2020-2029). Institut National de Recherche Pédagogique and ERME.
• Punch, K. F. (2005). Introduction to social research: Quantitative and qualitative approaches (2nd ed.). Sage.
• Rowland, T. (2005). The knowledge quartet: A tool for developing mathematics teaching. In A. Gagatsis (Ed.), Proceedings of the 4th Mediterranean conference on mathematics education (pp. 69–81). Nicosia: Cyprus Mathematical Society.
• Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8, 255-281. https://doi.org/10.1007/s10857-005-0853-5
• Rowland, T., Thwaites, A., & Jared, L. (2011). Triggers of contingency in mathematics teaching. In B. Ubuz (Ed.), Proceedings of the 35th conference of the international group for the psychology of mathematics education (Vol. 4, pp. 73–80). International Group for the Psychology of Mathematics Education.
• Rowland, T., Thwaites, A., & Jared, L. (2015). Triggers of contingency in mathematics teaching. Research in Mathematics Education, 17(2), 74-91. https://doi.org/10.1080/14794802.2015.1018931
• Rowland, T., Turner, F., Thwaites, A., & Huckstep, P. (2009). Developing primary mathematics teaching: Reflecting on practice with the knowledge quartet. Sage.
• Ryan, J., & Williams, J. (2007). Children’s mathematics 4-15: Learning from errors and misconceptions. McGraw-Hill Education.
• Shulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-23. https://doi.org/10.17763/haer.57.1.j463w79r56455411
• Stockero, S. L., & Van Zoest, L. R. (2013). Characterizing pivotal teaching moments in beginning mathematics teachers’ practice. Journal of Mathematics Teacher Education, 16, 125-147. https://doi.org/10.1007/s10857-012-9222-3
• Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory (2nd ed.). Sage Publications.
• Thwaites, A., Huckstep, P., & Rowland, T. (2005). The knowledge quartet: Sonia’s reflections. In D. Hewitt & A. Noyes (Eds.), Proceedings of the 6th British congress of mathematics education (pp. 168-175). British Society for Research into Learning Mathematics.
• Thwaites, A., Jared, L., & Rowland, T. (2011). Analysing secondary mathematics teaching with the knowledge quartet. Research in Mathematics Education, 13(2), 227-228. https://doi.org/10.1080/14794802.2011.585834
• Turner, F. (2005). “I wouldn’t do it that way”: Trainee teachers’ reaction to observations of their own teaching. In D. Hewitt (Ed.), Proceedings of the British society for research into learning mathematics (pp. 87-93). British Society for Research into Learning Mathematics.