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Examination of Argumentation Processes of Middle School Pre-Service Mathematics Teachers in Real Classroom Practices

Year 2025, Volume: 25 Issue: 1, 28 - 54
https://doi.org/10.17240/aibuefd.2025..-1412361

Abstract

In this study, it is aimed to examine the pre-service middle school mathematics teachers’ argumentation processes in real classroom practices. In this context, the pre-service teachers were educated about constructing an argumentation process within the scope of the Practicum course, and their questions and actions supporting the argumentation process they implemented in real classroom practices and the argumentation components they directly presented were examined. The case study, which is one of the qualitative research paradigms, was used in this study. The participants were four volunteer female pre-service middle school mathematics teachers. video recordings of pre-service teachers’ real classroom practices (total 8 lesson hours) were the data of the study. The results revealed that pre-service teachers included different components of the argumentation process in their lessons, used and benefited from different questions and actions, and tried to construct the argumentation process with direct contributions. In addition, the pre-service teachers were able to manage the argumentation process by including various components in their lessons. Based on the results, it was shown that the research process supported the pre-service teachers in terms of providing them with knowledge and awareness about the argumentation process.

Project Number

2021.KB.EGT.002

References

  • Anthony, G., & Walshaw, M. (2009). Characteristics of effective teaching of mathematics: A view from the West. Journal of Mathematics Education, 2(2), 147–164.
  • Ayalon, M., & Hershkowitz, R. (2018). Mathematics teachers' attention to potential classroom situations of argumentation. Journal of Mathematical Behavior, 49, 163–173. https://doi.org/10.1016/j.jmathb.2017.11.010
  • Ayalon, M., & Even, R. (2016). Factors shaping students’ opportunities to engage in argumentative activity. International Journal of Science and Mathematics Education, 14(3), 575–601. https://doi.org/10.1007/s10763-014-9584-3
  • Güç, F. A., & Kuleyin, H. (2021). Argümantasyon kalitesinin matematiksel modelleme sürecine yansıması. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 34(1), 222-262. https://doi.org/10.19171/uefad.850230
  • Bieda, K. N. (2010). Enacting proof-related tasks in middle school mathematics: Challenges and opportunities. Journal for Research in Mathematics Education, 41(4), 351–382.
  • Brown, R., Redmond, T., Sheehy, J., & Lang, D. (2015). Mathematical modelling - An example from an inter-school modelling challenge. In N. H. Lee & K. E. D. Ng (Eds.), Mathematical modelling: From theory to practice (pp. 143–160). World Scientific. https://doi.org/10.1142/9789814546928_0009
  • Conner, A., Singletary, L. M., Smith, R. C., Wagner, P. A., & Francisco, R. T. (2014). Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities. Educational Studies in Mathematics, 86(3), 401–429. https://doi.org/10.1007/s10649-014-9532-8
  • Cirillo, M., Steele, M. D., Otten, S., Herbel-Eisenmann, B. A., McAneny, K., & Riser, J. Q. (2014). Teacher discourse moves: Supporting productive and powerful discourse. In K. Karp (Ed.), Annual perspectives inmathematics education (APME) 2014: Using research to improve instruction. National Council of Teachers of Mathematics.
  • Estrella, S., Morales, S., Méndez-Reina, M., Vidal-Szabó, P., & Mondaca-Saavedra, A. (2024). Collective argumentation in elementary school: an experience of reasoning with data in an online open class. International Journal for Lesson & Learning Studies, 13(3), 205–220. https://doi.org/10.1108/IJLLS-12-2023-0180
  • Erkek, Ö., & Işıksal Bostan, M. (2019). A different look at the reasoning process of prospective middle school mathematics teachers: Global argumentation structures. Education and Science, 44(199), 75–101. http://dx.doi.org/10.15390/EB.2019.7867
  • Forman, E. A., Larreamendy-Joerns, J., Stein, M. K., & Brown, C. A. (1998). “You're going to want to find out which and prove it”: Collective argumentation in a mathematics classroom. Learning and Instruction, 8(6), 527–548. https://doi.org/10.1016/S0959-4752(98)00033-4
  • Hunter, R. (2007). Can you convince me: Learning to use mathematical argumentation. In J. H. Woo, H. C. Lew, K. S. Park & D. Y. Seo (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol 3, pp. 81-88). PME.
  • Inglis, M., Mejia-Ramos, J. P., & Simpson, A. (2007). Modelling mathematical argumentation: The importance of qualification. Educational Studies in Mathematics, 66(1), 3–21.
  • Koleza, E., Metaxas, N., & Poli, K. (2017). Primary and secondary students’ argumentation competence: a case study, CERME 10, Dublin, Ireland, available at: https://hal.archivesouvertes.fr/hal-01865661/document
  • Kosko, K. W., Rougee, A., & Herbst, P. (2014). What actions do teachers envision when asked to facilitate mathematical argumentation in the classroom? Mathematics Education Research Journal, 26(3), 459–476.
  • Krummheuer, G. (1995). The ethnography of argumentation. In P. Cobb & H. Bauersfeld (Eds.), Emergence of mathematical meaning (pp. 229-269). Lawrence Erlbaum.
  • Makar, K., Bakker, A., & Ben-Zvi, D. (2015). Scaffolding norms of argumentation–based inquiry in a primary mathematics classroom. ZDM Mathematics Education, 47(7), 1107–1120. https://doi.org/10.1007/s11858-015-0732-1
  • McCrone, S. S. (2005). The development of mathematical discussions: An investigation in a fifth-grade classroom. Mathematical Thinking and Learning, 7(2), 111–133.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Sage.
  • Milli Eğitim Bakanlığı [MEB]. (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Talim ve Terbiye Kurulu Başkanlığı.
  • Mueller, M., Yankelewitz, D., & Maher, C. (2014). Teachers promoting student mathematical reasoning. Investigations in Mathematics Learning, 7(2), 1–20.
  • National Council of Teachers of Mathematics [NCTM], (2000). Principles and Standards for School Mathematics. NCTM .
  • Sahin, A., & Kulm, G. (2008). Sixth grade mathematics teachers’ intentions and use of probing, guiding, and factual questions. Journal of Mathematics Teacher Education, 11(3), 221–241. https://doi.org/10.1007/s10857-008-9071-2
  • Schwarz, B. B. (2009). Argumentation and learning. In N. Muller Mirza & A. N. Perret-Clermont (Eds.), Argumentation and Education: Theoretical Foundations and Practices (pp. 91–126). Springer.
  • Solar, H., Ortiz, A., Deulofeu, J., & Ulloa, R. (2020). Teacher support for argumentation and the incorporation of contingencies in mathematics classrooms. International Journal of Mathematical Education in Science and Technology, 52(7), 977–1005.
  • Staples, M. (2014). Supporting student justification in middle school mathematics classrooms: Teachers' work to create a context for justification. CRME Publications. 4. Retrieved from: http://digitalcommons.uconn.edu/merg_docs/4.
  • Şengül, S., & Tavşan, S. (2019). 8. sınıf öğrencilerinin matematiksel problemler bağlamındaki argümantasyon süreçlerinin incelenmesi. Kastamonu Eğitim Dergisi, 27(4), 1679–1693.
  • Tekin Dede, A. (2019). Arguments constructed within the mathematical modelling cycle. International Journal of Mathematical Education in Science and Technology, 50(2), 292–314.
  • Toulmin, S. E. (2003). The uses of argument (updated ed.). Cambridge University Press. (Original work published 1958).
  • Urhan, S. & Bülbül, A. (2016). Argümantasyon ve matematiksel kanıt süreçleri arasındaki ilişkiler. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 10(1), 351–373.
  • Uygun, T., & Akyüz, D. (2019). Ortaokul matematik öğretmen adaylarının üçgen eşitsizliğini toplu argümantasyonla kavrayışları. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 20(1), 27–41.
  • Wood, T. (1999). Creating a context for argument in mathematics class. Journal for Research in Mathematics Education, 30(2), 171–191. https://doi.org/10.2307/749609
  • Yackel, E. (2002). What we can learn from analyzing the teacher’s role in collective argumentation. Journal of Mathematical Behavior, 21, 423–440.
  • Yackel, E. (2004). Theoretical perspectives for analyzing explanation, justification and argumentation in mathematics classrooms. Communications of Mathematical Education, 18(1), 1–18.
  • Yin, R. K. (2018). Case study research and applications: Design and methods (6 th ed.). Sage.
  • Zhuang, Y., & Conner, A. (2022). Teachers’ use of rational questioning strategies to promote student participation in collective argumentation. Educational Studies in Mathematics, 111, 345–365. https://doi.org/10.1007/s10649-022-10160-6

Ortaokul Matematik Öğretmeni Adaylarının Gerçek Sınıf Uygulamalarındaki Argümantasyon Süreçlerinin İncelenmesi

Year 2025, Volume: 25 Issue: 1, 28 - 54
https://doi.org/10.17240/aibuefd.2025..-1412361

Abstract

Bu çalışmada ortaokul matematik öğretmeni adaylarının gerçek sınıf uygulamalarında yürüttükleri argümantasyon süreçlerinin incelenmesi amaçlanmaktadır. Bu bağlamda, öğretmen adaylarına öğretmenlik uygulaması dersi kapsamında argümantasyon süreci oluşturma konusunda eğitim verilmiş ve çevrim içi ortamda gerçek sınıf uygulamalarında yürüttükleri argümantasyon sürecini destekleyici soru ve eylemleri ile doğrudan sundukları argümantasyon bileşenleri incelenmiştir. Çalışmada nitel araştırma paradigmalarından durum çalışması benimsenmiştir. Katılımcılar gönüllü dört son sınıf ortaokul matematik öğretmeni adayıdır. Öğretmen adaylarının gerçek sınıf uygulamalarını içeren 8 ders saatine ilişkin video kayıtları araştırmanın verilerini oluşturmaktadır. Çalışmanın bulguları öğretmen adaylarının gerçekleştirdikleri derslerde argümantasyon sürecinin farklı bileşenlerine yer verdiklerini, farklı soru ve eylemlerden yararlandıklarını ve doğrudan katkılar ile argümantasyon sürecini oluşturmaya çalıştıklarını göstermektedir. Bununla birlikte öğretmen adayları derslerinde çeşitli bileşenlere yer vererek argümantasyon sürecini sürdürebilmişlerdir. Çalışmanın bulgularından hareketle araştırma sürecinin öğretmen adaylarına argümantasyon sürecine ilişkin bilgi ve farkındalık kazandırması bakımından katkı sağladığı görülmüştür.

Supporting Institution

Dokuz Eylül Üniversitesi Bilimsel Araştırma Projeleri Koordinasyon Birimi

Project Number

2021.KB.EGT.002

References

  • Anthony, G., & Walshaw, M. (2009). Characteristics of effective teaching of mathematics: A view from the West. Journal of Mathematics Education, 2(2), 147–164.
  • Ayalon, M., & Hershkowitz, R. (2018). Mathematics teachers' attention to potential classroom situations of argumentation. Journal of Mathematical Behavior, 49, 163–173. https://doi.org/10.1016/j.jmathb.2017.11.010
  • Ayalon, M., & Even, R. (2016). Factors shaping students’ opportunities to engage in argumentative activity. International Journal of Science and Mathematics Education, 14(3), 575–601. https://doi.org/10.1007/s10763-014-9584-3
  • Güç, F. A., & Kuleyin, H. (2021). Argümantasyon kalitesinin matematiksel modelleme sürecine yansıması. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 34(1), 222-262. https://doi.org/10.19171/uefad.850230
  • Bieda, K. N. (2010). Enacting proof-related tasks in middle school mathematics: Challenges and opportunities. Journal for Research in Mathematics Education, 41(4), 351–382.
  • Brown, R., Redmond, T., Sheehy, J., & Lang, D. (2015). Mathematical modelling - An example from an inter-school modelling challenge. In N. H. Lee & K. E. D. Ng (Eds.), Mathematical modelling: From theory to practice (pp. 143–160). World Scientific. https://doi.org/10.1142/9789814546928_0009
  • Conner, A., Singletary, L. M., Smith, R. C., Wagner, P. A., & Francisco, R. T. (2014). Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities. Educational Studies in Mathematics, 86(3), 401–429. https://doi.org/10.1007/s10649-014-9532-8
  • Cirillo, M., Steele, M. D., Otten, S., Herbel-Eisenmann, B. A., McAneny, K., & Riser, J. Q. (2014). Teacher discourse moves: Supporting productive and powerful discourse. In K. Karp (Ed.), Annual perspectives inmathematics education (APME) 2014: Using research to improve instruction. National Council of Teachers of Mathematics.
  • Estrella, S., Morales, S., Méndez-Reina, M., Vidal-Szabó, P., & Mondaca-Saavedra, A. (2024). Collective argumentation in elementary school: an experience of reasoning with data in an online open class. International Journal for Lesson & Learning Studies, 13(3), 205–220. https://doi.org/10.1108/IJLLS-12-2023-0180
  • Erkek, Ö., & Işıksal Bostan, M. (2019). A different look at the reasoning process of prospective middle school mathematics teachers: Global argumentation structures. Education and Science, 44(199), 75–101. http://dx.doi.org/10.15390/EB.2019.7867
  • Forman, E. A., Larreamendy-Joerns, J., Stein, M. K., & Brown, C. A. (1998). “You're going to want to find out which and prove it”: Collective argumentation in a mathematics classroom. Learning and Instruction, 8(6), 527–548. https://doi.org/10.1016/S0959-4752(98)00033-4
  • Hunter, R. (2007). Can you convince me: Learning to use mathematical argumentation. In J. H. Woo, H. C. Lew, K. S. Park & D. Y. Seo (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol 3, pp. 81-88). PME.
  • Inglis, M., Mejia-Ramos, J. P., & Simpson, A. (2007). Modelling mathematical argumentation: The importance of qualification. Educational Studies in Mathematics, 66(1), 3–21.
  • Koleza, E., Metaxas, N., & Poli, K. (2017). Primary and secondary students’ argumentation competence: a case study, CERME 10, Dublin, Ireland, available at: https://hal.archivesouvertes.fr/hal-01865661/document
  • Kosko, K. W., Rougee, A., & Herbst, P. (2014). What actions do teachers envision when asked to facilitate mathematical argumentation in the classroom? Mathematics Education Research Journal, 26(3), 459–476.
  • Krummheuer, G. (1995). The ethnography of argumentation. In P. Cobb & H. Bauersfeld (Eds.), Emergence of mathematical meaning (pp. 229-269). Lawrence Erlbaum.
  • Makar, K., Bakker, A., & Ben-Zvi, D. (2015). Scaffolding norms of argumentation–based inquiry in a primary mathematics classroom. ZDM Mathematics Education, 47(7), 1107–1120. https://doi.org/10.1007/s11858-015-0732-1
  • McCrone, S. S. (2005). The development of mathematical discussions: An investigation in a fifth-grade classroom. Mathematical Thinking and Learning, 7(2), 111–133.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Sage.
  • Milli Eğitim Bakanlığı [MEB]. (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Talim ve Terbiye Kurulu Başkanlığı.
  • Mueller, M., Yankelewitz, D., & Maher, C. (2014). Teachers promoting student mathematical reasoning. Investigations in Mathematics Learning, 7(2), 1–20.
  • National Council of Teachers of Mathematics [NCTM], (2000). Principles and Standards for School Mathematics. NCTM .
  • Sahin, A., & Kulm, G. (2008). Sixth grade mathematics teachers’ intentions and use of probing, guiding, and factual questions. Journal of Mathematics Teacher Education, 11(3), 221–241. https://doi.org/10.1007/s10857-008-9071-2
  • Schwarz, B. B. (2009). Argumentation and learning. In N. Muller Mirza & A. N. Perret-Clermont (Eds.), Argumentation and Education: Theoretical Foundations and Practices (pp. 91–126). Springer.
  • Solar, H., Ortiz, A., Deulofeu, J., & Ulloa, R. (2020). Teacher support for argumentation and the incorporation of contingencies in mathematics classrooms. International Journal of Mathematical Education in Science and Technology, 52(7), 977–1005.
  • Staples, M. (2014). Supporting student justification in middle school mathematics classrooms: Teachers' work to create a context for justification. CRME Publications. 4. Retrieved from: http://digitalcommons.uconn.edu/merg_docs/4.
  • Şengül, S., & Tavşan, S. (2019). 8. sınıf öğrencilerinin matematiksel problemler bağlamındaki argümantasyon süreçlerinin incelenmesi. Kastamonu Eğitim Dergisi, 27(4), 1679–1693.
  • Tekin Dede, A. (2019). Arguments constructed within the mathematical modelling cycle. International Journal of Mathematical Education in Science and Technology, 50(2), 292–314.
  • Toulmin, S. E. (2003). The uses of argument (updated ed.). Cambridge University Press. (Original work published 1958).
  • Urhan, S. & Bülbül, A. (2016). Argümantasyon ve matematiksel kanıt süreçleri arasındaki ilişkiler. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 10(1), 351–373.
  • Uygun, T., & Akyüz, D. (2019). Ortaokul matematik öğretmen adaylarının üçgen eşitsizliğini toplu argümantasyonla kavrayışları. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 20(1), 27–41.
  • Wood, T. (1999). Creating a context for argument in mathematics class. Journal for Research in Mathematics Education, 30(2), 171–191. https://doi.org/10.2307/749609
  • Yackel, E. (2002). What we can learn from analyzing the teacher’s role in collective argumentation. Journal of Mathematical Behavior, 21, 423–440.
  • Yackel, E. (2004). Theoretical perspectives for analyzing explanation, justification and argumentation in mathematics classrooms. Communications of Mathematical Education, 18(1), 1–18.
  • Yin, R. K. (2018). Case study research and applications: Design and methods (6 th ed.). Sage.
  • Zhuang, Y., & Conner, A. (2022). Teachers’ use of rational questioning strategies to promote student participation in collective argumentation. Educational Studies in Mathematics, 111, 345–365. https://doi.org/10.1007/s10649-022-10160-6
There are 36 citations in total.

Details

Primary Language Turkish
Subjects Mathematics Education
Journal Section Articles
Authors

Ayşe Tekin Dede 0000-0002-8971-1970

Berna Tataroğlu Taşdan 0000-0002-5851-6144

Melike Yiğit Koyunkaya 0000-0002-7872-3917

Project Number 2021.KB.EGT.002
Early Pub Date March 9, 2025
Publication Date
Submission Date December 30, 2023
Acceptance Date February 4, 2025
Published in Issue Year 2025 Volume: 25 Issue: 1

Cite

APA Tekin Dede, A., Tataroğlu Taşdan, B., & Yiğit Koyunkaya, M. (2025). Ortaokul Matematik Öğretmeni Adaylarının Gerçek Sınıf Uygulamalarındaki Argümantasyon Süreçlerinin İncelenmesi. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi, 25(1), 28-54. https://doi.org/10.17240/aibuefd.2025..-1412361