Ortaokul Matematik Öğretmeni Adaylarının Derslerindeki Argümantasyon Sürecine İlişkin Fark Etme Becerilerinin İncelenmesi

Year 2023, Volume: 11 Issue: 2, 220 - 244, 20.12.2023

Berna Tataroğlu Taşdan , Melike Yiğit Koyunkaya , Ayşe Tekin Dede

https://doi.org/10.52826/mcbuefd.1373777

Abstract

Bu çalışmanın temel amacı ortaokul matematik öğretmeni adaylarının matematik derslerinde argümantasyon sürecini destekleyecek soru ve eylemleri nasıl fark ettiklerini incelemektir. Durum çalışması ile desenlenen bu araştırmanın katılımcıları, araştırmaya gönüllü olarak katılan dört ortaokul matematik öğretmeni adayıdır. Çalışmanın verilerini her bir öğretmen adayının gerçek sınıf ortamında gerçekleştirdiği derslerin video kayıtları ve öğretmen adayları ile derslerine ilişkin yapılan bireysel görüşmelerin video kayıtları oluşturmaktadır. Öğretmen adaylarının ders anlatımları argümantasyon sürecini destekleyici soru ve eylemler açısından, görüşmeler ise ders anlatımlarında argümantasyon sürecine ilişkin fark ettikleri durumlar açısından analiz edilmiştir. Analiz sonuçları öğretmen adaylarının derslerinde oluşturabildikleri argümantasyon süreçleri kadar oluşturma olasılıkları olan argümantasyon süreçlerinin de farkında olduğunu göstermiştir. Fark etme bileşenleri bağlamında öğretmen adayları derslerinde en fazla dikkat etme bileşenine ilişkin görüş belirtmişlerdir. Ulaşılan sonuçlar ayrıca öğretmen adaylarının dikkat ettikleri durumlar kapsamlı olmasına rağmen bu durumları yeterince yorumlayamadıklarını ve karşılık veremediklerini göstermektedir.

Keywords

Fark etme, Argümantasyon, Ortaokul matematik öğretmeni adayı

Supporting Institution

DOKUZ EYLÜL ÜNİVERSİTESİ BİLİMSEL ARAŞTIRMA PROJELERİ KOORDİNASYON BİRİMİ

Project Number

2021.KB.EGT.002

Thanks

Bu makale Dokuz Eylül Üniversitesi Bilimsel Araştırma Projeleri Koordinasyon Birimi tarafından desteklenen 2021.KB.EGT.002 numaralı projeden oluşturulmuştur.

Examination of Pre-Service Middle School Mathematics Teachers' Noticing Skills Regarding the Argumentation Process in their Lessons

Abstract

The aim of this study is to examine how pre-service middle school mathematics teachers noticed the questions and actions that supported the argumentation process in their teaching. The participants of this research, which was designed as a case study, were four volunteer pre-service middle school mathematics teachers. The data of the study consisted of video recordings of each pre-service teacher’s teaching in the classroom and video recordings of individual interviews conducted with each pre-service teacher about their teaching. The pre-service teachers’ teaching was analyzed in terms of questions and actions that supported the argumentation process, and the interviews were analyzed in terms of the situations they noticed about the argumentation process in their teaching. The results showed that the pre-service teachers were aware of the argumentation process that they were able to create in their teaching as well as the argumentation process that they had a potential to construct. In the context of noticing, the pre-service teachers’ noticing about their teaching were mostly in the component of attention. The results show that although the situations that pre-service teachers paid attention were comprehensive, they could not interpret and respond enough to these situations.

Keywords

Noticing, Argumentation, Pre-service middle school mathematics teacher

Project Number

2021.KB.EGT.002

References

• Ayalon, M. (2019). Exploring changes in mathematics teachers' envisioning of potential argumentation situations in the classroom. Teaching and Teacher Education, 85, 190-203. https://doi.org/10.1016/j.tate.2019.06.019
• 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
• 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
• Ball, D. L. (2011). Foreword. M. G. Sherin, V. R. Jacobs & R. A. Philipp (Ed.), Mathematics teacher noticing: Seeing through teachers’ eyes içinde (s. xx-xxiv). New York: Routledge.
• Barnhart, T., & van Es, E. (2015). Studying teacher noticing: Examining the relationship among pre-service science teachers' ability to attend, analyze and respond to student thinking. Teaching and Teacher Education, 45, 83-93. https://doi.org/10.1016/j.tate.2014.09.005
• 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. https://doi.org/10.5951/jresematheduc.41.4.0351
• Brown, R., Redmond, T., Sheehy, J., & Lang, D. (2015). Mathematical modelling - An example from an inter-school modelling challenge. N. H. Lee & K. E. D. Ng (Ed.), Mathematical modelling: From theory to practice içinde (s. 143–160). Singapore: World Scientific.
• Cobb, P., Wood, T., Yackel, E., & McNeal, B. (1992). Characteristics of classroom mathematics traditions: An interactional analysis. American Educational Research Journal, 29(3), 573-604. https://doi.org/10.3102/00028312029003
• Conner, A. (2008). Expanded Toulmin diagrams: A tool for investigating complex activity in classrooms. O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano & A. Sepulveda (Ed.), Proceedings of the Joint Meeting of PME 32 and PME-NA XXX (2. baskı) içinde (s. 361–368). Morelia, Mexico: Cinvestav-UMSNH.
• 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
• Diamond, J. M., Kalinec-Craig, C. A., & Shih, J. C. (2018). The problem of Sunny's pennies: A multi-institutional study about the development of elementary preservice teachers' professional noticing. Mathematics Teacher Education and Development, 20(2), 114-132.
• Erbay, H. N. (2018). Matematik öğretmeni adaylarının fark etme becerilerin video-kulüp uygulamalarıyla gelişim sürecinin incelenmesi. (Yayınlanmamış doktora tezi). Marmara Üniversitesi Eğitim Bilimleri Enstitüsü, İstanbul.
• Fisher, M. H., Thomas, J., Jong, C., Schack, E. O., & Dueber, D. (2019). Comparing preservice teachers’ professional noticing skills in elementary mathematics classrooms. School Science and Mathematics, 119(3), 142-149. https://doi.org/10.1111/ssm.12324
• Fisher, M. H., Thomas, J., Schack, E. O., Jong, C., & Tassell, J. (2018). Noticing numeracy now! Examining changes in preservice teachers’ noticing, knowledge, and attitudes. Mathematics Education Research Journal, 30(2), 209-232. https://doi.org/10.1007/s13394-017-0228-0
• 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
• Girit Yildiz, D., Osmanoglu, A. & Gundogdu Alayli, F. (2023). Providing a video-case-based professional development environment for prospective mathematics teachers to notice students’ misconceptions in measurement. Journal of Mathematics Teacher Education, 26(2), 179-209. https://doi.org/10.1007/s10857-021-09525-0
• Güner, P., & Akyüz, D. (2017). Ders imecesi (lesson study) mesleki gelişim modeli: Öğretmen adaylarının fark etme becerilerinin incelenmesi. İlköğretim Online, 16(2), 428-452. https://doi.org/10.17051/ilkonline.2017.304709
• Jacobs, V. R., Lamb, L. L., Philipp, R. A., & Schappelle, B. P. (2011). Deciding how to respond on the basis of children’s understandings. In M. Sherin, V. Jacobs, & R. Philipp (Ed.), Mathematics teacher noticing: Seeing through teachers’ eyes içinde (pp. 97-116). New York: Routledge.
• Jacobs, V., Lamb, L., & Philipp, R. (2010). Professional noticing of children's mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202. https://doi.org/10.5951/jresematheduc.41.2.0169
• Jacobs, V. R., Philipp, R. A., & Sherin, M. G. (2018). Noticing of mathematics teachers. S. Lerman (Ed.) Encyclopedia of Mathematics Education içinde (s. 1-3). Cham: Springer.
• König, J., Santagata, R., Scheiner, T., Adleff, A.‑K., Yang, X., & Kaiser, G. (2022). Teacher noticing: A systematic literature review of conceptualizations, research designs, and findings on learning to notice. Educational Research Review, 36, 100453. https://doi.org/10.1016/j.edurev.2022.100453
• Krummheuer, G. (1995). The ethnography of argumentation. P. Cobb & H. Bauersfeld (Ed.), Emergence of mathematical meaning içinde (s. 229-269). Hillsdale, NJ: Lawrence Erlbaum.
• Krummheuer, G. (2007). Argumentation and participation in the primary mathematics classroom: Two episodes and related theoretical abductions. The Journal of Mathematical Behavior, 26(1), 60-82. https://doi.org/10.1016/j.jmathb.2007.02.001
• Lee, M. Y., & Choy, B. (2017). Mathematical teacher noticing: The key to learning from lesson study. E. O. Schack, J. Wilhelm & M. H. Fisher (Ed.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks içinde (s. 121–140). Cham: Springer.
• Lee, M. Y., & Francis, D. C. (2018). Investigating the relationships among elementary teachers’ perceptions of the use of students’ thinking, their professional noticing skills, and their teaching practices. The Journal of Mathematical Behavior, 51, 118-128. https://doi.org/10.1016/j.jmathb.2017.11.007
• Lottero-Perdue, P. S., Masters, H. L., Mikeska, J. N., Thompson, M., Park Rogers, M., & Cross Francis, D. (2023). Elementary preservice teachers' responsiveness while eliciting students' initial arguments and encouraging critique in online simulated argumentation discussions. Science Education, 1–35. https://doi.org/10.1002/sce.21847
• Magiera, M. T. & Zambak, V. S. (2021). Prospective K-8 teachers’ noticing of student justifications and generalizations in the context of analyzing written artifacts and video-records. International Journal of STEM Education, 8(1), 1-21. https://doi.org/10.1186/s40594-020-00263-y
• Mason, J. (2002). Researching your own practice: The discipline of noticing. New York: Routledge-Falmer.
• McDuffie, A. R., Choppin, J., Drake, C., & Davis, J. (2018). Middle school mathematics teachers’ orientations and noticing of features of mathematics curriculum materials. International Journal of Educational Research, 92, 173-187. https://doi.org/10.1016/j.ijer.2018.09.019
• Melhuish, K., Thanheiser, E., & Fagan, J. (2019). The student discourse observation tool: Supporting teachers in noticing justifying and generalizing. Mathematics Teacher Educator, 7(2), 57-74. https://doi.org/10.5951/mathteaceduc.7.2.0057
• Melhuish, K., Thanheiser, E., & Guyot, L. (2018). Elementary school teachers’ noticing of essential mathematical reasoning forms: Justification and generalization. Journal of Mathematics Teacher Education, 23(1), 35-67. https://doi.org/10.1007/s10857-018-9408-4
• Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Thousands Oaks, CA: Sage Publications.
• Mitchell, R. N., & Marin, K. A. (2015). Examining the use of a structured analysis framework to support prospective teacher noticing. Journal of Mathematics Teacher Education, 18(6), 551–575. https://doi.org/10.1007/s10857-014-9294-3
• Mueller, M., Yankelewitz, D., & Maher, C. (2014). Teachers promoting student mathematical reasoning. Investigations in Mathematics Learning, 7(2), 1–20. https://doi.org/10.1080/24727466.2014.11790339
• Nama, S., & Ayalon, M. (2022). Exploring change in secondary mathematics teachers' noticing of argumentation. C. Fernández, S. Llinares, A. Gutiérrez & N. Planas (Ed.). Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education (3. Basım) içinde (s. 227-234). PME.
• National Council of Teachers of Mathematics [NCTM], (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM.
• Özdemir Baki, G., & Işık, A. (2018). Öğrencilerin matematiksel düşünmelerine yönelik öğretmenlerin farkındalık düzeylerinin incelenmesi: Ders imecesi modeli. Turkish Journal of Computer and Mathematics Education, 9(1), 122-146. https://doi.org/10.16949/turkbilmat.359103
• Patton, M. Q. (2014). Qualitative research & evaluation methods: Integrating theory and practice. London: Sage Publications.
• Roller, S. A. (2016). What they notice in video: A study of prospective secondary mathematics teachers learning to teach. Journal of Mathematics Teacher Education, 19(5), 477-498. https://doi.org/10.1007/s10857-015-9307-x Sánchez-Matamoros, G., Fernández, C., & Llinares, S. (2019). Relationships among prospective secondary mathematics teachers’ skills of attending, interpreting and responding to students’ understanding. Educational Studies in Mathematics, 100(1), 83-99. https://doi.org/10.1007/s10649-018-9855-y
• Santagata, R., Zannoni, C., & Stigler, J. W. (2007). The role of lesson analysis in pre-service teacher education: An empirical investigation of teacher learning from a virtual video-based field experience. Journal of Mathematics Teacher Education, 10(2), 123-140. https://doi.org/10.1007/s10857-007-9029-9 Schack, E., Fisher, M., & Wilhelm, J. (2017). Teacher noticing: Bridging and broadening perspective contexts, and frameworks. Cham: Springer International Publishing.
• Schwarz, B. B. (2009). Argumentation and learning. N. Muller Mirza & A. N. Perret-Clermont (Ed.), Argumentation and Education: Theoretical Foundations and Practices içinde (s. 91-126). Boston, MA: Springer.
• Schwarz, B. B., & Asterhan, C. S. C. (2010). Argumentation and reasoning. K. Littleton, C. Wood & J. Kleine Staarman (Ed.), International Handbook of Psychology in Education içinde (s. 137–176). Bradford: Emerald Group.
• Sherin, M., & van Es, E. (2005). Using video to support teachers’ ability to notice classroom interactions. Journal of Technology and Teacher Education, 13(3), 475-491.
• Sherin, M. G., & van Es, E. A. (2009). Effects of video club participation on teachers’ professional vision. Journal of Teacher Education, 60(1), 20-37. https://doi.org/10.1177/0022487108328155
• Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (2011). Situating the study of teacher noticing. M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Ed.), Mathematics teacher noticing: Seeing through teachers’ eyes içinde (s. 3-13). New York: Routledge.
• Staples, M. (2014). Supporting student justification in middle school mathematics classrooms: Teachers' work to create a context for justification. CRME Publications4. Erişim adresi: http://digitalcommons.uconn.edu/merg_docs/4
• Tataroğlu Taşdan, B., Tekin Dede, A., & Yiğit Koyunkaya, M. (2022). Examining pre-service mathematics teachers’ argumentation-supported lesson plans and their noticing during planning. International Journal of Mathematical Education in Science and Technology, 1-21. https://doi.org/10.1080/0020739X.2022.2054741
• Tekin-Sitrava, R., Kaiser, G., & Işıksal-Bostan, M. (2022). Development of prospective teachers’ noticing skills within initial teacher education. International Journal of Science and Mathematics Education, 20(7), 1611-1634. https://doi.org/10.1007/s10763-021-10211-z
• Toulmin, S. E. (2003). The Uses of Argument (updated ed.). New York, NY: Cambridge University Press. (Original work published 1958).
• Ulusoy, F., & Çakıroğlu, E. (2018). Using video cases and small-scale research projects to explore prospective mathematics teachers’ noticing of student thinking. EURASIA Journal of Mathematics, Science and Technology Education, 14(9), 1-14. https://doi.org/10.29333/ejmste/92020
• Ulusoy, F., & Çakıroğlu, E. (2021). Exploring prospective teachers’ noticing of students' understanding through micro-case videos. Journal of Mathematics Teacher Education, 24(3), 253-282. https://doi.org/10.1007/s10857-020-09457-1
• van Es, E. A. & Sherin, M. G. (2002). Learning to notice: Scaffolding new teachers’ interpretations of classroom interactions. Journal of Technology and Teacher Education, 10(4), 571–596.
• van Es, E. A., & Sherin, M. G. (2021). Expanding on prior conceptualizations of teacher noticing. ZDM Mathematics Education, 53(1), 17–27. https://doi.org/10.1007/s11858-020-01211-4
• van Es, E. A. (2011). A framework for learning to notice student thinking. M. G. Sherin, V. R. Jacobs & R. A. Philipp (Ed.), Mathematics teacher noticing: Seeing through teachers’ eyes içinde (s. 134–151). New York: Routledge.
• van Es, E. A., Cashen, M., Barnhart, T., & Auger, A. (2017). Learning to notice mathematics instruction: Using video to develop preservice teachers' vision of ambitious pedagogy. Cognition and Instruction, 35(3), 165-187. https://doi.org/10.1080/07370008.2017.1317125
• Walkoe, J. (2015). Exploring teacher noticing of student algebraic thinking in a video club. Journal of Mathematics Teacher Education, 18(6), 523-550. https://doi.org/10.1007/s10857-014-9289-0
• Wallin, A. J., & Amador, J. M. (2019). Supporting secondary rural teachers’ development of noticing and pedagogical design capacity through video clubs. Journal of Mathematics Teacher Education, 22(5), 515-540. https://doi.org/10.1007/s10857-018-9397-3
• Yackel, E. (2002). What we can learn from analyzing the teacher’s role in collective argumentation. Journal of Mathematical Behavior, 21, 423–440. https://doi.org/10.1016/S0732-3123(02)00143-8
• Yackel, E. (2004). Theoretical perspectives for analyzing explanation, justification and argumentation in mathematics classrooms. Communications of Mathematical Education, 18(1), 1-18.
• Yılmaz, H. K., & Özdemir-Baki, G. (2023). Bir ortaokul matematik öğretmeninin fark etme becerisinin alan ölçme öğretimine yansımaları. Buca Eğitim Fakültesi Dergisi, 55, 95-118. https://doi.org/10.53444/deubefd.1195881
• Yin, R. K. (2018). Case study research and applications: Design and methods (6th ed). London: Sage.