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Dönel Cisimlerin Yüzey Alanının Hesaplanması Sürecindeki Argümanların İncelenmesi

Year 2022, Volume: 11 Issue: 4, 587 - 603, 30.12.2022

Ayşe Tekin Dede , Ali Özgün Özer , Esra Bukova Güzel

https://doi.org/10.30703/cije.1072163

Abstract

Çalışmada Analiz I dersinde dönel cisimlerin yüzey alanını hesaplamayı sağlayacak modelin oluşturulması sürecinde ilköğretim matematik öğretmenliği öğrencilerinin ortaklaşa argümanlarının incelenmesi amaçlanmaktadır. Durum çalışması olarak desenlenen çalışmanın katılımcıları Analiz I dersine kayıtlı kırk iki ilköğretim matematik öğretmenliği öğrencileridir. Veriler dönel cisimlerin yüzey alanı modelinin oluşturulması esnasındaki argümantasyon sürecinin video kayıtları ile araştırmacının gözlem notlarından oluşmaktadır. Veriler analiz edilerek argümantasyon sürecinin bileşenlerini içeren Toulmin argümantasyon şemaları oluşturulmuştur. Çalışmanın bulguları öğrencilerin birbirlerinin iddialarına gerekçe sunarak ve bu iddiaları çürüterek argümantasyon sürecine aktif katılım sağladıklarını ortaya koymaktadır. Bu aktif katılımda dersi yürüten araştırmacının argümantasyon sürecini destekleyici eylemleri, öğrencilerin ön öğrenmeleri ve sınıf içindeki normlar etkili olmuştur. Argümantasyon sürecinin bileşenlerinden veri, iddia, gerekçe ve çürütücü bileşenleri ortaya çıkmıştır. Özellikle öğrencilerin birbirlerinin açıklamalarını dikkatle dinleyerek çürütücüler öne sürdükleri ve bu çürütücülerin kendinden sonraki gelen argümanların gerekçeleri olması dikkat çekici bir bulgu olmuştur. Çürütücülerin başka bir görevi de sadece iddiayı değil bazı durumlarda veri, iddia ve gerekçeyi içeren alt argümanların da geçerliğini yok etmek olmuştur. Ayrıca verilerden iddiaya geçişte araştırmacının sorgulatmasıyla birlikte öğrencilerin gerekçelerini ifade ettikleri anlaşılmaktadır. Tüm bunlarla birlikte katılımcıların argümantasyon sürecinde destekleyici ya da niteleyicileri ifade etmedikleri de görülmektedir.

Keywords

argümantasyon analiz dönel cisim yüzey alanı çürütücü Argumentation calculus solid of revolution surface area components of the argumentation process

Supporting Institution

Dokuz Eylül Üniversitesi Bilimsel Araştırma Projeleri Birimi

Project Number

2018.KB.EGT.008

References

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Examination of the Arguments in the Process of Calculating the Surface Area of the Solids of Revolution

Year 2022, Volume: 11 Issue: 4, 587 - 603, 30.12.2022

Ayşe Tekin Dede , Ali Özgün Özer , Esra Bukova Güzel

https://doi.org/10.30703/cije.1072163

Abstract

In the study, it is aimed to examine the collective arguments of students in the process of constructing a model to calculate the surface area of the solids of revolution in the Calculus I course. The participants of the study, which was designed as a case study, were forty-two students enrolled in Calculus I course in the elementary mathematics teaching department. The data consisted of the video recordings of the argumentation process and the observation notes of the researcher during the construction of the surface area model of the solids of revolution. By analysing the data, Toulmin argumentation schemes containing the components of the argumentation process were created. The findings of the study revealed that the students actively participated in the argumentation process by justifying and refuting each other's claims. In this active participation, the actions of the researcher who conducted the course to support the argumentation process, the students' pre-learning and the norms in the classroom were effective. Data, claim, warrant and rebuttal components emerged from the components of the argumentation process. Particularly, it was a remarkable finding that the students put forward rebuttals by listening to each other's explanations carefully and that these rebuttals were justifications for the subsequent arguments. Another task of the rebuttals was to invalidate not only the claim but also, in some cases, the sub-arguments containing data, claim and justification. In addition, it was understood that the students expressed their justifications with the researcher's questioning in the transition from the data to the claim. In addition to all these, it was seen that the participants did not express backings or qualifiers in the argumentation process.

Keywords

Argumentation calculus solid of revolution surface area components of the argumentation process

Project Number

2018.KB.EGT.008

References

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  • Berry, J. S., & Nyman, M. A. (2003). Promoting students’ graphical understanding of the calculus. The Journal of Mathematical Behavior, 22(4), 479-495. https://doi.org/10.1016/j.jmathb.2003.09.006
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  • Çetin, İ., & Dev, Ş. (2021): Pre-service elementary mathematics teachers’ methods when solving integral-volume problems and the rationale behind their selections. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2021.1951859
  • Delice, A., & Sevimli, E. (2010). Mathematics teacher candidates’ multiple representation and conceptual-procedural knowledge level in definite integral. Gaziantep Üniversity Journal of Social Sciences, 9(3), 581–605.
  • Dogruer, S.S., & Akyuz, D. (2020). Mathematical practices of eighth graders about 3d shapes in an argumentation, technology, and design-based classroom environment. International Journal of Science and Mathematics Education, 18, 1485–1505. https://doi.org/10.1007/s10763-019-10028-x
  • Doruk, M. (2016). İlköğretim matematik öğretmeni adaylarının analiz alanındaki argümantasyon ve ispat süreçlerinin incelenmesi. Yayımlanmamış Doktora Tezi, Atatürk Üniversitesi Eğitim Bilimleri Enstitüsü, Erzurum, Türkiye.
  • Doruk, M., Duran, M., & Kaplan, A. (2018). Argümantasyon tabanlı olasılık öğretiminin ortaokul öğrencilerinin matematiksel üstbiliş farkındalıklarına ve olasılıksal muhakeme becerilerine etkisinin incelenmesi. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 12(1), 83-121. https://doi.org/10.17522/balikesirnef.437714
  • Erkek, Ö., & Işıksal Bostan, M. (2019). Prospective middle school mathematics teachers’ global argumentation structures. International Journal of Science and Mathematics Education, 17(3), 613-633. https://doi.org/10.1007/s10763-018-9884-0
  • Forman, E. A. (2003). A sociocultural approach to mathematics reform: Speaking, inscribing, and doing mathematics within communities of practice. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A Research Companion to Principles and Standards for School Mathematics (pp. 333-352). Reston, VA: NationalCouncil of Teachers of Mathematics. 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
  • Goos, M. (2004). Learning mathematics in a classroom community of inquiry. Journal for Research in Mathematics Education, 35(4), 258–291. https://doi.org/30034810
  • Hathaway, RA. (2008). Simple acronym for doing calculus: CAL. PRIMUS, 18. 542–545. https://doi.org/10.1080/10511970701604014
  • Herbel-Eisenmann, B. A., Steele, M. D., & Cirillo, M. (2013). (Developing) Teacher discourse moves: a framework for professional development. Mathematics Teacher Educator, 1(2), 181–196. https://doi.org/10.5951/mathteaceduc.1.2.0181
  • Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws, (Ed.), Handbook of research on mathematics teaching and learning: (A project of the national council of teachers of mathematics) (pp. 65–97). Macmillan.
  • Hollebrands, K. F., Conner, A., & Smith, R. C. (2010). The nature of arguments provided by college geometry students with access to technology while solving problems. Journal for Research in Mathematics Education, 41(4), 324-350.
  • Hufferd-Ackles, K., Fuson, K. C., & Sherin, M. G. (2004). Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education, 35(2), 81–116. https://doi.org/30034933
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There are 64 citations in total.

Details

Primary Language Turkish
Journal Section Research Article
Authors

Ayşe Tekin Dede 0000-0002-8971-1970

Ali Özgün Özer 0000-0002-4204-9115

Esra Bukova Güzel 0000-0001-7571-1374

Project Number 2018.KB.EGT.008
Early Pub Date December 30, 2022
Publication Date December 30, 2022
Published in Issue Year 2022Volume: 11 Issue: 4

Cite

APA Tekin Dede, A., Özer, A. Ö., & Bukova Güzel, E. (2022). Dönel Cisimlerin Yüzey Alanının Hesaplanması Sürecindeki Argümanların İncelenmesi. Cumhuriyet Uluslararası Eğitim Dergisi, 11(4), 587-603. https://doi.org/10.30703/cije.1072163
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