Yıl 2018, Cilt 9, Sayı 3, Sayfalar 636 - 661 2018-12-17

Matematik Eğitimi Alanındaki Ortaklaşa Argümantasyon Çalışmalarının İncelenmesi
Examination of the Collective Argumentation Studies in the Mathematics Education Field

Ayşe Tekin Dede [1]

136 534

Bireysel öğrenmeden sosyal bağlamda öğrenmeye doğru gelişim gösteren matematik eğitimi çalışmalarında farklı sosyo-kültürel teoriler kullanılmaya başlanmıştır. Bu teorilerden biri de Toulmin’in argümantasyon çalışmalarına dayalı olan ortaklaşa argümantasyon teorisidir. Ortaklaşa argümantasyon öğrenciler ve öğretmenin iddialarda bulundukları ve bu iddiaları kanıtlarla destekledikleri etkileşimli bir süreç olarak ele alınmaktadır. Bu çalışmada matematik eğitimi alanındaki ortaklaşa argümantasyon çalışmalarının tanıtılarak bu çalışmaların benzer ve farklı yönlerinin ortaya koyulması amaçlanmaktadır. Bu bağlamda gerçekleştirilen alanyazın taraması sonucunda on dört çalışmayla karşılaşılmıştır. Bu çalışmaların ortak yönü her birinin öğretmen veya öğrenci söylemlerine dayalı olmaları ve bu söylemleri analiz etmek için Toulmin’in argümantasyon şemasının bileşenlerinden yararlanıyor olmalarıdır. Kimi çalışmalar farklı kuramsal çerçeveleri argümantasyon ile ilişkilendirirken, kimisi kuramsal çerçeve oluşturmayı kimisi de argümantasyon bileşenlerine ilişkin kavramsal tanıtım yapmayı hedeflemektedir. Ülkemizde ortaklaşa argümantasyon alanındaki çalışmalarda eksiklikler olması sebebiyle farklı öğrenci grupları ve öğretmenlerle, farklı sınıf bağlamlarında yapılacak çalışmaların hem ulusal hem de uluslararası alana katkı sağlayacağı düşünülmektedir.

Different socio-cultural theories have begun to be used in mathematics education studies, which have developed from individual learning to learning in its social context. One of these theories is the collective argumentation theory based on Toulmin's argumentation studies. The collective argumentation is dealt with as an interactive process in which students and teachers are claiming and supporting these claims through evidence. In this study, it is aimed to introduce similar and different aspects of the collective argumentation studies in the field of mathematics education by introducing it. As a result of the literature review carried out in this context, fourteen studies were encountered. The common feature of these studies is that each one is based on the teacher or student discourse, and that they use the components of Toulmin's argumentation schema to analyze these discourses. While some studies link different theoretical frameworks with argumentation, some aim to develop a theoretical framework and some aim to make conceptual presentations about the components of the argumentation. It is thought that the work to be done in different class contexts with different student groups and teachers will contribute to both the national and international fields because there are deficiencies in the studies in the field of the collective argumentation in our country.

  • Boero, P. (2011). Argumentation and proof: Discussing a “successful” classroom discussion. In M. Pytlak, T. Rowland & E. Swoboda (Eds.), Proceedings of the 7th Congress of the European Society for Research in Mathematics Education (pp. 120-130). Rszéskow, Polonia: ERME.
  • Boero, P., Douek, N., Morselli, F., & Pedemonte, B. (2010). Argumentation and proof: A contribution to theoretical perspectives and their classroom implementation. In M. F. F. Pinto & T. F. Kawasaki (Eds.), Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 179–205). Belo Horizonte: PME.
  • Brown, R. A. J. (1994). Collective mathematical thinking in the primary classroom: A conceptual and empirical analysis within a sociocultural framework (Unpublished bachelor of educational studies (hons) thesis). University of Queensland, Brisbane.
  • Brown, R. A. J. (1997). "You can't explain infinity!": Collective argumentation discourse across primary school subject domains. In M. Goos, K. Moni & J. Knight (Eds.), Scholars in context: Prospects and transitions (pp. 17-22). Brisbane: Post Pressed.
  • Brown, R. A. J. (1998). "Where do you people get your ideas from?": Negotiating zones of collaborative learning within an upper primary classroom. In B. Baker, M. Tucker & C. Ng (Eds.), Education's new timespace: Visions from the present (pp.107-112). Brisbane: Postpressed.
  • Brown, R. A. J. (2017). Using collective argumentation to engage students in a primary mathematics classroom. Mathematics Education Research Journal, 29(2), 183-199.
  • Brown, R. A. J., & Renshaw, P. (2000). Collective argumentation: A sociocultural approach to reframing classroom teaching and learning. In H. Cowie & G. Aalsvoort (Eds.), Social interaction in learning and instruction: The meaning of discourse for the construction of knowledge (pp. 52-66). Oxford: Elsevier Science.
  • Brown, R. A. J., & Renshaw, P. D. (1995). Developing collective mathematical thinking within the primary classroom. In B. Atweh & S. Flavel (Eds.), Proceedings of the Eighteenth Annual Conference of the Mathematics Education Research Group of Australasia (MERGA) (pp. 128-134). Darwin: Mathematics Education Research Group of Australasia.
  • Brown, R. A. J., & Renshaw, P. D. (1996). Collective argumentation in the primary mathematics classroom: Towards a community of practice. In P. C. Clarkson (Ed.), Proceedings of the Nineteenth Annual Conference of the Mathematics Education Research Group of Australasia (MERGA) (pp.85- 92). Melbourne: Mathematics Education Research Group of Australasia.
  • Brown, R. A. J., & Renshaw, P. D. (2006). Transforming practice: Using collective argumentation to bring about teacher change in a year 7 mathematics classroom. In P. Grootenboer, R. Zevenbergen & M. Chinnappan (Eds.), Proceedings of the 29th Annual Conference of the Mathematics Education Research Group of Australasia (MERGA) (pp. 99-106). Sydney: Mathematics Education Research Group of Australasia.
  • Brown, R. A. J., & Renshaw, P. D. (1999). Speaking with authority in episodes of mathematical discourse. In J. Trunan & K. M. Trunan (Eds.), Proceedings of the Twenty-Second Annual Conference of the Mathematics Education Research Group of Australasia (MERGA) (pp.113-119). Adelaide: Mathematics Education Research Group of Australasia.
  • Cobb, P., Jaworski, B., & Presmeg, N. (1996). Emergent and sociocultural views of mathematical activity. In L. P. Steffe, P. Nesher, P. Cobb, G. A. Goldin & B. Greer (Eds.), Theories of mathematical learning (pp. 3-20). Mahwah, NJ: Lawrence Erlbaum.
  • 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.
  • Common Core State Standards for Mathematics [CCSSM]. (2010). Common core state standards initiative. Retrieved April 10, 2018 from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
  • Conner, A. (2008). Expanded Toulmin diagrams: A tool for investigating complex activity in classrooms. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano & A. Sepulveda (Eds.), Proceedings of the Joint Meeting of PME 32 and PME-NA XXX (Vol. 2, pp. 361–368). Morelia, Mexico: Cinvestav-UMSNH.
  • Conner, A. (2012). Warrants as indications of reasoning patterns in secondary mathematics classes. In S. J. Cho (Ed.), Proceedings of the 12th International Congress on Mathematical Education (ICME-12), Topic Study Group 14 (pp. 2819–2827). Seoul, Korea: Springer, Cham.
  • Conner, A., Singletary, L. M., Smith, R. C., Wagner, P. A., & Francisco, R. T. (2014a). 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.
  • Conner, A., Singletary, L. M., Smith, R. C., Wagner, P. A., & Francisco, R. T. (2014b). Identifying kinds of reasoning in collective argumentation. Mathematical Thinking and Learning, 16(3), 181-200.
  • Dinçer, S. (2011). Matematik lisans derslerindeki tartışmaların Toulmin modeline göre analizi (Yayınlanmamış doktora tezi). Hacettepe Üniversitesi, Fen Bilimleri Enstitüsü, Ankara.
  • Douek, N., & Pichat, M. (2003). From oral to written texts in grade 1 and the approach to mathematical argumentation. In N. A. Pateman, B. J. Dougherty & J. T. Zilliox (Eds.), Proceedings of the International Group for the Psychology of Mathematics Education (Vol. 2., pp. 341–348). University of Hawaii: Honolulu, Hawaii, USA
  • Duran, M., Doruk, M. ve Kaplan, A. (2017). Argümantasyon tabanlı olasılık öğretiminin ortaokul öğrencilerinin başarılarına ve kaygılarına etkililiğinin incelenmesi. Eğitimde Kuram ve Uygulama, 13(1), 55-87.
  • 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.
  • 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.
  • Hunter, R., & Anthony, G. (2011). Learning to “friendly argue” in a community of mathematical inquiry (Teaching and learning research ınitiative report). Wellington: New Zealand Educational Research Council.
  • Inglis, M., Mejia-Ramos, J. P., & Simpson, A. (2007). Modelling mathematical argumentation: The importance of qualification. Educational Studies in Mathematics, 66(1), 3-21.
  • Knipping, C. (2004). Argumentations in proving discourses in mathematics classrooms. In E. Cohors-Fresenborg, H. Maier, K. Reiss, G. Toerner & H. G. Weigand (Eds.), Selected Papers from the Annual Conference on Didactics of Mathematics (pp. 73–84). Hildesheim: Franzbecker Verlag. Knipping, C. (2008). A method for revealing structures of argumentation in classroom proving processes. Zentralblatt für Didaktik der Mathematik-ZDM, 40(3), 427–441.
  • Knipping, C., & Reid, D. (2013). Revealing structures of argumentation in classroom proving processes. In A. Aberdein & I. J. Dove (Eds.), The argument of mathematics (pp. 181– 208). Dordrecht, Springer.
  • Knipping, C., & Reid, D. (2015). Reconstructing argumentation structures: A perspective on proving processes in secondary mathematics classroom interactions. In A. Bikner-Ahsbahs, C. Knipping & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education (pp. 75–101). Springer: Dordrecht.
  • Krummheuer, G. (1995). The ethnography of argumentation. In P. Cobb & H. Bauersfeld (Eds.), Emergence of mathematical meaning (pp. 229-269). Hillsdale, NJ: Lawrence Erlbaum.
  • Krummheuer, G. (2000). Studies of argumentation in primary mathematics education. Zentralblatt für Didaktik der Mathematik-ZDM, 32(5), 155-161.
  • 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.
  • Krummheuer, G. (2015). Methods for reconstructing processes of argumentation and participation in primary mathematics interaction. In A. Bikner-Ahsbahs, C. Knipping & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education. (pp. 51–74). Dordrecht: Springer.
  • Lampert, M., & Cobb, P. (2003). Communication and language. In J. Kilpatrick, W. G. Martin & D. Schifter (Eds.), A research companion to NCTM’s principles and standards (pp. 237-249). Reston, VA: National Council of Teachers of Mathematics.
  • le Roux, A., Olivier, A., & Murray, H. (2004). Children struggling to make sense of fractions: An analysis of their argumentation. South African Journal of Education, 24(1), 88-94.
  • Lerman, S. (2000). The social turn in mathematics education research. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 19-44). Westport, CN: Ablex.
  • Lerman, S. (2001). Cultural, discursive psychology: A sociocultural approach to studying the teaching and learning of mathematics. Educational Studies in Mathematics, 46(1-3), 87-113.
  • McCrone, S. S. (2005). The development of mathematical discussions: An investigation in a fifth-grade classroom. Mathematical Thinking and Learning, 7(2), 111-133.
  • Mercan, E. (2015). Fonksiyonlar konusunun öğretiminde argümantasyon tabanlı öğrenme yaklaşımının etkisinin farklı değişkenler açısından İncelenmesi (Yayınlanmamış doktora tezi). Atatürk Üniversitesi, Eğitim Bilimleri Enstitüsü, Erzurum.
  • Miller, M. (1987). Argumentation and cognition. In M. Hickmann (Ed.), Social and functional approaches to language and thought (pp. 225–249). London: Academic Press.
  • Milli Eğitim Bakanlığı [MEB]. (2017a). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Ankara: Talim ve Terbiye Kurulu Başkanlığı.
  • Milli Eğitim Bakanlığı [MEB]. (2017b). Ortaöğretim matematik dersi öğretim programı. Ankara: Talim ve Terbiye Kurulu Başkanlığı. National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • Pedemonte, B. (2002). Relation between argumentation and proof in mathematics: Cognitive unity or break? In J. Novotna´ (Ed.), Proceedings of the 2nd Conference of the European Society for Research in Mathematics Education (pp. 70–80). Marienbad: ERME.
  • Pedemonte, B. (2008). Argumentation and algebraic proof. Zentralblatt für Didaktik der Mathematik-ZDM, 40(3), 385-400.
  • Peirce, C. S. (1956). Sixth paper: Deduction, induction, and hypothesis. In M. R. Cohen (Ed.), Chance, love, and logic: Philosophical essays (pp. 131–153). New York, NY: G. Braziller.
  • Planas, N., & Morera, L. (2011). Revoicing in processes of collective mathematical argumentation among students. In M. Pytlak, T. Rowland & E. Swoboda (Eds.), Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (pp. 1356–1365). Rzeszów, Poland: University of Rzeszów.
  • Rasmussen, C., & Stephan M. (2008). A methodology for documenting collective activity. In A. E. Kelly, R. A. Lesh, & J. Y. Baek (Eds.), Handbook of design research methods in education: Innovations in science, technology, engineering and mathematics learning and teaching (pp. 195–215). New York, NY: Routledge.
  • Renshaw P. D., & Brown R. A. J. (1997). Learning partnerships: The role of teachers in a community of learners. In L. Logan & J. Sachs (Eds.), Meeting the challenges of primary schools (pp. 200-211). London: Routledge.
  • Schwarz, B. B., & Asterhan, C. S. C. (2010). Argumentation and reasoning. In K. Littleton, C. Wood & J. Kleine Staarman (Eds.), International handbook of psychology in education (pp. 137–176). Bradford: Emerald Group.
  • Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46(1-3), 13-57.
  • Stephan, M., & Rasmussen, C. (2002). Classroom mathematical practices in differential equations. The Journal of Mathematical Behavior, 21(4), 459-490.
  • Toulmin, S. E. (2003). The uses of argument (Updated ed.). New York, NY: Cambridge University Press.
  • Urhan, S. ve Bülbül, A. (2016). Argümantasyon ve matematiksel kanıt süreçleri arasındaki ilişkiler. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 10(1), 351-373.
  • Wagner, P. A., Smith, R. C., Conner, A., Singletary, L. M., & Francisco, R. T. (2014). Using Toulmin's model to develop prospective secondary mathematics teachers' conceptions of collective argumentation. Mathematics Teacher Educator, 3(1), 8-26.
  • Weber, K., Maher, C., Powell, A., & Lee, H. S. (2008). Learning opportunities from group discussions: Warrants become the objects of debate. Educational Studies in Mathematics, 68(3), 247-261.
  • Whitenack, J. W., & Knipping, N. (2002). Argumentation, instructional design theory and students’ mathematical learning: a case for coordinating interpretive lenses. The Journal of Mathematical Behavior, 21(4), 441-457.
  • Yackel, E. (2001). Explanation, justification and argumentation in mathematics classrooms. In M. van den Heuvel-Panhuizen (Ed.), Proceeding of the 25th PME International Conference, (Vol 1, pp. 9-24). Utrecht, Holland: IGPME.
  • Yackel, E. (2002). What we can learn from analyzing the teacher’s role in collective argumentation. The Journal of Mathematical Behavior, 21(4), 423-440.
  • Yackel, E. (2004). Theoretical perspectives for analyzing explanation, justification and argumentation in mathematics classrooms. Communications of Mathematical Education, 18(1), 1-18.
Birincil Dil tr
Konular Sosyal
Dergi Bölümü Derleme Makaleleri
Yazarlar

Yazar: Ayşe Tekin Dede (Sorumlu Yazar)
Kurum: DOKUZ EYLÜL ÜNİVERSİTESİ
Ülke: Turkey


Bibtex @derleme { turkbilmat386722, journal = {Turkish Journal of Computer and Mathematics Education (TURCOMAT)}, issn = {}, eissn = {1309-4653}, address = {Türkbilmat Eğitim Hizmetleri}, year = {2018}, volume = {9}, pages = {636 - 661}, doi = {10.16949/turkbilmat.386722}, title = {Matematik Eğitimi Alanındaki Ortaklaşa Argümantasyon Çalışmalarının İncelenmesi}, key = {cite}, author = {Tekin Dede, Ayşe} }
APA Tekin Dede, A . (2018). Matematik Eğitimi Alanındaki Ortaklaşa Argümantasyon Çalışmalarının İncelenmesi. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 9 (3), 636-661. DOI: 10.16949/turkbilmat.386722
MLA Tekin Dede, A . "Matematik Eğitimi Alanındaki Ortaklaşa Argümantasyon Çalışmalarının İncelenmesi". Turkish Journal of Computer and Mathematics Education (TURCOMAT) 9 (2018): 636-661 <http://dergipark.gov.tr/turkbilmat/issue/41275/386722>
Chicago Tekin Dede, A . "Matematik Eğitimi Alanındaki Ortaklaşa Argümantasyon Çalışmalarının İncelenmesi". Turkish Journal of Computer and Mathematics Education (TURCOMAT) 9 (2018): 636-661
RIS TY - JOUR T1 - Matematik Eğitimi Alanındaki Ortaklaşa Argümantasyon Çalışmalarının İncelenmesi AU - Ayşe Tekin Dede Y1 - 2018 PY - 2018 N1 - doi: 10.16949/turkbilmat.386722 DO - 10.16949/turkbilmat.386722 T2 - Turkish Journal of Computer and Mathematics Education (TURCOMAT) JF - Journal JO - JOR SP - 636 EP - 661 VL - 9 IS - 3 SN - -1309-4653 M3 - doi: 10.16949/turkbilmat.386722 UR - http://dx.doi.org/10.16949/turkbilmat.386722 Y2 - 2018 ER -
EndNote %0 Turkish Journal of Computer and Mathematics Education (TURCOMAT) Matematik Eğitimi Alanındaki Ortaklaşa Argümantasyon Çalışmalarının İncelenmesi %A Ayşe Tekin Dede %T Matematik Eğitimi Alanındaki Ortaklaşa Argümantasyon Çalışmalarının İncelenmesi %D 2018 %J Turkish Journal of Computer and Mathematics Education (TURCOMAT) %P -1309-4653 %V 9 %N 3 %R doi: 10.16949/turkbilmat.386722 %U 10.16949/turkbilmat.386722
ISNAD Tekin Dede, Ayşe . "Matematik Eğitimi Alanındaki Ortaklaşa Argümantasyon Çalışmalarının İncelenmesi". Turkish Journal of Computer and Mathematics Education (TURCOMAT) 9 / 3 (Aralık 2018): 636-661. http://dx.doi.org/10.16949/turkbilmat.386722