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Prospective Middle School Mathematics Teachers’ Global Argumentation Structures

  • Özlem ErkekEmail author
  • Mine Işıksal Bostan
Article

Abstract

The aim of the present study was to investigate the nature of global argumentation structures of prospective middle school mathematics teachers in a technology enhanced environment. A qualitative case study was conducted with 8 participants from an Elementary Mathematics Education undergraduate program of one of the public universities in Ankara. Two implementations, 1 of which included 2 geometry tasks on triangles and another which included 2 geometry tasks based on circles, were conducted. Subsequently, global argumentation structures were revealed via data analysis. The findings indicated that the prospective middle school mathematics teachers resort frequently to simple global argumentation structures since their mathematical reasoning was insufficient. On the other hand, technology had a positive impact on argument construction and global argumentation structures of prospective middle school mathematics teachers. However, it was deduced that prospective middle school mathematics teachers need to be challenged on argumentation and about how to facilitate argumentation effectively in their future classroom experiences.

Keywords

Argumentation GeoGebra Prospective middle school mathematics teachers Technology 

Supplementary material

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References

  1. Anderson, R. C., Chinn, C., Chang, J., Waggoner, M., & Yi, H. (1997). On the logical integrity of children’s arguments. Cognition and Instruction, 15, 135–167.CrossRefGoogle Scholar
  2. Antonini, S., & Martignone, F. (2011). Argumentation in exploring mathematical machines: A study on pantographs. In B. Ubuz (Ed.), Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 41–48). Ankara, Turkey: Can Tekin Publisher.Google Scholar
  3. Ceylan, T. (2012). Geogebra yazılımı ortamında ilköğretim matematik öğretmen adaylarının geometrik ispat biçimlerinin incelenmesi [Investigating geometry proof structures of prospective elementary mathematics teachers in GeoGebra environment] (Unpublished master’s thesis). Ankara, Turkey: Ankara University.Google Scholar
  4. Conner, A., Singletary, L. M., Smith, R. C., Wagner, P. A., & Francisco, R. T. (2014). Identifying kinds of reasoning in collective argumentation. Mathematical Thinking and Learning, 16, 180–200.CrossRefGoogle Scholar
  5. Coşkun, Ş. (2011). A multiple case study investigating the effects of technology on students’ visual and nonvisual thinking preferences: comparing paper-pencil and dynamic software based strategies of algebra word problems (Unpublished doctoral dissertation). Florida: University of Central Florida.Google Scholar
  6. De Villiers, M. (2004). Using dynamic geometry to expand mathematics teachers’ understanding of proof. International Journal of Mathematical Education in Science and Technology, 35(5), 703–724.CrossRefGoogle Scholar
  7. Hanna, G., & De Villiers, M. (2008). ICMI study 19: Proof and proving in mathematics education. ZDM––The International Journal on Mathematics Education, 40(2), 329–336.CrossRefGoogle Scholar
  8. Inglis, M., Mejia-Ramos, J. P., & Simpson, A. (2007). Modelling mathematical argumentation: The importance of qualification. Educational Studies in Mathematics, 66, 3–21.CrossRefGoogle Scholar
  9. Iranzo Domènech, N. (2009). Influence of dynamic geometry software on plane geometry problem solving strategies (Unpublished doctoral dissertation). Barcelona, Spain: Universitat Autònoma de Barcelona.Google Scholar
  10. Jones, K. (2002). Research on the use of dynamic geometry software: Implications for the classroom. Micromath, 18(3), 18–20.Google Scholar
  11. Knipping, C. (2008). A method for revealing structures of argumentations in classroom proving processes. ZDM Mathematics Education, 40(3), 427–441.CrossRefGoogle Scholar
  12. 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.CrossRefGoogle Scholar
  13. Krummheuer, G. (1995). The ethnography of argumentation. In P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning: Interaction in classroom cultures (pp. 229–269). Hillsdale, MI: Lawrence Erlbaum Associates.Google Scholar
  14. Mariotti, A. M. (2006). Proof and proving in mathematics education. In A. Gutierrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education (pp. 173–204). Rotterdam, The Netherlands: Sense Publishers.Google Scholar
  15. Nardi, E., Biza, I., & Zachariades, T. (2012). “Warrant” revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation. Educational Studies in Mathematics, 79(2), 157–173.CrossRefGoogle Scholar
  16. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.Google Scholar
  17. Pedemonte, B., & Reid, D. (2011). The role of abduction in proving process. Educational Studies in Mathematics, 76, 281–303.CrossRefGoogle Scholar
  18. Posamentier, A. S., & Salkind, C. T. (1988). Challenging problems in geometry. New York, NY: Dover Publications Inc.Google Scholar
  19. Reid, D. A., & Knipping, C. (2010). Proof in mathematics education: Research, learning, and teaching. Rotterdam, The Netherlands: Sense Publishers.Google Scholar
  20. Strom, D., Kemeny, V., Lehrer, R., & Forman, E. (2001). Visualizing the emergent structure of children’s mathematical argument. Cognitive Science, 25(5), 733–773.  https://doi.org/10.1207/s15516709cog2505_6.CrossRefGoogle Scholar
  21. Toulmin, S. (1958). The uses of argument. New York, NY: Cambridge University Press.Google Scholar
  22. Vincent, J., Chick, H. & McCrae, B. (2005). Argumentation profile charts as tools for analysing students’ argumentations. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29 th PME Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 281–288). Melbourne, Australia: PME.Google Scholar
  23. Walter, J. G., & Barros, T. (2011). Students build mathematical theory: Semantic warrants in argumentation. Educational Studies in Mathematics, 78(3), 323–342.CrossRefGoogle Scholar
  24. Walter, J., & Johnson, C. (2007). Linguistic invention and semantic warrant production: Elementary teachers’ interpretation of graphs. International Journal of Science and Mathematics Education, 5(4), 705–727.CrossRefGoogle Scholar
  25. Weiss, R. E. (2003). Designing problems to promote higher-order thinking. New directions for teaching and learning, 95, 25–31.CrossRefGoogle Scholar
  26. Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.CrossRefGoogle Scholar
  27. Yackel, E., Ramussen, C., & King, K. (2000). Social and sociomathematical norms in an advanced undergraduate mathematic s course. Journal of Mathematical Behavior, 19, 275–287.CrossRefGoogle Scholar
  28. Yemen-Karpuzcu, S., Ulusoy, F., & Işıksal-Bostan, M. (2017). Prospective middle school mathematics teachers’covariational reasoning for interpreting dynamic events during peer interactions. International Journal of Science and Mathematics Education, 15(1), 89–108.CrossRefGoogle Scholar

Copyright information

© Ministry of Science and Technology, Taiwan 2018

Authors and Affiliations

  1. 1.Faculty of Education, Mathematics and Science Education Departmentİstanbul Medipol UniversityIstanbulTurkey
  2. 2.Eğitim Fakültesi, Güney Yerleşkeİstanbul Medipol UniversityIstanbulTurkey
  3. 3.Faculty of education, Mathematics and Science Education DepartmentMiddle East Technical UniversityAnkaraTurkey
  4. 4.Eğitim FakültesiOrta Doğu Teknik ÜniversitesiAnkaraTurkey

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