Article Sidebar

Published
Sep 21, 2020
Download
PDF
Statistic
Read Counter : 623 Download : 570

Main Article Content

Abstract

This study investigates the aspects that influence students' justification of the four types of arguments constructed by students, namely: inductive, algebraic, visual, and perceptual. A grounded theory type qualitative approach was chosen to investigate the emergence of the four types of arguments and how the characteristics of students from each type justify the arguments constructed. Four people from 75 students were involved in the interview after previously getting a test of mathematical argumentation. The results of the study found that three factors influenced students' justification for mathematical arguments, namely: students' understanding of claims, treatment given, and facts found in arguments. Claims influence the way students construct arguments, but facts in arguments are the primary consideration for students in choosing convincing arguments compared to representations. Also, factor treatment turns out to change students' decisions in choosing arguments, and these changes tend to lead to more formal arguments.

Keywords

Mathematical argumentation Type of argument Justifying to argument Claim

Article Details

References

  1. Aberdein, A. (2009). Mathematics and argumentation. Foundations of Science, 14(1), 1–8. doi:10.1007/s10699-008-9158-3
  2. Bergqvist, T. (2005). How students verify conjectures: Teachers’ expectations. Journal of Mathematics Teacher Education, 8(1), 171–191. doi:10.1007/s10857-005-4797-6
  3. Creswell, J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches. Sage publications.
  4. Douek, N. (1999). Argumentation and conceptualization in context: A case study on sun shadows in primary school. Educational Studies in Mathematics, 39(1/3), 89–110. doi:10.1023/a:1003800814251
  5. Erduran, S., Simon, S., & Osborne, J. (2004). TAPping into argumentation: Developments in the application of Toulmin’s Argument Pattern for studying science discourse. Science Education, 88(6), 915–933. doi:10.1002/sce.20012
  6. Freeman, J. B. (2005). Systematizing Toulmin’s warrants: An epistemic approach. Argumentation, 19(3), 331–346. doi:10.1007/s10503-005-4420-0
  7. Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. In A. H. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in Collegiate Mathematics Education, 234–283. doi:10.1090/cbmath/007/07
  8. Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396–428. doi:10.2307/749651
  9. Hidayat, W., Wahyudin, W., & Prabawanto, S. (2018). The mathematical argumentation ability and adversity quotient (AQ) of pre-service mathematics teacher. Journal on Mathematics Education, 9(2), 239-248. doi:10.22342/jme.9.2.5385.239-248
  10. Inglis, M., Mejia-Ramos, J. P., & Simpson, A. (2007). Modeling mathematical argumentation: The importance of qualification. Educational Studies in Mathematics, 66(1), 3–21. doi:10.1007/s10649-006-9059-8
  11. Jones, M., & Alony, I. (2011). Guiding the use of grounded theory in doctoral studies – an example from the Australian film industry. International Journal of Doctoral Studies, 6, 95–114.
  12. Lin, P.-J. (2018). Improving knowledge for teaching mathematical argumentation in primary classrooms. Journal of Mathematics Education, 11(1), 17–30. doi:10.26711/007577152790018
  13. Liu, Y. (2013). Aspects of mathematical arguments that influence eight grade students’ judgment of their validity. The Ohio State University.
  14. Liuа, Y., Tagueb, J., & Somayajulub, R. (2016). What Do Eighth Grade Students Look for When Determining If a Mathematical Argument Is Convincing. International Electronic Journal of Mathematics Education, 11(7), 2373-2401.
  15. NCTM. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
  16. NCTM. (2014). Principles to Actions: Ensuring Mathematical Success for All. National Council of Teachers of Mathematics.
  17. OECD. (2015). Draft mathematics framework. The Organisation for Economic Co-operation and Development (OECD).
  18. Pedemonte, B. (2008). Argumentation and algebraic proof. ZDM - International Journal on Mathematics Education, 40(3), 385–400. doi:10.1007/s11858-008-0085-0
  19. Rumsey, C., & Langrall, C. W. (2016). Promoting mathematical argumentation. Teaching Children Mathematics, 22(7), 412–419. doi:10.5951/teacchilmath.22.7.0412
  20. Spector, J. M., & Park, S. W. (2012). Argumentation, critical reasoning, and problem-solving. In S. B. Fee & B. R. Belland (Eds.), The Role of Criticism in Understanding Problem Solving (pp. 13–33). Springer. doi:10.1007/978-1-4614-3540-2_2
  21. Stylianides, A. J., & Stylianides, G. J. (2006). Content knowledge for mathematics teaching: The case of reasoning and proving. In J. Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education, 5, 201–208.
  22. Stylianides, A. J., & Stylianides, G. J. (2009). Proof constructions and evaluations. Educational Studies in Mathematics, 72(2), 237–253. doi:10.1007/s10649-009-9191-3
  23. Sukirwan, Darhim, Herman, T., & Prahmana, R. C. I. (2017). The students’ mathematical argumentation in geometry. Journal of Physics: Conference Series, 943(1), 1–6. doi:10.1088/1742-6596/943/1/012026
  24. Toulmin, S. E. (2003). The uses of argument: Updated edition. Cambridge University Press.
  25. Varghese, T. (2011). Balacheff’s 1988 taxonomy of mathematical proofs. Eurasia Journal of Mathematics, Science & Technology Education, 7(3), 181–192. doi:10.12973/ejmste/75192
  26. Viholainen, A. (2011). The view of mathematics and argumentation. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of the 7th Congress of the European Society for Research in Mathematics Education, 243–252.
  27. Wood, T. (1999). Creating a context for argument in mathematics class. Journal for Research in Mathematics Education, 30(2), 171–191. doi:10.2307/749609
  28. Zarębski, T. (2009). Toulmin’s model of argument and the logic of scientific discovery. Studies in Logic, Grammar, and Rhetoric, 16(29), 267–283.