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FACTORS SHAPING STUDENTS’ OPPORTUNITIES TO ENGAGE IN ARGUMENTATIVE ACTIVITY

  • Michal AyalonEmail author
  • Ruhama Even
Article

Abstract

This study examines how students’ opportunities to engage in argumentative activity are shaped by the teacher, the class, and the mathematical topic. It compares the argumentative activity between two classes taught by the same teacher using the same textbook and across two beginning algebra topics—investigating algebraic expressions and equivalence of algebraic expressions. The study comprises two case studies in which each teacher taught two 7th grade classes. Analysis of classroom videotapes revealed that the opportunities to engage in argumentative activity with the topic investigating algebraic expressions were similar in each teacher's two classes. By contrast, substantial differences were found between one teacher's classes with regard to the opportunities to engage in argumentative activity with the topic equivalence of algebraic expressions. The discussion highlights how the interplay between the characteristics of the mathematical topic, the characteristics of the class, and the characteristics of the teacher contributed to the shaping of students’ opportunities to engage in argumentative activity.

Key words

algebra argumentative activity class classroom research equivalence of algebraic expressions mathematical topic teacher 

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References

  1. Asterhan, C. S. C. & Schwarz, B. B. (2009). Argumentation and explanation in conceptual change: Indications from protocol analyses of peer-to-peer dialogue. Cognitive Science, 33(3), 374–400.Google Scholar
  2. Ayalon, M. & Even, R. (2010). Mathematics educators’ views on mathematics learning and the development of deductive reasoning. International Journal of Science and Mathematics Education, 8(6), 1131–1154.Google Scholar
  3. Ayalon, M. & Even, R. (2014). Students' Opportunities to Engage in Transformational Algebraic Activity in Different Beginning Algebra Topics and Classes. International Journal of Science and Mathematics Education, doi: 10.1007/s10763-013-9498-5
  4. Balacheff, N. (1999). Is argumentation an obstacle? Invitation to a debate. International newsletter on the teaching and learning of mathematical proof. Retrieved from: http://eric.ed.gov/PDFS/ED435644.pdf
  5. 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.Google Scholar
  6. Douek, N. (1999). Argumentation and conceptualization in context: a case study on sunshadows in primary school. Educational Studies in Mathematics, 39, 89–110.CrossRefGoogle Scholar
  7. Eisenmann, T. & Even, R. (2009). Similarities and differences in the types of algebraic activities in two classes taught by the same teacher. In J. T. Remillard, B. A. Herbel-Eisenmann & G. M. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 152–170). New York: Routledge.Google Scholar
  8. Eisenmann, T. & Even, R. (2011). Enacted types of algebraic activity in different classes taught by the same teacher. International Journal of Science and Mathematics Education, 9(4), 867–891.Google Scholar
  9. Even, R. (1998). Factors involved in linking representations of function. Journal of Mathematical Behavior, 17(1), 105–121.Google Scholar
  10. 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.Google Scholar
  11. Haggarty, L. & Pepin, B. (2002). An investigation of mathematics textbooks and their use in English, French and German classrooms: who gets an opportunity to learn what? British Educational Research Journal, 28(4), 567–590.CrossRefGoogle Scholar
  12. Healy, L. & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396–428.Google Scholar
  13. Herbel-Eisenmann, B. A., Lubienski, S. T. & Id-Deen, L. (2006). Reconsidering the study of mathematics instructional practices: the importance of curricular context in understanding local and global teacher change. Journal of Mathematics Teacher Education, 9, 313–345.CrossRefGoogle Scholar
  14. Hiebert, J., Gallimore, R., Garnier, H., Givvin, K. B., Hollingsworth, H., Jacobs, J. & Stigler, J. (2003). Teaching mathematics in seven countries: Results from the TIMSS 1999 video study. Washington, DC: National Centre for Education Statistics.Google Scholar
  15. Knipping, C. (2008). A method for revealing structures of argumentations in classroom proving processes. ZDM: The International Journal on Mathematics Education, 40(3), 427–441.CrossRefGoogle Scholar
  16. Krummheuer, G. (1995). The ethnography of argumentation. In P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning: Interaction in classroom cultures 42(1) (pp. 229–269). Hillsdale: Erlbaum.Google Scholar
  17. Manouchehri, A. & Goodman, T. (2000). Implementing mathematics reform: The challenge within. Educational Studies in Mathematics, 42, 1–34.CrossRefGoogle Scholar
  18. Martinez, M.V. & Pedemonte, B. (2014). Relationship between inductive arithmetic argumentation and deductive algebraic proof Educational Studies in Mathematics, 86(1), 125–149.Google Scholar
  19. Nisbett, R. E., Krantz, D. H. Jepson, C. & Kunda, Z. (1983). The use of statistical heuristics in everyday inductive reasoning. Psychological Review, 90(4), 339–363.Google Scholar
  20. Nussbaum, E. M. (2008). Collaborative discourse, argumentation, and learning: preface and literature review. Contemporary Educational Psychology, 33, 345–359.CrossRefGoogle Scholar
  21. Schwarz, B.B. (2009). Argumentation and Learning. In Muller-Mirza and A-N. Perret-Clermont (Eds.), Argumentation and Education – Theoretical Foundations and Practices (pp. 91–126). New York: Springer Verlag.Google Scholar
  22. Smith, J. P. & Phillips, E. A. (2000). Listening to middle school students’ algebraic thinking. Mathematics Teaching in the Middle School, 6(3), 156–161.Google Scholar
  23. Toulmin, S. E. (1958). The uses of argument. Cambridge: Cambridge University Press.Google Scholar
  24. Weber, K., Maher, C., Powell, A. & Lee, H. (2008). Learning opportunities from group discussion: warrants become the objects of debate. Educational Studies in Mathematics, 68(3), 247–261.Google Scholar
  25. Yackel, E. (2002). What we can learn from analysing the teacher’s role in collective argumentation. The Journal of Mathematical Behavior, 21(4), 423–440.Google Scholar

Copyright information

© Ministry of Science and Technology, Taiwan 2014

Authors and Affiliations

  1. 1.RehovotIsrael

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