This article documents the classroom mathematical practices observed in a collegiate level teacher education course related to the circle topic. The course, which was prepared as design research, utilized a dynamic geometry environment which influenced the type and nature of the evolved mathematical practices. The study uses emergent perspective as the theoretical framework and Toulmin’s model of argumentation to analyze social interactions within the classroom. Findings reveal three sequentially emergent mathematical practices that are in increasing order of complexity. The significance of this analysis stems from the fact that it contributes to an emerging body of knowledge on inquiry-based and technology-supported teaching in social contexts for which more research is needed.


circle classroom mathematical practices design research dynamic geometry environment emergent perspective inquiry-based learning Toulmin’s model of argumentation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Battista, M. T. & Clements, D. H. (1995). Geometry and proof. Mathematics Teacher, 88(1), 48–54.Google Scholar
  2. Brown, A. L. (1992). Design experiments: Theoretical and methodological challenges in creating complex interventions in classroom settings. The Journal of the Learning Sciences, 2(2), 141–178.CrossRefGoogle Scholar
  3. Chapman, O. (2011). Elementary school teachers’ growth in inquiry-based teaching of mathematics. ZDM, 43(6–7), 951–963.CrossRefGoogle Scholar
  4. Christou, C., Mousoulides, N., Pittalis, M. & Pitta-Pantazi, D. (2004). Proofs through exploration in dynamic geometry environments. International Journal of Science and Mathematics Education, 2(3), 339–352.CrossRefGoogle Scholar
  5. Cobb, P. (2001). Supporting the improvement of learning and teaching in social and institutional context. In S. Carver & D. Klahr (Eds.), Cognition and instruction: Twenty-five years of progress, (pp. 455-478). Mahwah, NJ: Erlbaum.Google Scholar
  6. Cobb, P. & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31(3–4), 175–190.CrossRefGoogle Scholar
  7. Cobb, P., Gravemeijer, K., Yackel, E., McClain, K. & Whitenack, J. (1997). Mathematizing and symbolizing: The emergence of chains of signification in one first-grade classroom. In D. Kirshner & J. A. Whitson (Eds.), Situated cognition theory: Social semiotic, and psychological perspectives (pp. 151–233). Mahwah: Lawrence Erlbaum Associates, Inc.Google Scholar
  8. Cobb, P., Stephan, M., McClain, K. & Gravemeijer, K. (2011). Participating in classroom mathematical practices. In Sfard, A., Yackel, E., Gravemeijer, K. & Cobb, P. (Eds.), A Journey in Mathematics Education Research (pp. 117– 782163). Netherlands: Springer.Google Scholar
  9. Common Core State Standards Initiative (CCSSI). (2010). Common Core State Standards for Mathematics. Washington DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.Google Scholar
  10. 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
  11. Drijvers, P., Doorman, M., Boon, P., Reed, H. & Gravemeijer, K. (2010). The teacher and the tool: Instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 75(2), 213–234.CrossRefGoogle Scholar
  12. Fennema, E., Carpenter, T. P., Jacobs, V. R., Franke, M. L. & Levi, L. W. (1998). A longitudinal study of gender differences in young children’s mathematical thinking. Educational Researcher, 6–11.Google Scholar
  13. Font, V., Godino, J. D. & Gallardo, J. (2013). The emergence of objects from mathematical practices. Educational Studies in Mathematics, 82(1), 97–124.CrossRefGoogle Scholar
  14. Goodchild, S., Fuglestad, A. B. & Jaworski, B. (2013). Critical alignment in inquiry-based practice in developing mathematics teaching. Educational Studies in Mathematics, 84(3), 393–412.CrossRefGoogle Scholar
  15. Goos, M., Galbraith, P., Renshaw, P. & Geiger, V. (2003). Perspectives on technology mediated learning in secondary school mathematics classrooms. The Journal of Mathematical Behavior, 22(1), 73–89.CrossRefGoogle Scholar
  16. Gravemeijer, K. (1994). Educational development and educational research in mathematics education. Journal for Research in Mathematics Education, 25(5), 443–471.CrossRefGoogle Scholar
  17. Hähkiöniemi, M. & Leppäaho, H. (2012). Prospective mathematics teachers’ ways of guiding high school students in geogebra-supported inquiry tasks. International Journal for Technology in Mathematics Education, 19 (2), 45–57.Google Scholar
  18. Healy, L. & Hoyles, C. (2002). Software tools for geometrical problem solving: Potentials and pitfalls. International Journal of Computers for Mathematical Learning, 6(3), 235–256.CrossRefGoogle Scholar
  19. Johnston-Wilder, S. & Mason, J. (Eds.). (2005). Developing Thinking in Geometry. Wiltshire: Sage.Google Scholar
  20. Lavy, I. & Shriki, A. (2010). Engaging in problem posing activities in a dynamic geometry setting and the development of prospective teachers’ mathematical knowledge. The Journal of Mathematical Behavior, 29(1), 11–24.CrossRefGoogle Scholar
  21. Leinhardt, G. & Steele, M. D. (2005). Seeing the complexity of standing to the side: Instructional dialogues. Cognition and Instruction, 23(1), 87–163.CrossRefGoogle Scholar
  22. Leung, A. & Lee, A. M. S. (2013). Students’ geometrical perception on a task-based dynamic geometry platform. Educational Studies in Mathematics, 82(3), 361–377.CrossRefGoogle Scholar
  23. Mishra, P. & Koehler, M. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017–1054.CrossRefGoogle Scholar
  24. Moschkovich, J. N. (2002). Chapter 1: An introduction to examining everyday and academic mathematical practices. Journal for Research in Mathematics Education Monograph, 11, 1–11.Google Scholar
  25. Schoenfeld, A. (1987). What’s all the fuss about metacognition? In A. Schoenfeld (Ed.), Cognitive Science and Mathematics Education, (pp. 189-215). Hillsdale, NJ: ErlbaumGoogle Scholar
  26. Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114–145.CrossRefGoogle Scholar
  27. Stein, M. K., Engle, R. A., Smith, M. S. & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313–340.CrossRefGoogle Scholar
  28. Stephan, M. & Akyuz, D. (2012). A proposed instructional theory for integer addition and subtraction. Journal for Research in Mathematics Education, 43(4), 428–464.CrossRefGoogle Scholar
  29. Stephan, M. & Rasmussen, C. (2002). Classroom mathematical practices in differential equations. The Journal of Mathematical Behavior, 21(4), 459–490.CrossRefGoogle Scholar
  30. Stephan, M., Bowers, J., Cobb, P. & Gravemeijer, K. (2003). Supporting one first-grade classroom’s development of measuring conceptions: analyzing learning in social context. Journal for Research in Mathematics Education Monograph, 12.Google Scholar
  31. Straesser, R. (2002). Cabri-Geometre: Does dynamic geometry software (DGS) change geometry and its teaching and learning? International Journal of Computers for Mathematical Learning, 6(3), 319–333.CrossRefGoogle Scholar
  32. Toulmin, S. (1969). The uses of argument. Cambridge: Cambridge University Press.Google Scholar
  33. Triantafillou, C. & Potari, D. (2010). Mathematical practices in a technological workplace: the role of tools. Educational Studies in Mathematics, 74(3), 275-294.Google Scholar
  34. Trouche, L. (2004). Managing the complexity of human/machine interactions in computerized learning environments: Guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9(3), 281–307.Google Scholar
  35. Wells, G. (1999). Dialogic inquiry: Towards a socio-cultural practice and theory of education. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  36. Zwiep, S. G. & Benken, B. M. (2013). Exploring teachers’ knowledge and perceptions across mathematics and science through content-rich learning experiences in a professional development setting. International Journal of Science and Mathematics Education, 11(2), 299–324.CrossRefGoogle Scholar

Copyright information

© Ministry of Science and Technology, Taiwan 2014

Authors and Affiliations

  1. 1.Middle East Technical UniversityAnkaraTurkey

Personalised recommendations