Skip to main content
Log in

Introducing a symbolic interactionist approach on teaching mathematics: the case of revoicing as an interactional strategy in the teaching of probability

  • Published:
Journal of Mathematics Teacher Education Aims and scope Submit manuscript

Abstract

This study examines an interactional view on teaching mathematics, whereby meaning is co-produced with the students through a process of negotiation. Further, teaching is viewed from a symbolic interactionism perspective, allowing the analysis to focus on the teacher’s role in the negotiation of meaning. Using methods inspired by grounded theory, patterns of teachers’ interaction are categorized. The results show how teachers’ actions, interpretations and intentions form interactional strategies that guide the negotiation of meaning in the classroom. The theoretical case of revoicing as a teacher action, together with interpretations of mathematical objects from probability theory, is used to exemplify conclusions from the proposed perspective. Data are generated from a lesson sequence with two teachers working with known and unknown constant sample spaces with their classes. In the lessons presented in this article, the focus is on negotiations of the meaning of chance. The analysis revealed how the teachers indicate their interpretations of mathematical objects and intentions to the students to different degrees and, by doing so, create opportunities for the students to ascribe meaning to these objects. The discussion contrasts the findings with possible interpretations from other perspectives on teaching.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. Anonymization of the participants has been achieved by changing the names in the research reports, which was also a condition of the informed consent every participant provided. Although complete anonymization is difficult to achieve since there might be people who remember our involvement at the school and read this report (Miles and Huberman 1994), careful steps have been taken to ensure the participants’ integrity.

References

  • Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on the teaching and learning of mathematics (pp. 83–104). Westport, CT: Ablex.

    Google Scholar 

  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.

    Article  Google Scholar 

  • Barwell, R. (2013). Discursive psychology as an alternative perspective on mathematics teacher knowledge. ZDM, 45(4), 595–606.

    Article  Google Scholar 

  • Blumer, H. (1986). Symbolic interactionism: Perspective and method. Berkeley: University of California Press.

    Google Scholar 

  • Brousseau, G., Brousseau, N., & Warfield, V. (2001). An experiment on the teaching of statistics and probability. The Journal of Mathematical Behavior, 20(3), 363–411.

    Article  Google Scholar 

  • Burgess, T. A. (2006). A framework for examining teacher knowledge as used in action while teaching statistics. Paper presented at the working cooperatively in statistics education: Proceedings of the Seventh International Conference on Teaching Statistics. Salvador, Brazil.

  • Burgess, T. A. (2008). Teacher knowledge for teaching statistics through investigations. Paper presented at The Joint ICMI/IASE Study: Teaching statistics in school mathematics: Challenges for teaching and teacher education, Monterrey, Mexico.

  • Charmaz, K. (2006). Constructing grounded theory: A practical guide through qualitative analysis. London: Sage.

    Google Scholar 

  • Charmaz, K. (2008a). A future for symbolic interactionism. Studies in Symbolic Interaction, 32, 51–59.

    Article  Google Scholar 

  • Charmaz, K. (2008b). The legacy of Anselm Strauss in constructivist grounded theory. Studies in Symbolic Interaction, 32, 127–141.

    Article  Google Scholar 

  • Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2001). Participating in classroom mathematical practices. Journal of the Learning Sciences, 10(1), 113–163.

    Article  Google Scholar 

  • Davis, B., & Simmt, E. (2006). Mathematics-for-teaching: An ongoing investigation of the mathematics that teachers (need to) know. Educational Studies in Mathematics, 61(3), 293–319.

    Article  Google Scholar 

  • Flyvbjerg, B. (2006). Five misunderstandings about case-study research. Qualitative Inquiry, 12(2), 219–245.

    Article  Google Scholar 

  • Forman, E. A., Larreamendy-Joerns, J., Stein, M. K., & Brown, C. A. (1998a). “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.

    Article  Google Scholar 

  • Forman, E. A., Mccormick, D. E., & Donato, R. (1998b). Learning what counts as a mathematical explanation. Linguistics and Education, 9(4), 313–339.

    Article  Google Scholar 

  • Gellert, A. (2014). Students discussing mathematics in small-group interactions: Opportunities for discursive negotiation processes focused on contentious mathematical issues. ZDM, 46(6), 855–869.

    Article  Google Scholar 

  • Groth, R. E. (2013). Characterizing key developmental understandings and pedagogically powerful ideas within a statistical knowledge for teaching framework. Mathematical Thinking and Learning: An International Journal, 15(2), 121–145.

    Article  Google Scholar 

  • Herbel-Eisenmann, B., Drake, C., & Cirillo, M. (2009). “Muddying the clear waters”: Teachers’ take-up of the linguistic idea of revoicing. Teaching and Teacher Education: An International Journal of Research and Studies, 25(2), 268–277.

    Article  Google Scholar 

  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.

    Article  Google Scholar 

  • Jaworski, B. (1994). Investigating mathematics teaching: A constructivist enquiry. London: Falmer.

    Google Scholar 

  • Jones, G. A., Langrall, C. W., & Mooney, E. S. (2007). Research in probability: Responding to classroom realities. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2, pp. 909–956). Charlotte, NC: Information Age Pub.

    Google Scholar 

  • Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. California: Sage.

    Google Scholar 

  • Liu, Y., & Thompson, P. (2007). Teachers’ understandings of probability. Cognition & Instruction, 25(2/3), 113–160.

    Article  Google Scholar 

  • Ma, L. (1999). Knowing and teaching mathematics: Teachers understanding of fundamental mathematics in China and the United States. Mahwah: Lawrence Eribaum.

    Google Scholar 

  • Miles, M., & Huberman, M. (1994). Qualitative data analysis: An expanded sourcebook. Thousand Oaks, California: Sage.

    Google Scholar 

  • Nilsson, P. (2007). Different ways in which students handle chance encounters in the explorative setting of a dice game. Educational Studies in Mathematics, 66(3), 293–315.

    Article  Google Scholar 

  • Nilsson, P., & Lindström, T. (2013). Prolifing Swedish teachers’ knowledge base in probability. Nomad, 18(4), 51–72.

    Google Scholar 

  • O’Connor, M. C., & Michaels, S. (1993). Aligning academic task and participation status through revoicing—analysis of a classroom discourse strategy. Anthropology & Education Quarterly, 24(4), 318–335.

    Article  Google Scholar 

  • Ordbok över svenska språket. (1893). Lund: Svenska akademien.

  • Petrou, M., & Goulding, M. (2011). Conceptualising teachers’ mathematical knowledge in teaching. In T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching (pp. 9–26). Netherlands: Springer.

    Chapter  Google Scholar 

  • Putnam, R. T., & Borko, H. (2000). What do new views of knowledge and thinking have to say about research on teacher learning? Educational Researcher, 29(1), 4–15.

    Article  Google Scholar 

  • Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255–281.

    Article  Google Scholar 

  • Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27(3), 379–423.

    Article  Google Scholar 

  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.

    Article  Google Scholar 

  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–22.

    Article  Google Scholar 

  • Speer, N., King, K., & Howell, H. (2014). Definitions of mathematical knowledge for teaching: Using these constructs in research on secondary and college mathematics teachers. Journal of Mathematics Teacher Education, 18(2), 105–122.

    Article  Google Scholar 

  • Steinbring, H. (1991). The concept of chance in everyday teaching: Aspects of a social epistemology of mathematical knowledge. Educational Studies in Mathematics, 22(6), 503–522.

    Article  Google Scholar 

  • Steinbring, H. (1993). The context for the concept of chance—everyday experiences in classroom interactions. Acta didactica Universitatis Comenianae Mathematics, 2, 20–32.

    Google Scholar 

  • Steinbring, H. (1998). Elements of epistemological knowledge for mathematics teachers. Journal of Mathematics Teacher Education, 1(2), 157–189.

    Article  Google Scholar 

  • Stohl, H., & Tarr, J. E. (2002). Developing notions of inference using probability simulation tools. Journal of Mathematical Behavior, 21(3), 319–337.

    Article  Google Scholar 

  • Strauss, A. L., & Corbin, J. (1997). Grounded theory in practice. Thousand Oaks: Sage.

    Google Scholar 

  • Voigt, J. (1996). Negotiation of mathematical meaning in classroom processes: Social interaction and learning mathematics. In L. P. Steffe, P. Nesher, P. Cobb, G. A. Goldin, & B. Greer (Eds.), Theories of mathematical learning. Mahwah, New Jersey: Lawrence Erlbaum Associates.

    Google Scholar 

  • Watson, J. M. (2001). Profiling teachers’ competence and confidence to teach particular mathematics topics: The case of chance and data. Journal of Mathematics Teacher Education, 4(4), 305–337.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Andreas Eckert.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Eckert, A., Nilsson, P. Introducing a symbolic interactionist approach on teaching mathematics: the case of revoicing as an interactional strategy in the teaching of probability. J Math Teacher Educ 20, 31–48 (2017). https://doi.org/10.1007/s10857-015-9313-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10857-015-9313-z

Keywords

Navigation