Skip to main content

Advertisement

SpringerLink
Log in

Analyzing effective communication in mathematics group work: The role of visual mediators and technical terms

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

Analyzing and designing productive group work and effective communication constitute ongoing research interests in mathematics education. In this article we contribute to this research by using and developing a newly introduced analytical approach for examining effective communication within group work in mathematics education. By using data from 12 to 13-year old students playing a dice game as well as from a group of university students working with a proof by induction, the article shows how the link between visual mediators and technical terms is crucial in students’ attempts to communicate effectively. The critical evaluation of visual mediators and technical terms, and of links between them, is useful for researchers interested in analyzing effective communication and designing environments providing opportunities for students to learn mathematics.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. The concept of effective communication is used in accordance with Sfard and Kieran (2001), and is discussed and defined below.

References

  • Amigues, R. (1988). Peer interaction in solving physics problems: Socio cognitive confrontation and metacognitive aspects. Journal of Experimental Child Psychology, 45(1), 141–158.

    Article  Google Scholar 

  • Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215–241.

    Article  Google Scholar 

  • Barron, B. (2003). When smart groups fail. The Journal of the Learning Sciences, 12(3), 307–359.

    Article  Google Scholar 

  • Bergqvist, K., & Säljö, R. (1994). Conceptually blindfolded in the optics laboratory: Dilemmas of inductive learning. European Journal of Psychology in Education, 9, 149–158.

    Article  Google Scholar 

  • Bryman, A. (2004). Social research methods (2nd ed.). Oxford, UK: Oxford University Press.

    Google Scholar 

  • Cobb, P. (1999). Individual and collective mathematical learning: The case of statistical data analysis. Mathematical Thinking and Learning, 1, 5–43.

    Article  Google Scholar 

  • Coleman, E. (1998). Using explanatory knowledge during collaborative problem solving in science. The Journal of the Learning Sciences, 7, 387–427.

    Google Scholar 

  • David, M. M., & Tomaz, V. S. (2012). The role of visual representations for structuring classroom mathematical activity. Educational Studies in Mathematics, 80(3), 413–431.

    Article  Google Scholar 

  • Grice, H. P. (1968). Logic and conversation: The William James lectures. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Howe, C. (2009). Expert support for group work in elementary science: The role of consensus. In B. Schwarz, T. Dreyfus, & R. Hershkowitz (Eds.), Transformation of knowledge through classroom interaction (pp. 93–104). New York: Routledge.

    Google Scholar 

  • Kieran, C. (2001). The mathematical discourse of 13-year-old partnered problem solving and its relation to the mathematics that emerges. Educational Studies in Mathematics, 46, 187–228.

    Article  Google Scholar 

  • Kieran, C., & Dreyfus, T. (1998). Collaborative versus individual problem solving: Entering another’s universe of thought. In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd international conference for the Psychology of Mathematics Education (Vol. 3, pp. 112–119). Stellenbosch, South Africa: PME.

    Google Scholar 

  • Linn, M. C., & Burbules, N. C. (1993). Construction of knowledge and group learning. In K. Tobin (Ed.), The practice of constructivism in science education (pp. 91–119). Washington, DC: American Association for the Advancement of Science.

    Google Scholar 

  • Martin, L., Towers, J., & Pirie, S. (2005). Collective mathematical understanding as improvisation. Mathematical Thinking and Learning, 8(2), 149–183.

    Article  Google Scholar 

  • Mason, J. (1998). Enabling teachers to be real teachers: Necessary levels of awareness and structure of attention. Journal of Mathematics Teacher Education, 1, 243–267.

    Article  Google Scholar 

  • McCrone, S. S. (2005). The development of mathematical discussion: An investigation in a fifth grade classroom. Mathematical Thinking and Learning, 7(2), 111–133.

    Article  Google Scholar 

  • Nilsson, P. (2009). Conceptual variation and coordination in probability reasoning. Journal of Mathematical Behavior, 28, 247–261.

    Article  Google Scholar 

  • Nilsson, P., & Ryve, A. (2010). Focal event, contextualization, and effective communication in the mathematics classroom. Educational Studies in Mathematics, 74, 241–258.

    Article  Google Scholar 

  • Pettersson, K. (2008). Växelverkan mellan intuitiva idéer och formella resonemang: En fallstudie av universitetsstudenters arbete med en analysuppgift [Interplay between intuitive ideas and formal justification. A case study of university students’ work on a calculus task]. Nordic Studies in Mathematics Education, 13(1), 29–50.

    Google Scholar 

  • Prusak, N., Hershkowitz, R., & Schwarz, B. (2012). From visual reasoning to logical necessity through argumentative design. Educational Studies in Mathematics, 79, 19–40.

    Article  Google Scholar 

  • Radford, L. (2008). “No! He starts walking backwards!”: Interpreting motion graphs and the question of space, place, and distance. ZDM, 41, 467–480.

    Article  Google Scholar 

  • Radford, L. (2011). Book Review: Classroom interaction: Why is it good, really? In B. Schwarz, T. Dreyfus & R. Hershkowitz (Eds.) (2009) Transformation of knowledge through classroom interaction. Educational Studies in Mathematics, 76, 101–115.

  • Roth, W.-M., & Lee, Y. J. (2004). Interpreting unfamiliar graphs: A generative activity theoretical model. Educational Studies in Mathematics, 57, 265–290.

    Article  Google Scholar 

  • Ryve, A. (2006). Making explicit the analysis of students’ mathematical discourses: Revisiting a newly developed methodological framework. Educational Studies in Mathematics, 62, 191–210.

    Article  Google Scholar 

  • Ryve, A. (2011). Discourse research in mathematics education: A critical evaluation of 108 journal articles. Journal for Research in Mathematics Education, 42, 167–198.

    Google Scholar 

  • Ryve, A., Larsson, M., & Nilsson, P. (2011). Analyzing content and participation in classroom discourse: Dimensions of variation, mediating tools, and conceptual accountability. Scandinavian Journal of Educational Research. Advance online publication. doi: 10.1080/00313831.2011.628689

  • Ryve, A., Nilsson, P., & Mason, J. (2012). Establishing mathematics for teaching within classroom interactions in teacher education. Educational Studies in Mathematics, 81(1), 1–14.

    Google Scholar 

  • Salomon, G., & Globerson, T. (1989). When teams do not function the way they ought to. In N. M. Webb (Ed.), Peer interaction, problem-solving, and cognition: Multidisciplinary perspectives (pp. 89–99). Oxford, UK: Pergamon Press.

    Google Scholar 

  • Schwarz, B., Dreyfus, T., & Hershkowitz, R. (Eds.). (2009). Transformation of knowledge through classroom interaction. New York: Routledge.

    Google Scholar 

  • Sfard, A. (2001). There is more to the discourse than meets the ears: Looking at thinking as communication to learn more about mathematical learning. Educational Studies in Mathematics, 46, 13–57.

    Article  Google Scholar 

  • Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge, UK: Cambridge University Press.

    Book  Google Scholar 

  • Sfard, A., & Kieran, C. (2001). Cognition as communication: Rethinking learning-by-talking through multi-faceted analysis of students’ mathematical interactions. Mind, Culture, and Activity, 8, 42–76.

    Article  Google Scholar 

  • Valero, P., & Stentoft, D. (2010). The ‘post’ move of critical mathematics education. In A. O. Ravn & P. Valero (Eds.), Critical mathematics education: Past, present, future (pp. 183–195). Rotterdam: Sense.

    Google Scholar 

  • Weber, K., Maher, C., Powell, A., & Lee, H. S. (2008). Learning opportunities from group discussions: Warrants become the objects of debate. Educational Studies in Mathematics, 68, 247–261.

    Article  Google Scholar 

  • Wegerif, R., Boero, P., Andriessen, J., & Forman, E. (2009). A dialogue on dialogue and its place within education. In B. Schwarz, T. Dreyfus, & R. Hershkowitz (Eds.), Transformation of knowledge through classroom interaction (pp. 184–199). New York: Routledge.

    Google Scholar 

  • Wertsch, J. V. (2007). Mediation. In H. Daniels, M. Cole, & J. V. Wertsch (Eds.), The Cambridge companion to Vygotsky (pp. 178–192). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • Wertsch, J. V., & Kazak, S. (2011). Saying more than you know in instructional settings. In T. Koschmann (Ed.), Theorizing learning practice (pp. 134–167). New York: Springer.

    Google Scholar 

  • West, C., & Zimmerman, D. H. (1983). Small insults: A study of interruptions in cross-sex conversations between unacquainted persons. In B. Thorne, C. Kramarae, & N. Henley (Eds.), Language, gender and society (pp. 103–117). Rowley, MA: Newbury House.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Education, Mälardalen University, Box 883, 721 23, Västerås, Sweden

    Andreas Ryve

  2. Umeå University, Umeå, Sweden

    Andreas Ryve

  3. Linnaeus University, Växjö, Sweden

    Per Nilsson

  4. Stockholm University, Stockholm, Sweden

    Kerstin Pettersson

Authors
  1. Andreas Ryve
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Per Nilsson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kerstin Pettersson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andreas Ryve.

Additional information

Ryve is the first author and Nilsson and Pettersson have contributed equally to the article.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ryve, A., Nilsson, P. & Pettersson, K. Analyzing effective communication in mathematics group work: The role of visual mediators and technical terms. Educ Stud Math 82, 497–514 (2013). https://doi.org/10.1007/s10649-012-9442-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10649-012-9442-6

Keywords

Search

Navigation