Skip to main content
Log in

Communicative characteristics of teachers’ mathematical talk with children: from knowledge transfer to knowledge investigation

  • Original Article
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

In-service teachers actively collaborated in a developmental research project. The main aim of the research project was the advancement of one central aspect of teacher professionalism: teachers’ diagnostic competencies. Conditions of understanding and possibilities of enriching teachers’ talk are of special interest because mathematics teaching is particularly affected by speech and communication (Söbbeke and Steinbring in Mathematik für Kinder—Mathematik von Kindern, pp. 26–38, 2004). One research focus was on the support of a productive enhancement of the teachers’ talk with one child. Is the teacher’s talk mainly a kind of knowledge transfer similar to traditional instruction or can it be seen as an investigation of the child’s own views and ideas of elementary mathematical knowledge? These teachers’ talks with one child should offer more reflective communication between teacher and child and result in a changed view of the child’s mathematical understanding. Using an elaborate interpretation based on a theoretical instrument of analysis, called “Forms of teachers’ mathematical Interaction (Formal-In)”, we describe the development from the first diagnostic talk with one child, at the beginning to the last talk at the end of the research project. Using an elaborate analysis of short episodes of teachers’ talk distinguishing the interactive and the epistemological dimensions, we can describe how both dimensions influence each other. The theoretically identified characteristics of teachers’ talk together with compatible video cases can be used in theory-based (in-service) teacher training aimed at enhancing professionalism.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Notes

  1. The following interpretative discussion is based on especially chosen and carefully transcribed episodes of the corresponding diagnostic talks. The numbers used (i.e. “1” or “5–11”) in the ongoing presentation of student’s and teacher’s statements and comments are original from the transcript, in which every verbal/non-verbal contribution is numbered. The transcripts used in this article can be requested from the authors.

References

  • Ball, D. L. (1997). What do students know? Facing challenges of distance, context and desire in trying to hear children. In B. J. Biddle, T. L. Good, & I. F. Goodson (Eds.), International handbook of teachers and teaching (pp. 769–818). Dordrecht: Kluwer.

    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 

  • Bauersfeld, H. (1995). “Language games” in the mathematics classrooms: Their function and their effects. In P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning (pp. 271–291). Hillsdale: Erlbaum.

    Google Scholar 

  • Benke, G., Hošpesová, A., & Tichá, M. (2008). The use of action research in teacher education. In K. Krainer & T. Wood (Eds.), Participants in mathematics teacher education (Vol. 3, pp. 283–308). Rotterdam: Sense Publishers.

    Google Scholar 

  • Brendefur, J., & Frykholm, J. (2000). Promoting mathematical communication in the classroom. Journal of Mathematics Teacher Education, 3, 125–153.

    Article  Google Scholar 

  • Buschman, L. (2001). Using student interviews to guide classroom instruction. Teaching Children Mathematics, 8(4), 222–227.

    Google Scholar 

  • Carpenter, T. P., Fennema, E., & Franke, M. L. (1996). Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction. The Elementary School Journal, 97(1), 3–20.

    Article  Google Scholar 

  • Gellert, U. (2007). Gemeinschaftliches Interpretieren mit Studierenden und Lehrern. Journal für Mathematik-Didaktik JMD, 28(1), 31–48.

    Google Scholar 

  • Gellert, U., Amato, S., Bairral, M., Zanette, L., Bloch, I., Gadanidis, G., et al. (2009). Practising mathematics teacher education: Expanding the realm of possibilities. In R. Even & D. L. Ball (Eds.), The Professional Education and Development of Teachers of Mathematics: The 15th ICMI Study (pp. 35–55). New York: Springer.

    Chapter  Google Scholar 

  • Gellert, U., & Krummheuer, G. (2005). Collaborative interpretation of classroom interaction: Stimulating practice by systematic analysis of videotaped classroom episodes. Paper presented at the conference of the 15th ICMI Study on the Professional Education and Development of Teachers of Mathematics.

  • Helmke, A. (2009). Unterrichtsqualität und Lehrerprofessionalität. Diagnose, Evaluation und Verbesserung des Unterrichts. Seelze: Klett-Kallmeyer.

  • Hengartner, E., Hirt, U., Wälti, B., & Lupsingen, P. (2006). Lernumgebungen für Rechenschwache bis Hochbegabte (1 Auflage ed.). Zug: Klett und Balmer.

    Google Scholar 

  • Jacobs, V. R., & Philipp, R. A. (2004). Helping prospective and practicing teachers focus on the children’s mathematical thinking in student-work examples. Center for Research in Mathematics and Science Education San Diego State University, 11(4).

  • Krainer, K. (1988). Intervieweneine Forschungsmethode zur Beobachtung und Analyse von Denkprozessen bei Schülern. Unpublished manuscript, Mariazell.

  • Krummheuer, G. (2000). Analyses: Interpretative research in primary mathematics education. Some preliminary remarks. Zentralblatt für Didaktik der Mathematik, 32(5), 124–125.

    Article  Google Scholar 

  • Kultusministerkonferenz. (2005). Standards für die Lehrerbildung. Bildungswissenschaften. Beschluss der Kultusministerkonferenz vom 16.12.2004. Zeitschrift für Pädagogik, 51(2), 280–290.

    Google Scholar 

  • Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge: Cambridge University Press.

    Google Scholar 

  • Maher, C. A. (2008). Video recordings as pedagogical tools in mathematics teacher education. In D. Tirosh & T. Wood (Eds.), Tools and processes in mathematics teacher education (Vol. 2, pp. 65–83). Rotterdam: Sense Publishers.

    Google Scholar 

  • Matos, J. F., Powell, A., Sztajn, P., Ejersbø, L., & Hovermill, J. (2009). Mathematics teachers’ professional development: Processes of learning in and from practice. In R. Even & D. L. Ball (Eds.), The Professional Education and Development of Teachers of Mathematics: The 15th ICMI Study (pp. 167–183). New York: Springer.

    Chapter  Google Scholar 

  • Moyer, P. S., & Milewicz, E. (2002). Learning to question: categories of questioning used by preservice teachers during diagnostic mathematics interviews. Journal of Mathematics Teacher Education, 5, 293–315.

    Article  Google Scholar 

  • National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston: NCTM.

    Google Scholar 

  • National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston: NCTM.

    Google Scholar 

  • Nicol, C. (1999). Learning to teach mathematics: Questioning, listening, and responding. Educational Studies in Mathematics, 37, 45–66.

    Article  Google Scholar 

  • Ogden, C. K., & Richards, I. A. (1972). The meaning of meaning. A study of the influence of language upon thought and of the science of symbolism (10th ed.). London: Routledge & Kegan Paul.

    Google Scholar 

  • Scherer, P., & Steinbring, H. (2006). Noticing children’s learning processes—teachers jointly reflect on their own classroom interaction for improving mathematics teaching. Journal of Mathematics Teacher Education, 9, 157–185.

    Google Scholar 

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

    Google Scholar 

  • Söbbeke, E., & Steinbring, H. (2004). Was ist Mathematik—Vorstellungen von Grundschulkindern. In P. Scherer & D. Bönig (Eds.), Mathematik für Kinder—Mathematik von Kindern (pp. 26–38). Frankfurt: Arbeitskreis Grundschule.

    Google Scholar 

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

    Article  Google Scholar 

  • Steinbring, H. (2005). The Construction of New Mathematical Knowledge in Classroom Interaction. An Epistemological Perspective (Vol. 38). Berlin: Springer.

  • Steinbring, H. (2008). Individuals, teams and networks: fundamental constraints of professional communication processes of teachers and scientists about teaching and learning mathematics. In K. Krainer & T. Wood (Eds.), Participants in Mathematics Teacher Education (pp. 369–382). Rotterdam: Sense Publishers.

  • Voigt, J. (1994). Entwicklung mathematischer Themen und Normen im Unterricht. In H. Maier (Ed.), Verstehen und Verständigung—Arbeiten zur interpretativen Unterrichtsforschung (pp. 77–111). Köln: Aulis.

    Google Scholar 

  • Wallach, T., & Even, R. (2005). Hearing students: The complexity of understanding what they are saying, showing, and doing. Journal of Mathematics Teacher Education, 8, 393–417.

    Article  Google Scholar 

  • Wassermann, S. (1992). Asking the right question: The essence of teaching. Bloomington: Phi Delta Kappa Educational Foundation.

    Google Scholar 

  • Wertsch, J. V., & Toma, C. (1995). Discourse and learning in the classroom: A sociocultural approach. In L. P. Steffe & J. Gale (Eds.), Constructivism in education (pp. 159–174). Hillsdale: Lawrence Erlbaum Associates.

    Google Scholar 

  • Wilson, S. M., & Berne, J. (1999). Teacher learning and the acquisition of professional knowledge: An examination of research on contemporary professional development. Review of Research in Education, 24, 173–209.

    Google Scholar 

  • Wittmann, E. C. (2003). Was ist Mathematik und welche pädagogische Bedeutung hat das wohlverstandene Fach für den Mathematikunterricht auch in der Grundschule? In M. Baum & H. Wielpütz (Eds.), Mathematik in der Grundschule. Seelze: Kallmeyer.

    Google Scholar 

  • Wood, T. (1998). Alternative patterns of communication in mathematics classes: Funneling or focusing? In H. Steinbring, M. G. Bartolini Bussi, & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 167–178). Reston: NCTM.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kerstin Bräuning.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bräuning, K., Steinbring, H. Communicative characteristics of teachers’ mathematical talk with children: from knowledge transfer to knowledge investigation. ZDM Mathematics Education 43, 927–939 (2011). https://doi.org/10.1007/s11858-011-0351-4

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-011-0351-4

Keywords

Navigation