Advertisement

ZDM

, Volume 50, Issue 6, pp 1089–1099 | Cite as

An interactionist perspective on mathematics learning: conditions of learning opportunities in mixed-ability groups within linguistic negotiation processes

  • Judith Jung
  • Marcus Schütte
Original Article

Abstract

This paper illustrates that focusing on processes of interaction is crucial to a closer understanding of mathematical learning processes in mixed-ability groups. In doing so, the paper’s focus is on expounding a theoretical-methodological framework of an interactionist perspective in mathematics education. This framework interlinks sociological and social-constructivist theories with subject-specific educational theories. As a result of two examples of analyses it becomes apparent that investigations on mathematics learning within linguistic negotiation processes, based on an interactionist-oriented theoretical frame, provide in-depth insights into individual learning possibilities of a diverse student body. These insights are made possible only by means of a detailed micro-sociological examination of collectively occurring learning processes within linguistic negotiation processes.

Supplementary material

11858_2018_999_MOESM1_ESM.pdf (91 kb)
Supplementary material 1 (PDF 91 KB)

References

  1. Austin, J. L., & Howson, A. G. (1979). Language and mathematical education. Educational Studies in Mathematics, 10, 161–197.CrossRefGoogle Scholar
  2. Barwell, R. (2003). Discursive psychology and mathematics education: Possibilities and challenges. ZDM, 35(5), 201–207.Google Scholar
  3. Bauersfeld, H. (1985). Ergebnisse und Probleme von Mikroanalysen mathematischen Unterrichts. In W. Dörfler & R. Fischer (Eds.), Empirische Untersuchungen zum Lehren und Lernen von Mathematik (pp. 7–25). Wien: Hölder-Pichler-Tempsky.Google Scholar
  4. Bauersfeld, H., Krummheuer, G., & Voigt, J. (1988). Interactional theory of learning and teaching mathematics and related microethnographical studies. In H.-G. Steiner, & A. Vermandel (Eds.), Foundations and methodology of the discipline mathematics education (pp. 174–188). Antwerp: University of Antwerp.Google Scholar
  5. Blumer, H. (1969). Symbolic interactionism. Perspective and method. Englewood Cliffs: Prentice-Hall.Google Scholar
  6. Bottge, B. A., Heinrichs, M., Mehta, Z. D., & Hung, Y. (2002). Weighing the benefits of anchored math instruction for students with disabilities in general education classes. Journal of Special Education, 35, 186–200.CrossRefGoogle Scholar
  7. Bruner, J. (1983). Childs’s talk. Learning to use language. New York: Norton.Google Scholar
  8. Doise, W., & Mugny, G. (1979). Individual and collective conflicts of centration in cognitive development. European Journal of Social Psychology, 9, 245–247.CrossRefGoogle Scholar
  9. Garfinkel, H. (1967). Studies in ethnomethodology. Englewood Cliffs: Prentice-Hall.Google Scholar
  10. Goffman, E. (1974). Frame analysis. An essay on the organisation of experience. Cambridge: Harvard University Press.Google Scholar
  11. Goffman, E. (1981). Forms of talk. Philadelphia: University of Pennsylvania Press.Google Scholar
  12. Ingram, J. (2018). Moving forward with ethnomethodological approaches to analysing mathematics classroom interactions. ZDM.  https://doi.org/10.1007/s11858-018-0951-3 CrossRefGoogle Scholar
  13. Jensen, G. R. (2003). Arithmetic for teachers. With applications and topics from geometry. Providence. Rhode Island: American Mathematical Society.Google Scholar
  14. Krummheuer, G. (1992). Lernen mit »Format«. Elemente einer interaktionistischen Lerntheorie. Diskutiert an Beispielen mathematischen Unterrichts. Weinheim: Deutscher Studien Verlag.Google Scholar
  15. Krummheuer, G. (1995). The ethnography of argumentation. In P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning (pp. 229–270). Hillsdale: Lawrence Erlbaum.Google Scholar
  16. Krummheuer, G. (2007). Argumentation and participation in the primary mathematics classroom: Two episodes and related theoretical abductions. Journal of Mathematical Behavior, 26, 60–82.CrossRefGoogle Scholar
  17. Krummheuer, G., & Brandt, B. (2001). Paraphrase und Traduktion. Weinheim: Beltz Verlag.Google Scholar
  18. Kunsch, C. A., Jitendra, A. K., & Sood, S. (2007). The effects of peer-mediated instruction in mathematics for students with learning problems: A research synthesis. Learning Disabilities Research and Practice, 22, 1–12.CrossRefGoogle Scholar
  19. Langner, A., & Schütte, M. (2015). Teilhabe an Bildung von Anfang an. In U. Mahnke, H. Redlich, L. Schäfer, G. Wachtel, V. Moser & K. Zehbe (Eds.), Tagungsband: Perspektiven sonderpädagogischer Professionalisierung (pp. 273–281). Bad Heilbrunn: Klinkhardt Verlag.Google Scholar
  20. Lerman, S. (2000). The social turn in mathematics education research. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 19–44). Westport: Ablex.Google Scholar
  21. Miller, M. (1986). Kollektive Lernprozesse. Studien zur Grundlegung einer soziologischen Lerntheorie. Frankfurt am Main: Suhrkamp.Google Scholar
  22. Morgan, C., Craig, T., Schütte, M., & Wagner, D. (2014). Language and communication in mathematics education: An overview of research in the field. ZDMThe International Journal on Mathematics Education, 46(6), 843–853.CrossRefGoogle Scholar
  23. Moschkovich, J. (2002). A situated and sociocultural perspective on bilingual mathematics learners. Mathematical Thinking and Learning, 4(2), 189–212.CrossRefGoogle Scholar
  24. Moschkovich, J. N. (2015). Scaffolding mathematical practices. ZDM Mathematics Education, 47(7), 1067–1078.CrossRefGoogle Scholar
  25. Nührenbörger, M. (2010). Einsichtsvolles Mathematiklernen im Kontext von Heterogenität. In A. Lindmeier & S. Ufer (Eds.), Beiträge zum Mathematikunterricht (pp. 641–644). Münster: WTM-Verlag.Google Scholar
  26. Planas, N. (2018). Language as resource: A key notion for understanding the complexity of mathematics learning. Educational Studies in Mathematics, 87(1), 51–66.CrossRefGoogle Scholar
  27. Planas, N., & Civil, M. (2013). Language-as-resource and language-as-political: tensions in the bilingual mathematics classroom. Mathematics Education Research Journal, 25(3), 361–378.CrossRefGoogle Scholar
  28. Schütte, M. (2014). Language-related specialised learning in mathematics. ZDM—The International Journal on Mathematics Education, 46(6), 923–938.CrossRefGoogle Scholar
  29. Schütte, M. (2018). Subject-specific academic language versus mathematical discourse. In J. N. Moschkovich, D. Wagner, A. Bose, J. Rodrigues Mendes & M. Schütte (Eds.), Language and communication in mathematics education (pp. 25–36). Cham: Springer.CrossRefGoogle Scholar
  30. Schütte, M., & Krummheuer, G. (2017). Mathematische Diskurse im Kindesalter—Der narratorische Diskurs. In Institut für Mathematik der Universität Potsdam (Eds.), Beiträge zum Mathematikunterricht 2017 (pp. 877–880). Münster: WTM-Verlag.Google Scholar
  31. Schwarz, B., Neumann, Y., & Biezuner (2000). Two wrongs may make a right… if they argue together! Cognition and Instruction, 18(4), 461–494.CrossRefGoogle Scholar
  32. Schwarzkopf, R. (2000). Argumentationsprozesse im Mathematikunterricht. Hildesheim: Franzbecker.Google Scholar
  33. Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses and mathematizing. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  34. Solomon, Y. (2009). Mathematical literacy: Developing identities of inclusion. New York: Routledge.Google Scholar
  35. Toulmin, S. E. (2003). The uses of argument. Updated edition. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  36. vom Hofe, R., Kleine, M., Blum, W., & Pekrun, R. (2006). The effect of mental models for the development of mathematical competencies. In M. Bosch (Ed.), European research in mathematics education (pp. 142–151). Llull: IQS.Google Scholar
  37. Wessel, J. (2015). Grundvorstellungen und Vorgehensweisen bei der Subtraktion. Wiesbaden: Springer Spektrum.CrossRefGoogle Scholar

Copyright information

© FIZ Karlsruhe 2018

Authors and Affiliations

  1. 1.Technical University of DresdenDresdenGermany

Personalised recommendations