Explaining as Mathematical Discursive Practices of Navigating Through Different Epistemic Fields

  • Kirstin ErathEmail author
Part of the ICME-13 Monographs book series (ICME13Mo)


This chapter introduces a conceptualisation of explaining as mathematical discursive practices of navigating through different epistemic fields and uses this framework for analysing collective explanations in whole-class discussions. The framework coordinates Interactional Discourse Analysis from linguistics with interactionist and epistemological perspectives from mathematics education. After outlining the main ideas of the three perspectives on explaining, I describe how the notion of practices functionally links theories from linguistics and mathematics education. Furthermore, I show how the conceptualisation simultaneously highlights the interactive nature of explaining processes while also keeping the mathematical content in focus. Finally, I outline the method of identifying explaining practices in transcribed video data.


Practice Discourse Explaining Epistemological perspective Participation 


Grant Information

The research project INTERPASS (Interactive procedures for establishing matches and divergences in linguistic and microcultural practices) is funded by the German ministry BMBF (grant 01JC1112, grant holder S. Prediger). I have conducted it under the guidance of Susanne Prediger and Uta Quasthoff, together with Anna-Marietha Vogler and Vivien Heller.


  1. Anderson, L. W., Krathwohl, D. R., Airasian, P. W., Cruikshank, K. A., Mayer, R. E., Pintrich, P. R., et al. (Eds.). (2001). A taxonomy for learning, teaching, and assessing. A revision of Bloom’s taxonomy of educational objectives. New York, NY: Longman.Google Scholar
  2. Barwell, R. (2012). Discursive demands and equity in second language mathematics classroom. In B. Herbel-Eisenmann, J. Choppin, D. Wagner, & D. Pimm (Eds.), Equity in discourse for mathematics education. Theories, practices, and politics (pp. 147–163). Dordrecht, Netherlands: Springer.Google Scholar
  3. Barwell, R., Clarkson, P., Halai, A., Kazima, M., Moschkovich, J., Planas, N., et al. (Eds.). (2016). Mathematics education and language diversity. The 21st ICMI study. Cham, Switzerland: Springer.Google Scholar
  4. Barzel, B., Leuders, T., Prediger, S., & Hußmann, S. (2013). Designing tasks for engaging students in active knowledge organization. In A. Watson, M. Ohtani, J. Ainley, J. Bolite Frant, M. Doorman, C. Kieran, … Y. Yang (Eds.), ICMI study 22 on task design—Proceedings of study conference (pp. 285–294). Oxford, UK: ICME.Google Scholar
  5. Bergmann, J. R., & Luckmann, T. (1995). Reconstructive genres of everyday communication. In U. Quasthoff (Ed.), Aspects of oral communication (pp. 289–304). Berlin, Germany: de Gruyter.Google Scholar
  6. Blumer, H. (1969). Symbolic interactionism. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  7. Brousseau, G. (1997). The theory of didactical situations in mathematics. Dordrecht, Netherlands: Kluwer.Google Scholar
  8. Cobb, P. (1998). Analyzing the mathematical learning of the classroom community. The case of statistical data analysis. In O. Alwyn (Ed.), Proceedings of the 22nd conference of the international group for the psychology of mathematics education (Vol. 1, pp. 33–48). Stellenbosch, South Africa: University of Stellenbosch.Google Scholar
  9. Cobb, P., & Bauersfeld, H. (Eds.). (1995). The emergence of mathematical meaning. Interaction in classroom cultures. Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  10. Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2001). Participating in classroom mathematical practices. The Journal of the Learning Science, 10(1&2), 113–163.CrossRefGoogle Scholar
  11. Erath, K. (2017a). Mathematisch diskursive Praktiken des Erklärens. Rekonstruktion von Unterrichtsgesprächen in unterschiedlichen Mikrokulturen. Wiesbaden, Germany: Springer.Google Scholar
  12. Erath, K. (2017b). Implicit and explicit practices of establishing explaining practices. Ambivalent learning opportunities in classroom discourse. In T. Dooley & G. Gueudet (Eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (pp. 1260–1267). Dublin, Ireland: DCU Institute of Education and ERME.Google Scholar
  13. Erath, K., & Prediger, S. (2014). Mathematical practices as underdetermined learning goals. The case of explaining diagrams. In S. Oesterle, P. Liljedahl, C. Nicol, & D. Allan (Eds.), Proceedings of the joint meeting of PME 38 and PME-NA 36 (Vol. 3, pp. 17–24). Vancouver, Canada: PME.Google Scholar
  14. Erath, K., & Prediger, S. (2015). Diverse epistemic participation profiles in socially established explaining practices. In K. Krainer & N. Vondrova (Eds.), CERME 9. Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (pp. 1374–1381). Prague, Czech Republic: CERME.Google Scholar
  15. Erath, K., Prediger, S., Heller, V., & Quasthoff, U. (in review). Learning to explain or explaining to learn? Discourse competences as an important facet of academic language proficiency.Google Scholar
  16. Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht, Netherlands: Kluwer.Google Scholar
  17. Garfinkel, H. (1967). Studies in ethnomethodology. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  18. Gee, J. (1996). An introduction to discourse analysis. Theory and method. New York, NY: Routledge.Google Scholar
  19. Hiebert, J. (Ed.). (1986). Conceptual and procedural knowledge. The case of mathematics. Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  20. Kolbe, F.-U., Reh, S., Fritzsche, B., Idel, T.-S., & Rabenstein, K. (2008). Lernkultur. Überlegungen zu einer kulturwissenschaftlichen Grundlegung qualitativer Unterrichtsforschung. Zeitschrift Für Erziehungswissenschaft, 11(1), 125–143.CrossRefGoogle Scholar
  21. Krummheuer, G. (2011). Representation of the notion “learning-as-participation” in everyday situations of mathematics classes. ZDM Mathematics Education, 43, 81–90.CrossRefGoogle Scholar
  22. Lampert, M., & Cobb, P. (2003). Communication and learning in the mathematics classroom. In J. Kilpatrick & D. Shifter (Eds.), Research companion to the NCTM standards (pp. 237–249). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  23. Mayring, P. (2015). Qualitative content analysis. Theoretical background and procedures. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education (pp. 365–380). Dordrecht, Netherlands: Springer.Google Scholar
  24. Morek, M. (2012). Kinder erklären. Interaktion in Familie und Unterricht im Vergleich. Tübingen: Stauffenburg.Google Scholar
  25. Morek, M., Heller, V., & Quasthoff, U. (2017). Erklären und Argumentieren. Modellierungen und empirische Befunde zu Strukturen und Varianzen. In E. L. Wyss (Ed.), Erklären und Argumentieren. Konzepte und Modellierungen in der Angewandten Linguistik (pp. 11–46). Tübingen: Stauffenburg.Google Scholar
  26. Moschkovich, J. (2002). A situated and sociocultural perspective on bilingual mathematics learners. Mathematical Thinking and Learning, 4(2&3), 189–212.CrossRefGoogle Scholar
  27. Moschkovich, J. (2013). Issues regarding the concept of mathematical practices. In Y. Li & J. Moschkovich (Eds.), Proficiency and beliefs in learning and teaching mathematics (pp. 257–275). Rotterdam, Netherlands: Sense Publishers.CrossRefGoogle Scholar
  28. Moschkovich, J. (2015). Academic literacy in mathematics for English learners. Journal of Mathematical Behaviour, 40, 43–62.CrossRefGoogle Scholar
  29. Nickson, M. (1992). The culture of the mathematics classroom: An unknown quantity? In D. A. Grouws (Ed.), Handbook of the research on mathematics teaching and learning (pp. 101–114). New York, NY: Macmillan Publishing Company.Google Scholar
  30. Prediger, S. (2013). Darstellungen, Register und mentale Konstruktion von Bedeutungen und Beziehungen. Mathematikspezifische sprachliche Herausforderungen identifizieren und bearbeiten. In M. Becker-Mrotzek, K. Schramm, E. Thürmann, & H. J. Vollmer (Eds.), Sprache im Fach. Sprachlichkeit und fachliches Lernen (pp. 167–183). Münster: Waxmann.Google Scholar
  31. Prediger, S., Bikner-Ahsbahs, A., & Arzarello, F. (2008). Networking strategies and methods for connecting theoretical approaches. First steps towards a conceptual framework. ZDM Mathematics Education, 40, 165–178.CrossRefGoogle Scholar
  32. Prediger, S., & Erath, K. (2014). Content, or interaction, or both? Synthesizing two German traditions in a video study on learning to explain in mathematics classroom microcultures. Eurasia Journal of Mathematics, Science & Technology Education, 10(4), 313–327.CrossRefGoogle Scholar
  33. Quasthoff, U., & Heller, V. (2014). Mündlichkeit und Schriftlichkeit aus sprachwissenschaftlicher und sprachdidaktischer Sicht. Grundlegende Ein-/Ansichten und methodischen Anregungen. In A. Neumann & I. Mahler (Eds.), Empirische Methoden in der Deutschdidaktik. Audio- und videografierende Unterrichtsforschung (pp. 6–37). Baltmannsweiler: Schneider Verlag Hohengehren.Google Scholar
  34. Quasthoff, U., Heller, V., & Morek, M. (2017). On the sequential organization and genre-orientation of discourse units in interaction. An analytic framework. Discourse Studies, 19(1), 84–110.Google Scholar
  35. Quasthoff, U., & Morek, M. (2015). Diskursive Praktiken von Kindern in außerschulischen und schulischen Kontexten (DisKo). Abschlussbericht für das DFG-geförderte Forschungsprojekt. Accessed October 17, 2015.
  36. Sfard, A. (2008). Thinking as communicating. Human development, the growth of discourse, and mathematizing. Cambridge, MA: Cambridge University Press.Google Scholar
  37. Sierpinska, A., & Lerman, S. (1996). Epistemologies of mathematics and of mathematics education. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 827–876). Dordrecht, Netherlands: Kluwer.Google Scholar
  38. Vollrath, H.-J. (2001). Grundlagen des Mathematikunterrichts in der Sekundarstufe. Heidelberg: Spektrum Akademischer Verlag.Google Scholar
  39. vom Hofe, R., Kleine, M., Blum, W., & Pekrun, R. (2005). The effect of mental models (“Grundvorstellungen”) for the development of mathematical competencies. First results of the longitudinal study PALMA. In Proceedings of the 4th CERME, Sant Feliu de Guixols, Spain, 2005 (pp. 142–151). Barzelona, Spain: FUNDEMI IQS—Universitat Ramon Llull.Google Scholar
  40. Wagenschein, M. (1968). Verstehen lehren. Genetisch - Sokratisch - Exemplarisch. Weinheim: Beltz.Google Scholar
  41. Winter, H. (1983). Über die Entfaltung begrifflichen Denkens im Mathematikunterricht. Journal Für Mathematik-Didaktik, 4(3), 175–204.CrossRefGoogle Scholar
  42. Yackel, E. (2004). Theoretical perspectives for analyzing explanation, justification and argumentation in mathematics classrooms. Journal of the Korean Society of Mathematical Education Series D: Research in Mathematical Education, 8(1), 1–18.Google Scholar
  43. Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.CrossRefGoogle Scholar
  44. Yackel, E., Rasmussen, C., & King, K. (2000). Social and sociomathematical norms in an advanced undergraduate mathematics course. Journal of Mathematical Behaviour, 19, 275–287.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.TU Dortmund UniversityDortmundGermany

Personalised recommendations