Content, Interaction, or Both? Synthesizing Two German Traditions in a Video Study on Learning to Explain in Mathematics Classroom Microcultures

Susanne Prediger; Kirstin Erath

doi:10.12973/eurasia.2014.1085a

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Susanne Prediger ¹ ^* , Kirstin Erath ¹

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¹ TU Dortmund University, GERMANY^* Corresponding Author

Abstract

How do students learn to explain? We take this exemplary research question for present-ing two antagonist traditions in German mathematics education research and their synthe-sis in an ongoing video study. These two traditions are (1) the German Didaktik approach that can be characterized by its epistemologically sensitive analyses and specifications of mathematical contents, and (2) the interactionist approach. By presenting the theoretical framework and some empirical insights, the article shows that learning to explain can be conceptualized as increasingly participating in navigating practices through different epis-temic fields.

Keywords

mathematics education
interactionism
didaktik approach
explaining practices
video study

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 10, Issue 4, 2014, 313-327

https://doi.org/10.12973/eurasia.2014.1085a

Publication date: 15 Dec 2014

Article Views: 2391

Article Downloads: 1292

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References

Barzel, B., Leuders, T., Prediger, S., & Hußmann, S. (2013). Designing tasks for engaging students in active knowledge organization. In A. Watson et al. (Eds.), ICMI Study 22 on Task Design – Proceedings of Study Conference (pp. 285–294). Oxford: ICMI.
Bauersfeld, H. (1979). Research related to the mathematical learning process. In International Commission on Mathematical Instruction (Ed.), New trends in mathematics teaching (pp. 199–213). Paris: UNESCO.
Bauersfeld, H. (1988). Interaction, construction and knowledge: Alternative perspectives for mathematics education. In D. A. Grouws, T. J. Cooney & D. Jones (Eds.), Effective mathematics teaching (pp. 27–46). Reston, VA: NCTM & Lawrence Erlbaum.
Bauersfeld, H. (2012). Interview, conducted by Alexander Karp. International Journal for the History of Mathematics Education, 7(2), 67–92.
Blumer, H. (1969). Symbolic interactionism. Englewood Cliffs, NJ: Prentice-Hall. Brousseau, G. (1997). The theory of didactical situations in mathematics. Dordrecht: Kluwer.
Cobb, P. (1998). Analyzing the mathematical learning of the classroom community: The case of statistical data analysis. In A. Olivier (Ed.), Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 33–48). Stellenbosch: University of Stellenbosch / PME.
Cobb, P., & Bauersfeld, H. (Eds.) (1995). The emergence of mathematical meaning: Interaction in classroom cultures. Hillsdale, NJ: Lawrence Erlbaum.
Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2001). Participating in classroom mathematical practices. The Journal of the Learning Science, 10, 113–163.
Common Core State Standards Initiative (CCSSI) (2010). Common Core State Standards for Mathematics. http://www.corestandards.org/assets/ CCSSI_ Math%20Standards.pdf. Accessed 5 June 2014.
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 3 - 17 of PME 38 and PME-NA 36 (Vol. 3, pp. 17-24). Vancouver, Canada: PME.
Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht: Kluwer.
Griesel, H. (1974). Überlegungen zur Didaktik der Mathematik als Wissenschaft [Reflections on Didaktik of Mathematics as scientific discipline]. Zentralblatt für Didaktik der Mathematik, 6, 115–119.
Heller, V. (2014, submitted). Academic discourse practices in action: Invoking discursive norms in mathematics and language lessons. Submitted to Academic Discourse as Situated Practice. Special Issue of Linguistics & Education.
Hiebert, J. (1986). Conceptual and procedural knowledge: The case of mathematics. Hillsdale, NJ: Erlbaum.
Jungwirth, H., & Krummheuer, G. (2006) (Eds.). Der Blick nach innen: Aspekte der alltäglichen Lebenswelt Mathematikunterricht [A lense on the inside: Aspects of the everyday mathematics classroom]. Münster: Waxmann.
Kirsch, A. (1978). Aspects of simplification in mathematics teaching. In H. Athen & H. Kunle (Eds.), Proceedings of the Third International Congress on Mathematical Education, Karlsruhe 1976 (pp. 98–120). Karlsruhe: FIZ. (Reprinted in Westbury, Hopmann & Riquarts, 2000, pp. 267–284.)
Klafki, W. (1958). Didaktische Analyse als Kern der Unterrichtsvorbereitung. Die Deutsche Schule, 50, 450- 471. Reprinted in English:
Klafki, W. (1995). Didactic analyses as the core of preparation for instruction. Journal of Curriculum Studies, 27(1), 13–30.
Klein, F. (1924). Elementarmathematik vom höheren Standpunkte [Elementary mathematics from the higher point of view] (Vol. 1). Berlin: Springer.
Klette, K. (2009). Didactics meet classroom studies. In M. Meyer, M. Prenzel & S. Hellekamps (Eds.), Perspektiven der Didaktik (pp. 101–114). Wiesbaden: VS Verlag für Sozialwissenschaften.
Krummheuer, G., & Voigt, J. (1991). Interaktionsanalysen von Mathematikuntericht. Ein Überblick über einige Bielefelder Arbeiten [Interaction analysis of mathematics classrooms. A survey on some articles of the Bielefeld group]. In H. Maier & J. Voigt (Eds.), Interpretative Unterrichtsforschung (pp. 13–32). Köln: Aulis.
McClain, K., & Cobb, P. (2001). An analysis of development of sociomathematical norms in one first-grade classroom. Journal for Research in Mathematics Education, 32(3), 236–266.
Mehan, H. (1979). Learning lessons: Social organization in the classroom. Cambridge, MA: Harvard University Press.
MSW NRW – Ministry for school and professinal development, Northrhine Westfalia (MSW NRW) (2011). Kernlehrplan und Richtlinien für die Hauptschule in NordrheinWestfalen Mathematik [Curriculum and syllabus for the lower streamed school in NRW mathematics]. Düssseldorf: MSW.
Morek, M. (2012). Kinder erklären. Interaktionen in Familie und Unterricht im Vergleich [Children explain. Comparing interctions in families and classoms]. Tübingen: Stauffenburg.
Mottier Lopez, L., & Allal, L. (2007). Sociomathematical norms and the regulation of problem solving in classroom microcultures. International Journal of Educational Research, 46, 252-265.
Oehl, W. (1962). Der Rechenunterricht in der Grundschule [The primary classroom on calculating]. Hannover: Schroedel.
Prediger, S., Bikner-Ahsbahs, A., & Arzarello, F. (2008). Networking strategies and methods for connecting theoretical approaches. ZDM – The International Journal on Mathematics Education, 40(2), 165–178.
Reckwitz, A. (2003). Grundelemente einer Theorie sozialer Praktiken. [Basic elements of a theory of social practices]. Zeitschrift für Soziologie, 32(4), 282–301.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4–14.
Sierpinska, A., & Lerman, S. (1996). Epistemologies of mathematics and of mathematics education. In A. J. Bishop et al. (Eds.), International handbook of mathematics education (pp. 827–876). Dordrecht: Kluwer.
Sträßer, R. (1996). Stoffdidaktik und Ingénierie didactique – ein Vergleich [Comparing Stoffdidaktik and Ingénierie didactique]. In G. Kadunz et al. (Eds.), Trends und Perspektiven (pp. 369–376). Vienna: Hölder-PichlerTempsky.
Voigt, J. (1994). Entwicklung mathematischer Themen und Normen im Unterricht [The development of mathematical themes and norms in classrooms]. In H. Maier & J. Voigt (Eds.), Verstehen und Verständnis (pp. 77–111). Köln: Aulis.
Voigt, J. (1998). The culture of the mathematics classroom: Negotiating the mathematical meaning of empirical phenomena. In F. Seeger, J. Voigt & U. Waschescio (Eds.), The culture of the mathematics classroom (pp. 191– 220). Cambridge: Cambridge University Press.
Vollrath, H.-J. (1978). Rettet die Ideen! [Save the big ideas!] Der Mathematisch Naturwissenschaftliche Unterricht, 31, 449– 455.
Vollrath, H.-J. (2001). Grundlagen des Mathematikunterrichts in der Sekundarstufe [Foundations of teaching mathematics in secondary schools]. Heidelberg: Spektrum.
vom Hofe, R. (1998). On the generation of basic ideas and individual images. In A. Sierpinska & J. Kilpatrick (Eds.), Mathematics education as a research domain: A search for identity. An ICMI study (Vol. 2, pp. 317–331). Dordrecht: Kluwer.
Wagenschein, M. (1968). Verstehen lehren. Genetisch – Sokratisch – Exemplarisch [Teaching understanding. Genetic – socratic – paradigmatic]. Weinheim: Beltz.
Westbury, I., Hopmann, S., & Riquarts, K. (Eds.) (2000). Teaching as a reflective practice. The German Didaktik tradition. London: Lawrence Erlbaum.
Winter, H. (1983). Über die Entfaltung begrifflichen Denkens [On the development of conceptual thinking]. Journal für Mathematik-Didaktik, 4(3), 175–204.
Yackel, E. (2004). Theoretical perspectives for analyzing explanation, justification and argumentation in mathematics classrooms. Journal of the Korea Society of Mathematical Education, 8(1), 1–18.
Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.
Yackel, E., Rasmussen, C., & King, K. (2000). Social and sociomathematical norms in an advanced undergraduate mathematics course. Journal of Mathematical Behaviour, 19, 275–287.

How to cite this article

APA

Prediger, S., & Erath, K. (2014). Content, Interaction, or Both? Synthesizing Two German Traditions in a Video Study on Learning to Explain in Mathematics Classroom Microcultures. Eurasia Journal of Mathematics, Science and Technology Education, 10(4), 313-327. https://doi.org/10.12973/eurasia.2014.1085a

Vancouver

Prediger S, Erath K. Content, Interaction, or Both? Synthesizing Two German Traditions in a Video Study on Learning to Explain in Mathematics Classroom Microcultures. EURASIA J Math Sci Tech Ed. 2014;10(4):313-27. https://doi.org/10.12973/eurasia.2014.1085a

AMA

Prediger S, Erath K. Content, Interaction, or Both? Synthesizing Two German Traditions in a Video Study on Learning to Explain in Mathematics Classroom Microcultures. EURASIA J Math Sci Tech Ed. 2014;10(4), 313-327. https://doi.org/10.12973/eurasia.2014.1085a

Chicago

Prediger, Susanne, and Kirstin Erath. "Content, Interaction, or Both? Synthesizing Two German Traditions in a Video Study on Learning to Explain in Mathematics Classroom Microcultures". Eurasia Journal of Mathematics, Science and Technology Education 2014 10 no. 4 (2014): 313-327. https://doi.org/10.12973/eurasia.2014.1085a

Harvard

Prediger, S., and Erath, K. (2014). Content, Interaction, or Both? Synthesizing Two German Traditions in a Video Study on Learning to Explain in Mathematics Classroom Microcultures. Eurasia Journal of Mathematics, Science and Technology Education, 10(4), pp. 313-327. https://doi.org/10.12973/eurasia.2014.1085a

MLA

Prediger, Susanne et al. "Content, Interaction, or Both? Synthesizing Two German Traditions in a Video Study on Learning to Explain in Mathematics Classroom Microcultures". Eurasia Journal of Mathematics, Science and Technology Education, vol. 10, no. 4, 2014, pp. 313-327. https://doi.org/10.12973/eurasia.2014.1085a