Written Argumentation in Learning Groups [Schriftliche Argumentation in Lerngruppen]

Since the publication of the educational standards [Bildungsstandards der KMK] in 2003, argumentation has increasingly become the focus of teaching practice. Formulated as an output-oriented standard, it is about the ability of the individual learner independent of a specific teaching event. The study outlined here aims in the long term to be able to measure this ability and its development at the learning group or state level. In view of this goal, the development of a test instrument that can be characterized as a "probe" (Fahse 2011) is to be realized: It should be feasible with little effort in a short period of teaching time and allow indirect conclusions to be drawn about the teaching that has taken place, i.e., through correlations.

For this purpose, the written justification of the result of a division by 0 given by the learners was tested. The empirical study is based on test results from grades 7, 8, 9, 10, 11, 13 and from university students. This involves written argumentation on the stated topic, but also flanking other questions (Fahse 2013), as well as accompanying interviews. The study initially focuses on grades 7, 9, 11, 13 of a single school (Gymnasium, N=365) and thus also allows quasi-longitudinal statements.

As a theoretical background, two clarifications were necessary in particular. On the one hand the investigation of the different ideas about zero, on the other hand a clarification of the terms prove - justify - argue - explain.

In the empirical findings on the conceptions of zero, a "coding conception" of zero - zero as a sign for an exceptional situation - showed up in a surprisingly frequent way (Fahse 2014). This represents a result that is relevant for teaching practice and at the same time necessary to be able to classify the types of justification correctly.

The views found in the literature on the aforementioned clarification of terms differ fundamentally. For this study, the conceptualizations were explicated on the basis of models of communication theory (especially Toulmin 1958 and Kopperschmidt 1989 following Habermas) (Fahse 2013). The study does not aim at proving, but at the types of justifying found less frequently in the literature.

Qualitative content analysis according to Mayring (2008) is used to evaluate the texts. In order to measure reliability, one tandem at a time first codes individually and then consensually in a second step. Data collection has been completed, coding and statistical analysis has begun. An application of AI is in development with promising results.

Literature

Fahse, C. (2014). Vorstellungen zur Null im Kontext der Division durch Null. mathematica didactica, 37, 5-29.

Fahse, C. (2013). Argumentationstypen. In G. Greefrath, F. Käpnick & M. Stein (Hrsg.), Beiträge zum Mathematikunterricht 2013. Münster: WTM-Verlag.

Fahse, C. (2013). The Impact of Primary School on Secondary School - the Example of Division by Zero. Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education. Kiel: IPN.

Fahse, C. (2011). Sonden - eine Möglichkeit für die empirische Unterrichtsforschung? - Das Beispiel Division durch Null. In R. Haug & L. Holzäpfel (Hrsg.), Beiträge zum Mathematikunterricht 2011. Münster: WTM-Verlag.

Kopperschmidt, J. (1989). Methodik der Argumentationsanalyse. Stuttgart, Bad Cannstatt: Frommann-Holzboog.

Mayring, P. (2008). Qualitative Inhaltsanalyse. New York: Springer. (10. Auflage)

Toulmin, S. E. (1958). The uses of argument. New York: Cambridge University Press.

[This dissertation was written and is only available in german. Our summary was translated by our website team. Possible quotations have been translated in accordance with scientific regularia.]