Abstract
This paper presents two methods of analysis of interaction processes in mathematics classes—the analysis of argumentation and the analysis of participation –, and it furthermore explores the relationship between these methods and their resulting impact on the development of elements of an interaction theory of mathematics learning. The main theoretical assumption of this article is that learning mathematics depends on the student’s participation in processes of collective argumentation. On the empirical level such processes will be analyzed with methods that are based on Toulmin’s theory of argumentation (Toulmin, SE. (1969). The uses of argument. Cambridge, UK: Cambridge University Press) and Goffman’s idea of decomposition of the speaker’s role (Goffman, E. (1981). Footing. Forms of talk. ders. Philadelphia: University of Philadelphia Press). Different statuses of participation in processes of argumentation will be considered, which allow a theoretical description of different stages in the process of learning mathematics from the perspective of an interaction theory of mathematics learning.
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Notes
- 1.
Quoted from Wood (1995).
- 2.
For more details about this teaching intervention see Cobb et al. (1995).
- 3.
In the original German transcript we do not use the standard interpunctuation, and denote speaking pauses, raisings of the pinch and so forth. In the English translation we do not use these paralinguistic notations. Word order and tone of voice differ too much between German and English. The original transcripts are reproduced in the appendix.
- 4.
In contrast to the English word “thirteen“the German word for 13 contains the identical names for 3 (”drei”) and 10 “zehn”. The word for 13 is just the combination of “zehn” and “drei” to “dreizehn”. In colloquial German it is also common to use the word “und” (in English: “and”) for the arithmetic expression “plus”.
- 5.
As mentioned above, in this concrete situation of a smoothly running course of interaction, the participants by themselves keep the process of negotiation in an ambiguous state, in which it remains unclarified, what the single students might have thought, when presenting their answers. That impacts our results so that we, as analysists of this situation, have to consider a certain vagueness in our interpretation.
- 6.
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1 Appendix: Transcripts and Rules of Transcription
Thirteen Pearls
Mister X
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Krummheuer, G. (2015). Methods for Reconstructing Processes of Argumentation and Participation in Primary Mathematics Classroom Interaction. In: Bikner-Ahsbahs, A., Knipping, C., Presmeg, N. (eds) Approaches to Qualitative Research in Mathematics Education. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9181-6_3
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