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Learning to meet language demands in multi-step mathematical argumentations: Design research on a subject-specific genre

  • Susanne Prediger EMAIL logo and Kerstin Hein


Formal multi-step mathematical argumentations are a typical case of a highly specified subject-specific genre in the technical language with challenging demands in the academic language of schooling. The design research project presented here has the dual aim of (1) specifying the structural and language demands of formal mathematical argumentations and (2) designing a teaching-learning arrangement that uses structural scaffolding to foster students to successively meet these demands. These dual aims are pursued by an in-depth empirical analysis of students’ processes on the micro-level. For this purpose, 15 design experiments were conducted with 10 pairs of students in three design experiment cycles. The first two cycles served to develop the structural scaffolding and the third cycle served to investigate the initiated learning processes and the language demands on the lexical and syntactical level. The qualitative in-depth analysis of the teaching-learning processes in the design experiments shows how students can successively learn to conduct multi-step argumentations when supported by structural scaffolding. Expressing the argumentations in an adequate way, however, is an additional challenge. The empirical analysis reveals deep insights into the complex interplay of conditional, causal, and consecutive phrases that are necessary to combine premises, arguments, and conclusions in a logical sound way. The design research study has theoretical consequences for conceptualizing subject-specific discursive demands as well as practical implications as one design outcome is a prototype of the learning arrangement to foster students in a mathematics- and language-integrated way.


We thank Helmut Johannes Vollmer, John Mason, and the anonymous reviewers for their valuable comments, which helped to clarify our ideas.


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Published Online: 2017-8-18
Published in Print: 2017-9-5

© 2017 Walter de Gruyter GmbH, Berlin/Boston

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