Investigating the Dynamics of Stochastic Learning Processes: A Didactical Research Perspective, Its Methodological and T
Our didactical research perspective focuses on stochastic teaching–learning processes in a systematically designed teaching–learning arrangement. Embedded in the methodological framework of Didactical Design Research, this perspective necessitates the ite
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cades, a lot of research has been conducted on students’ biases and misconceptions which seem to persist even after school education (overview in Shaughnessy 1992, pp. 479ff). Whereas most of these studies mainly focus on the status of (mis-)conceptions (as results of learning processes or as their initial starting points), we want to present a Didactical research perspective that complements these important studies by two dimensions: (i) the dynamic focus lies on specifically initiated learning processes. For this, (ii) a theoretically guided and empirically grounded design of teaching–learning arrangements (with restructured learning contents and concrete learning opportunities) and its underlying design principles are developed. In Sect. 1 of this article, we present the didactical research perspective with its methodological framework of a process-oriented Didactical Design Research (Gravemeijer and Cobb 2006; Prediger and Link 2012). In Sect. 2, the perspective is exemplified by a report on six phases of research and (re-)design in a long term project on the distinction of short term and long term stochastic contexts for students in lower middle school. In Sect. 3, specific emphasis is put on the fourth phase, the investigation of the dynamics of stochastic learning processes on the micro-level. As the theory has been developed within these six phases, we present it together with
S. Prediger (B) · S. Schnell Institute for Development and Research in Mathematics Education, TU Dortmund University, Vogelpothsweg 87, 44227 Dortmund, Germany e-mail: [email protected] E.J. Chernoff, B. Sriraman (eds.), Probabilistic Thinking, Advances in Mathematics Education, DOI 10.1007/978-94-007-7155-0_29, © Springer Science+Business Media Dordrecht 2014
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each phase of the project (in Sects. 2 and 3). In Sect. 4, we conclude by extracting principles of a Didactical research perspective.
1 Methodological Framework 1.1 Didactical Design Research with a Focus on Learning Processes The scientific work in mathematics education research is sometimes dichotomised by two different aims (that appear in Fig. 1 as both ends of the left vertical arrow): (i) Practical developmental work aims at developing general approaches and designing concrete teaching–learning arrangements for mathematics classrooms. (ii) Fundamental empirical research, on the other hand, aims at understanding and explaining students’ thinking and teaching–learning processes. To overcome this unfruitful dichotomy, more and more researchers advocate the general idea to join empirical research and the design of teaching–learning arrangements in order to advance both: practical designs and theory development. Under varying titles like “design science” (Wittmann 1995), “design research” (e.g. van den Akker et al. 2006; Gravemeijer and Cobb 2006), “design-based research” (e.g. Barab and Squire 2004) or “design experiments” (e.g. Brown 1992; Cobb et al. 2003; Schoenfeld 2006), programmes have been developed with this common id
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