Developing Mathematics Education in a Systemic Process

Design Science and Its Importance in the German Mathematics Educational Discussion

“…Obviously, mathematics education belongs to the latter class for which a sharp separation between researchers and developers who design artefacts and users who simply apply them is not appropriate. The consequences for mathematics education have been indicated already in and further elaborated in more general terms in Wittmann (2001). In the following, the practical implications of this systemic principle are discussed.…”

“…By teaching examples Wittmann (2001) does not mean complete and detailed lesson units. Instead, he is more interested in substantial learning environments that reveal to learners an individual space for error and discovery as well as their own paths of learning.…”

“…One of our main goals is to design examples for learning opportunities that provide mathematical argumentation from the beginning of school (or even earlier) in order to help the children understand the mathematical structures behind arithmetical phenomena. Operative proofs are a very fruitful source for designing learning environments that provide mathematical argumentation, especially (but not exclusively) in the primary level of school (Wittmann and Müller 1988;Wittmann , 2001Steinweg 2006Steinweg , 2013.…”

“…Carefully designed teaching units should therefore become the core objects of study of research in mathematics education. On the high end, these carefully designed teaching units have been called, according to Wittmann ( , 2001a, substantial learning environments, which cover curriculum objectives at specified level, open up various possibilities for students to acquire important mathematical contents or abilities that go beyond that level, are flexible for adaptation to different classroom conditions, and integrate different aspects of mathematics teaching in such a way as to offer ample opportunities for empirical research.…”

On the Importance of Subject Matter in Mathematics Education: A Conversation with Erich Christian Wittmann

“…From the design science perspective, the construction, the empirical research and the implementation of substantial learning environments are the main tasks of research in mathematics education , Wittmann 2002. It is exactly these tasks that prove the autonomy of mathematics education (or 'didactics of mathematics') as a discipline on its own: "[…] mathematics education requires the crossing of boundaries between disciplines and depends on results and methods of considerably diverse fields, including mathematics, general didactics, pedagogy, sociology, psychology, history of science and others.…”