This open access book features a selection of articles written by Erich Ch. Wittmann between
1984 to 2019 which shows how the design science conception has been continuously developed
over a number of decades. The articles not only describe this conception in general terms but
also demonstrate various substantial learning environments that serve as typical examples. In
terms of teacher education the book provides clear information on how to combine
(well-understood) mathematics and methods courses to benefit of teachers.The role of
mathematics in mathematics education is often explicitly and implicitly reduced to the delivery
of subject matter that then has to be selected and made palpable for students using methods
imported from psychology sociology educational research and related disciplines. While these
fields have made significant contributions to mathematics education in recent decades it
cannot be ignored that mathematics itself if well understood provides essential knowledge for
teaching mathematics beyond the pure delivery of subject matter. For this purpose mathematics
has to be conceived of as an organism that is deeply rooted in elementary operations of the
human mind which can be seamlessly developed to higher and higher levels so that the full
richness of problems of various degrees of difficulty and different means of representation
problem-solving strategies and forms of proof can be used in ways that are appropriate for the
respective level. This view of mathematics is essential for designing learning environments and
curricula for conducting empirical studies on truly mathematical processes and also for
implementing the findings of mathematics education in teacher education where it is crucial to
take systemic constraints into account.
