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This ICME-13 Topical Survey reviews the state-of-the-art by first
exploring the roots and scope of design science. Second, it
presents two examples of current design science projects that focus
on substantial learning environments including a student and a
teacher perspective. Subsequently, the book elaborates on how
empirical research can be conceptualised within design science.
Lastly, it explores developments in design science from a national
and international perspective, while also discussing current trends
in design research. Within the German-language tradition,
considering 'mathematics education as a design science' primarily
draws on the works of Wittmann. The core of this approach
constitutes designing and investigating learning environments that
involve substantial mathematics.
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.
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