Titlebook: Connecting Mathematics and Mathematics Education; Collected Papers on Erich Christian Wittmann Book‘‘‘‘‘‘‘‘ 2021 The Editor(s) (if applica

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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 the978-3-030-61572-7978-3-030-61570-3

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,Mathematics Education as a ‘Design Science’,ve witnessed a vivid programmatic discussion on the role and nature of mathematics education in the German speaking part of Europe (cf., the papers by Bigalke, Griesel, Wittmann, Freudenthal, Otte, Dress and Tietz in the special issue 74/3 of the . as well as Krygowska .). Since then the status of m

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,Clinical Interviews Embedded in the “Philosophy of Teaching Units”—A Means of Developing Teachers’ y by internal motives but is also a reaction to pressures coming from well-established disciplines, which question the academic status of mathematics education, as well as from teachers’ associations, which question the utility of mathematics education for practice.

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,Mathematics Education as a ‘Design Science’,, there is the risk that by adopting standards, methods and research contexts from other well-established disciplines, the applied nature of mathematics education may be undermined. In order to preserve the specific status and the relative autonomy of mathematics education, the suggestion to conceiv

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Designing Teaching: The Pythagorean Theorem,namely, the design of teaching. As expressed in the title, a well-known topic of geometry, the Pythagorean theorem, is used for illustrating this integrative approach to student teachers. In other words, the emphasis of the paper is . on the Pythagorean theorem per se but . on general principles of

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The Alpha and Omega of Teacher Education: Organizing Mathematical Activities,r is structured as follows: It starts with a general plea for placing the mathematical training of any category of students into their professional context. Then the context of primary education in Germany, with its strong emphasis on the principle of learning by discovery, is sketched.