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

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https://doi.org/10.1007/b138811This paper gives an account of the conceptual and practical approach to “operative proofs” that has been developed in the Mathe 2000 project. By means of some typical learning environments, this notion and its theoretical background are explained.

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When Is a Proof a Proof?,In his famous talk at ICME 2 (Exeter 1972) the French mathematician R. Thom pointed out that any conception of mathematics teaching necessarily rests on a certain view of mathematics (Thom 1973, 204). As a consequence mathematics education cannot develop without close links to mathematics.

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Standard Number Representations in the Teaching of Arithmetic,The paper describes the specific approach towards the choice and use of number representations as developed by the project Mathe 2000.

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Operative Proofs in School Mathematics and Elementary Mathematics,This paper gives an account of the conceptual and practical approach to “operative proofs” that has been developed in the Mathe 2000 project. By means of some typical learning environments, this notion and its theoretical background are explained.

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