\input zb-basic \input zb-matheduc \iteman{ZMATH 2015c.00497} \itemau{Wittmann, Erich C.} \itemti{Operative proofs in school and elementary mathematics. (Operative Beweise in der Schul- und Elementarmathematik.)} \itemso{Math. Didact. 37, 213-232 (2014).} \itemab Zusammenfassung: In diesem Beitrag werden zun\"achst substanzielle Lernumgebungen vorgestellt, die den Begriff operativer Beweis" und seine curriculare Einbettung exemplarisch beleuchten. Darauf aufbauend wird dieser Begriff im zweiten Abschnitt formuliert und im letzten Abschnitt theoretisch fundiert. \itemrv{~} \itemab Summary: First some substantial learning environments are presented which are typical for the notion operative proof" and its curricular embedding. In the second section this notion is formulated, and in the last section conceptually underpinned. \itemrv{~} \itemcc{E50} \itemut{didactics of mathematics; design science; proving; teaching; genetic method; operative proofs; learning environments; primary education; lower secondary; even and odd numbers; multiplicative arithmetic chains; written addition; Egyptian fractions; unit fractions; elementary geometry; fitting; tessellations; patterns; quasi-empirical nature of mathematics; operations; operative principle; productive exercises; mathematical thinking} \itemli{http://mathdid.ph-freiburg.de/documents/md\_2014/md\_2014\_Wittmann\_Operative\_Beweise.pdf} \end