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"The origin of this book is the conference Explanation and Proof in Mathematics: Philosophical and Educational Perspectives (Essen, 2006) and it reflects different views from three fields: mathematics educators, philosophy of mathematics and history of mathematics. ... The authors and editors made a fine job providing a useful resource for all interested in proofs and proving in mathematical education." (Claudi Alsina, Zentralblatt MATH, Vol. 1196, 2010)