Cultural contexts for European research and design practices in Mathematics Education -- Barbara Jaworski, Maria G. Bartolini Bussi, Susanne Prediger and Edyta Nowinskarn34 Understanding randomness: Challenges for research and teaching -- Carmen Batanerorn50 Research in teacher education and innovation at schools: Cooperation, competition or two separate worlds? -- Jarmila NovotnárnIntroduction to the papers of TWG01: Argumentation and proof -- Samuele Antonini, Orly Buchbinder, Kirsten Pfeiffer and Gabriel J. StylianidesrnProof by reductio ad absurdum: An experience with university students -- Angelina Alvarado Monroy and María Teresa González AstudillornProof writing at undergraduate level -- Nadia Azrourn86 On a generality framework for proving tasks -- Andreas Bergwallrn93 Analyzing the transition to epsilon-delta Calculus: A case study -- Paolo Boerorn100 Pre-service teachers’ construction of algebraic proof through exploration of math-tricks -- Orly Buchbinder and Alice Cookrn107 A case study: How textbooks of a Spanish publisher justify results related to limits from the 70’s until today -- Laura Conejo, Matías Arce and Tomás Ortegarn114 Argumentation below expectation: A double-threefold Habermas explanation -- Jenny Christine Cramerrn121 Is the use of GeoGebra advantageous in the process of argumentation? -- Özlem Erkekand Mine Işıksal-Bostanrn128 Constructing validity in classroom conversations -- Manuel Goizueta and Maria Alessandra Mariottirn135 Pre-service teachers’ perceptions of generic proofs in elementary number theory -- Leander Kempen and Rolf Biehlerrn142 Disparate arguments in mathematics classrooms -- Christine Knipping, Daniela Rott and David A Reidrn149 E-assessment of understanding of geometric proofs using interactive diagrams -- Yael Luz and Michal Yerushalmyrn156 Building stories in order to reason and prove in mathematics class in primary school -- Marianne Moulin and Virginie Deloustal-Jorrandrn164 The genesis of proof in ancient Greece: The pedagogical implications of a Husserlian reading -- Andreas Moutsios-Rentzos and Panagiotis Spyrourn171 Discriminating proof abilities of secondary school students with different mathematical talent -- Juan Antonio Moya, Angel Gutiérrez and Adela Jaimern178 Proof evaluation tasks as tools for teaching? -- Kirsten Pfeiffer and Rachel Quinlanrn