Introduction to the Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10) -- Thérèse Dooley, Ghislaine GueudetrnStatistical overview of CERME10 -- Maurice OReillyrnFrom advanced mathematical thinking to university mathematics education: A story of emancipation and enrichment -- Elena NardirnYoung children’s early mathematical competencies: Analysis and stimulation -- Lieven Verschaffel, Joke Torbeyns, and Bert De SmedtrnSolid findings in mathematics education: What are they and what are they good for? -- Marianna Bosch, Tommy Dreyfus, Caterina Primi, Gerry ShielrnSolid findings in mathematics education: A necessary discussion -- Marianna BoschrnWhat are solid findings in mathematics education? -- Tommy DreyfusrnSolid findings in mathematics education: A psychometric approach -- Caterina PrimirnCan the outcomes of PISA 2015 contribute to evidence-based decision making in mathematics education? -- Gerry ShielrnIntroduction to the papers of TWG01: Argumentation and proof Meta-mathematical knowledge about proof -- Nadia AzrournConceptualizing reasoning-and-proving opportunities in textbook expositions: Cases from secondary calculus -- Andreas BergwallrnCognitive unity of theorems, theories and related rationalities -- Paolo BoerornSupporting classroom implementation of proof-oriented tasks: Lessons from teacher researcher collaboration -- Orly BuchbinderrnA framework for classifying mathematical justification tasks -- Boon Liang ChuarnAn application of Habermas’ rationality to the teacher’s actions: Analysis of argumentation in two classrooms -- AnnaMarie ConnerrnEvolution of proof form in Japanese geometry textbooks -- Marion Cousin and Takeshi MiyakawarnPre-service middle school mathematics teachers’ interpretation of logical equivalence in proof by contrapositive -- Esra Demiray and Mine Işıksal BostanrnIssues of a quasi-longitudinal study on different types ofrnargumentation in the context of division by zero -- Christian FahsernThe flow of a proof - Establishing a basis of agreement rnFostering and investigating students’ pathways to formal reasoning: A design research project on structural scaffolding for 9th graders -- Kerstin Hein and Susanne PredigerrnMisconceptions and developmental proof -- Kirsti Hemmi, Erika Julin and Ray PörnrnPrimary and secondary students’ argumentation competence: A case study -- Eugenia Koleza, Nikolaos Metaxas and Klio Poli Proofs and refutations in school mathematics: A task design in dynamic geometry environments -- Kotaro Komatsu and Keith JonesrnCan teacher trainees use inductive arguments during their problem solving activity? -- Eszter Kónya and Zoltán KovácsrnPrinciples towards justification: A focus on teacher actions -- Joana Mata-Pereira and João Pedro da PonternA reference for studying the teaching of logic -- Zoé MesnilrnRevisiting Odysseus’ proving journeys to proof: The ‘convergent-bounded’ question -- Andreas Moutsios-Rentzos and Faidra Kalozoumi-PaizirnPlay and pre-proving in the primary classroom -- Maria Pericleous and David PrattrnProof-based teaching as a basis for understanding why -- David Reid and Estela Vallejo VargasrnMathematical reasoning in the written argumentation of primary students -- Silke RuwischrnAn expanded theoretical perspective for proof construction and its teaching -- John Selden and Annie SeldenrnTool-based argumentation -- Kalliopi Siopi and Eugenia KolezarnLearning with the logic of inquiry: game-activities inside Dynamic Geometry Environments -- Carlotta Soldano and Ferdinando ArzarellornReasoning-and-proving in geometry in school mathematics textbooks in Hong Kong -- Kwong-Cheong WongrnAn exploratory teaching style in promoting the learning of proof - - Xiaoheng Yan, John Mason and Gila HannarnLooking for the roots of an argument: Textbook, teacher, and student influence on arguments in a traditional Czech classroom -- Jana ŽalskárnIdentifying phases and activities in the proving process of first-year undergraduates -- Katharina Kirstenrn