Christiane Benz is full professor of mathematics education at Karlsruhe University of Education in Germany. Her general research focuses the early mathematical learning especially in the domain of arithmetic in the transition of early mathematics education and primary school. Her other main research interest in professional development is linked with a long-term design-research project (MiniMa).Anna S. Steinweg is full professor of mathematics education and computer science education, at the University of Bamberg since 2004. She has previously worked at the University of Education in Heidelberg and the University of Dortmund. Her current research mainly focusses on two major transitions phases, which lay in early mathematics education towards primary school on the one hand and algebraic thinking in primary and secondary school mathematics education on the other hand.Hedwig Gasteiger is full professor in mathematics education at Osnabrueck University in Germany. She is director of the Center of Early Childhood Development and Education Research (CEDER) in Osnabrueck and a leading member of the German Center for Mathematics Teacher Education. Her research focuses on early mathematics education in natural learning situations, professional competence of kindergarten teachers, strategies in arithmetic and early geometry. Priska Schöner is researcher and lecturer at University of Education Karlsruhe. She teaches B.A. and M.A. courses in early mathematics education. Her research interests focus on perceiving und using structures when determining the cardinality. One research tool she is working with is Eye-Tracking to get deeper insights in children’s thinking.Helene Vollmuth is a primary school teacher and a former lecturer at the University of Education Karlsruhe. She mainly taught B.A. and M.A. courses for early and primary mathematics education and was involved in the research project for the professionalisation of kindergarten teachers (MiniMa).Johanna Zöllner is lecturer and researcher at University of Education Karlsruhe. Her research interests focus on early mathematics education especially in the domain of measurement, where she investigates the development of children’s’ thinking and playing environments in the long-term design-research project (MiniMa). She teaches B.A. and M.A. courses in early and primary mathematics education.

• Introduction.- Young Children’s Engagement with Mathematics: Expanding Teacher Educators’ Views.- Preservice Teachers Recognising and Responding to Young Children’s Engagement with Mathematics.- Using Children’s Patterning Tasks during Professional Development for Preschool Teachers.- Mathematics Education Competence of Professionals in Early Childhood Education: A Theory-Based Competence Model.- Stories Neglected About Children’s Mathematics Learning in Play.- The Genesis of Children’s Mathematical Thinking in Their Early Years.- Visual Structuring Processes of Children When Determining the Cardinality of Sets: The Contribution of Eye-Tracking.- Is Considering Numerical Competence Sufficient? The Structure of 6-Year-Old Preschool Children’s Mathematical Competence.- TellMEE: Telling Mathematics in Elementary Education.- Designing Playful Inquiry Based Mathematical Learning Activities for Kindergarten.- Talking about Measuring in Kindergarten: Linguistic Means in Small Group Interactions.- Early Maths Via App Use: Some Insights in the EfEKt Project.- How Can A Father Be Supportive for the Mathematics Learning Process of A Child? The Relationship between Scaffolding and the Interactional Niche in the Development of Mathematical Learning in the Familial Context.- Instruction and Contruction of Mathematics at Home: An Exploratory Study.- Index.