How do children learn mathematics? How can learners and educators present mathematics in a way that stimulates intensive communication processes during math learning? Do students interpret certain mathematical representations differently than educators during the learning process? How can educators support children in understanding mathematics? Teacher education students and educators grapple with these and similar questions almost daily. The authors of the contributions address these issues and present different viewpoints and perspectives. The range of contributions spans from an overview of mathematical concept formation and representations as necessary means of expression for mathematical ideas, through early mathematical learning in daycare centers and kindergartens, perspectives on primary and secondary education, to contributions on mathematical education.