Within the framework of the publication series "Wissenschaftliche Untersuchungen zur Arbeit der Stiftung 'Haus der kleinen Forscher'", scientific contributions from renowned experts in the field of early education are regularly published. This series of publications serves a professional dialogue between the Foundation, science and practice, with the aim of providing all day-care centres, after-schools and primary schools in Germany with well-founded support for their early childhood educational mission. This eighth volume of the series, with a foreword by Kristina Reiss, focuses on the goals and conditions for successful mathematical education in elementary and primary schools. Christiane Benz, Meike Grüßing, Jens Holger Lorenz, Christoph Selter and Bernd Wollring specify in their expertise the pedagogical and content-related target dimensions of mathematical education in nursery and primary school age. In addition to a theoretical foundation of various target areas, instruments for their measurement are listed. Furthermore, the authors discuss conditions for effective and effective early mathematical education in practice. They also give recommendations for the further development of the Foundation's services and the scientific support of the Foundation's work in the field of mathematics. The final chapter of the volume describes the implementation of these professional recommendations in the content of the "Haus der kleinen Forscher" foundation.