Mathematics education has become more demanding with the introduction of educational standards. The performance expectations for children have increased, as have those for teachers. Mathematikus incorporates precisely those ideas of modern mathematics didactics that are currently articulated in the standards. A central concern of Mathematikus is the development of mathematical competencies in the true sense. In addition to the necessary mastery of calculation algorithms, understanding of procedures, the development of number sense, and the flexible application of individual calculation strategies in complex situations are equally important. The emphasis on practical arithmetic as a starting point for modeling, problem-solving, and discovery-based learning is fundamental. The focus is on developing powerful, transferable core ideas that promote structural, overarching thinking.