A common theme of models of conceptual growth is to establish the hierarchical structures of abilities that can be interpreted along developmental lines. Integrating the literature on the development of mathematical concepts and skills in children, a comprehensive 6 level model for describing, explaining and predicting the development of key numerical concepts and arithmetic skills from age 4 to 8, is proposed. Two studies will be presented. In the first study, 1095 preschool children completed a mathematics test (MARKO-D0) based on a 5-level model. The test fitted with a one-dimensional Rasch model. The extension of the model to a sixth level was verified in a new study: 312 first-graders took part in a mathematics test based on the six levels (MARKO-D1). In order to check whether the data of both samples adhered to the principle of unidimensionality, the data of MARKO-0 and MARKO-1 were used in a common analysis for comparative purposes. The applicability of these findings for a qualitative diagnostics and an adaptive training will be discussed.