Process-oriented diagnostics require a theoretical framework which allows to describe and interpret individual competence changes. For MARKO-test, a corresponding dimension/scale of mathematical achievement in preschool age was developed on the basis of theoretical assumptions and empirical data. Five essential concepts are: numbers as counting sequence, ordinal number line, cardinal understanding, part – part – whole and concept of congruent intervals. There is empirical evidence for the validity of the model, using a unidimensional Rasch model. Therefore, a concept of testing is available which on the one hand allows to compare individual data with a social norm and on the other hand is usable to make valid statements about individual changes and the current development status of a child.