Abstract
Current learning trajectories and stage models of arithmetic development advocate the elaboration of counting on as an intermediate computation strategy. At the same time, there is empirical evidence that a considerable share of children fail to overcome this procedural approach to addition and subtraction, with damaging effects to their further mathematical thinking. This theoretical essay argues that it is fundamentally faulty to justify instructional measures by stage models that claim to capture a development without considering that its stages themselves reflect the conditions of children’s learning, inter alia: the very instructional measures. As an alternative, the paper uses structure-genetic didactical analysis to delineate a teaching design that derives addition and subtraction out of part-whole thinking from the very beginning, rendering counting on superfluous.