The developmental course in the distance-speed-time domain is still a matter of debate. Traditional stage models are contested by theories of continuous development and adaptive thinking. In the present work, we introduce a formal framework for modelling the developmental course in this domain, grounding on Competence-based Knowledge Space Theory. This framework, as a more general case, widely includes assumptions and facets of previous models and covers empirical findings collected based on different experimental paradigms. By a distinction of latent competences and observable performance, model validation is not bound to a certain experimental paradigm and no one-to-one correspondence between competences and tasks is required. Therefore, the framework has the potential to bridge the gap between stage models and models of continuous development. The approach also precisely defines misconceptions, for example overgeneralization, and empirically investigates their occurrence. In the present work, we established a prototypical model for the development of understanding the distance-speed-time system. We extended this model with definitions based on different perspectives of overgeneralization. The assumptions of the model and its extensions were examined on the basis of the results of two empirical investigations using six judgment task types. The results yielded a reasonably good fit of model and data. No evidence was found for the occurrence of overgeneralization in this domain. The theoretical model and empirical results are discussed with respect to their relationship to other developmental models and theories. (Contains 5 tables and 4 figures.)