This paper is a workshop report of an empirical study called DISUM, which deals with appropriate teacher interventions in the course of students' independence-oriented modelling processes. The project aims at developing and investigating corresponding instructional conceptions, based on an intensive analysis of modelling tasks and of students' learning processes. This is to be realized through a coordinated programme of task development, evaluation of instruction and analysis of laboratory and classroom sessions, and also by using tests and questionnaires. The basis of the evaluation is the empirically substantiated theoretical knowledge of quality teaching. The main subjects of this article are both the design and first results of the explorative preliminary study, which contain a short description of three exemplary fields of problems when teachers intervene in students' modelling processes. Those fields of problems were identified by analysing eight sessions in the laboratory, four mathematics lessons and 32 interviews.