One of the critical factors contributing to the effectiveness of human tutoring is the conversational aspect of the instruction. Our goal is to develop a general model for supporting dialogues with menu-based input that could be used in both well- and ill-defined instructional tasks. We have previously studied how human tutors provide additional support to students learning with an existing intelligent tutoring system. On the basis of these findings we developed a model for supporting dialogues, which we present in this paper. We used this model in a Wizard-of-Oz study to provide adaptive support. The results show that students did learn the relevant domain knowledge and that human tutors mostly agreed with the interventions generated from the model. (Contains 1 footnote, 1 table, and 12 figures.)