In this paper we present a framework for analysing when and how students engage in a specific form of interactive knowledge elaboration in CSCL environments: broadening and deepening understanding of a space of debate. The framework is termed "Rainbow," as it comprises seven principal analytical categories, to each of which a colour is assigned, thus enabling informal visualisation by the analyst of the extent to which students are engaging in interaction relating to potential achievement of its pedagogical goal. The categories distinguish between activities that are part of the prescribed assignment and activities that are not, and between task-focused and non-task-focused activities. Activities focused on managing the interaction itself are distinguished from argumentative interaction. Notably, an operational definition of what it means to broaden and deepen understanding in this case is also provided here. The functional Rainbow analysis is complemented by an analysis of topics and subtopics that enables identification of one form of conceptual deepening of the question. In comparison with existing analysis techniques, Rainbow synthesises much of what is known into a single framework, with a broad theoretical base. The usability and educational relevance of the framework has been validated experimentally across a variety of collaborative learning tasks and communication media. Possible and actual extensions to the framework are discussed, with respect to additional CSCL tools, domains and tasks.