We present a framework for measurement and diagnosis using knowledge-based models. Based on formulations of knowledge-level analysis, symbol-level analysis, constructivist learning, and situated cognition, we describe' the possible frames of reference and fundamental measurement approaches that may be adopted in the analysis of cognition and learning. In general, these frames of reference define how individuals, contexts, knowledge, and activity are constitutively defined. We then present several measurement models extending the objective measurement approach of Rasch models to the analysis of learning strategies and knowledge development. The structure and parameter estimates of such models can then be used in the specification of probabilistic belief networks that can perform on-line student modelling.