Students often experience a lack of educational care suited to their particular needs and conditions. To address that issue, teachers need appropriate methods to understand what students know. This dissertation claims that dynamic formative assessments of how learners are thinking about and responding to problem situations provide a viable approach. The studies of this dissertation thus focus on theories and methodologies applicable to formative assessment. The sequence of studies involves the following: (a) defining a cognitive model of learning progress in complex problem-solving contexts; (b) devising a robust concept map technology to elicit an individuals understanding to a problem situation; and (c) developing diagnostic methodologies to assess and respond appropriately to individual cognitive changes.The theory of mental models explains that students understand a complex problem based on their own knowledge base that is likely a structure. Drawing on the theory of mental models this dissertation suggested two theoretical frameworks involving (a) the features of knowledge structure (3S: Surface, Structure, and Semantic) and (b) the five-stage model of learning progress. Learning progress was considered as a process of transitioning from one stage to another within a students knowledge base.It is necessary that assessment methods take into account the complex, dynamic structure of mental models so that diagnostic, formative information becomes precise. The concept map technique was assumed to represent descriptive and complex knowledge structures in instances in which semantic relations elicited from students natural language responses were used. A comparison study in this dissertation proved that the semantic relation approach could construct more meaningful concept maps.The results from Confirmatory Factor Analyses (CFAs) supported that knowledge structure is likely to consist of the three features (3S: Surface, Structure, and Semantic). Latent class modeling methods were used to validate the stages of learning progress. The results did not confirm that all the stages assumed in the model exist in the data. It was argued that missing stages can be theoretically and statistically justified. In short, the proposed stage-sequential model of learning progress is able to serve as a diagnostic model of learning progress in problem-solving situations.