Complex skill mastery requires not only acquiring individual basic component skills, but also practicing integrating such basic skills. However, traditional approaches to knowledge modeling, such as Bayesian knowledge tracing, only trace knowledge of each decomposed basic component skill. This risks early assertion of mastery or ine ective remediation failing to address skill integration. We introduce a novel integration-level approach to model learners' knowledge and provide ne-grained diagnosis: a Bayesian network based on a new kind of knowledge graph with progressive integration skills. We assess the value of such a model from multifaceted aspects: performance prediction, parameter plausibility, expected instructional e ectiveness, and real-world recommendation helpfulness. Our experiments based on a Java programming tutor show that proposed model signi cantly improves two popular multipleskill knowledge tracing models on all these four aspects.

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Open Learner Models (OLM) show the learner model to users to assist their self-regulated learning by, for example, helping prompt re ection, facilitating planning and supporting navigation. OLMs can show di erent levels of detail of the underlying learner model, and can also structure the information di erently. As a result, a trade-o may exist between the potential for be er support for learning and the complexity of the information shown. is paper investigates students' perceptions about whether o ering more and richer information in an OLM will result in more e ective support for their self-regulated learning. In a rst study, questionnaire responses relating to designs for six visualisations of varying complexity led to the implementation of three variations on one of the designs. A second controlled study involved students interacting with these variations. e study revealed that the most useful variation for searching for suitable learning material was a visualisation combining a basic coloured grid, an extended bar chart-like visualisation indicating related concepts, and a learning gauge.