Stacking occurs in the composite creation of documents (e.g., such as academic papers, presentation slides, and notes) and when they are refined in research activities. It is important but actually difficult for researchers to satisfactorily accumulate the deliverables for each work and their circumstances so that they can skillfully conduct later work. This problem becomes particularly serious for research beginners. Therefore, there is an urgent need to train research beginners in skills to nail down gaze targets in contexts that continue to increase according to progress as research advances. The final goal of this research was to develop novel methods of training beginners in skills on refining research by extracting the candidates of gaze targets from accumulated contexts and visually presenting them to research beginners. Our project has proposed methods of accumulating the contexts involved with trial and error in the processes of refining research documents and of organizing them into context networks. This paper mainly gives a detailed description of the theoretical methods for dynamically extracting the important sub-network, which is to be carefully examined according to the focus node, from the context network.