Formal concept analysis provides powerful tools for constructing knowledge structures and finding learning paths. However, existing methods for recommending learning paths based on skill context require traversing the entire knowledge structure, which is inefficient in a big data environment. To address this issue, this paper proposes new methods for recommending learning paths based on skill context using both conjunctive and disjunctive models. First, the concept of the fringe of knowledge states regarding skills is defined under both models. Next, methods for recommending learning paths are presented based on these fringes. Finally, experiments conducted on three UCI datasets demonstrate the effectiveness of the proposed methods. By using the methods presented in this paper, personalized learning path recommendations can be achieved without constructing the entire knowledge structure, thus overcoming the limitations of existing methods.