In modern higher education, the emphasis is on the development of those skills and competences (called soft, generic, key, in Russia - universal), which, having a supra-professional, supra-subject, transmittable character, are valuable in all fields of activity. In this article, the authors attempted to consider explicit and implicit, contextual and non-contextual organizational forms of the formation of universal competencies through the prism of behaviorist and constructivist approaches and came to the conclusion that these forms should not be contrasted on the basis of their greater or lesser effectiveness. The focus on achieving effectiveness leads to a contradiction: The expectation of a direct correlation between educational strategies and educational results (competencies) lies in an outdated (behaviorist in essence) subject-object learning paradigm, from which the competence-based approach tends to escape. However, it is the introduction of universal competencies that makes it possible to remove this contradiction, since they are the source and consequence of this departure from the subject-object paradigm.