An approach for the problem of building such a component of e-learning system that gives the user a chance to get the desired knowledge of teaching course in a user adaptable manner is suggested in this article. This approach is based on socalled “teaching scenarios” (sequence of teaching units) being constructed during the process of learning. We will introduce the GeneticChooser Algorithm (GCA) where Genetic Algorithm (GA) is used in the process of creating user adaptable teaching scenarios. Via the quality and quantity characteristics of the teaching units and user’s knowledge, GA creates the appropriate sequence of teaching units from the course. The considered method is realized and introduced in the TeachArm e-learning system developed at the Department of Algorithmic Languages of YSU [1, 2].