Nondeterminism is an essential concept in mathematics and one of the important concepts in computer science. It is also among the most abstract ones. Thus, many students find it difficult to cope with. In this article, we describe some didactic considerations, which guided the development of a "Computational Models" course for high school students, a course in which the concept of nondeterminism is introduced. Some of these considerations are relevant to college and university students as well. We also discuss students' perceptions of nondeterminism and their achievements in this area. Our findings show that many students prefer to avoid nondeterminism, even when it can significantly simplify the solution's design process. We analyze and categorize the students' solutions, thus shedding light on their perceptions of the abstract concept of nondeterminism. (Contains 29 figures.)