The article discusses a current issue of college of arts students' readiness for the professional work with gifted children. The article outlines a range of problems of gifted students in the field of music education, including difficulties in adapting to traditional teaching methods, emotional vulnerability, difficulties in communication and mutual understanding of the child with peers, and other peculiarities of the psyche. The author highlights the concept of "abnotivity" as a necessary quality of the teacher’s personality, motivated to work with gifted children, able to arrange special conditions for this and achieve productive results: to educate the personality of a musician with strong subjectivity, creativity, and uniqueness. The structure of the teacher’s abnotivity is defined. It contains motivational, cognitive, and reflexive components, as well as such complex psychological formations as empathy, social intelligence, actual creativity, and supra-situational activity. The advantages of various practice-oriented learning models used in colleges are revealed. The author presents a practice-oriented model of forming abnotivity in students of the college of arts. A brief description of the proposed model components (target, diagnostic, procedural and performance-evaluation blocks), the features of its implementation in Saratov Regional College of Arts, and the results obtained during the experimental study are given.