According to numerous studies, intellectually gifted schoolchildren achieve greater academic success and satisfaction of learning in the homogeneously grouping on abilities classes than in heterogeneously grouped classes. Such differences are especially noticeable when using special programs for high ability students, such as acceleration or enrichment, subject-specific or interdisciplinary of education. In the recent decades digital devices and software provide opportunities for teachers to create a cognitively challenging environment for gifted students both in mainstream schools, in advanced classes and groups, and also individually. The data of qualitative researches demonstrate effectiveness of online education for intellectual gifted school children because it can permit to provide appropriate and individualized difficulties and challenges to each student. However, many questions regarding individualization, challenges, and student readiness for online learning, including Internet courses, still remain unresolved and need to be explored to help understand how gifted students and their teachers perceive their experience. The aim of our study is to analyze some of the issues of gifted children education in the digital age through the literature review and qualitative research. Evidence of many studies demonstrates that the variety of possibilities for intellectually gifted students to improve own knowledge and skills using the internet is much more than in pre-internet times. Virtual classroom, on-line discussion-clubs and other forms of media-associations benefit to educators in creating challenging environment for their high ability students. At the same time the teacher's role demands to take into account individuality of each student, specific needs and talents in cognitive sphere, emotional and social peculiarities, and variety of trajectories of giftedness development.
The researching results substantiate for appropriate professional, including special psychological, training for gifted education teachers and other school staff. The important directions and approaches to improving the qualifications of teachers are offered.