The paper is based on the premise that high quality experience in family and insti- tutional contexts are very important determinants for giftedness accomplishment. This framework highlights the fact that the paradigm in the fields of education and upbringing has been shifted in the last few decades: from the discourse of academic achievement towards the discourse of human development, from traditional towards the constructivist approach to education and upbringing. The discourse of human development requires education and upbringing to be adapted to the needs, interests and abilities of children; it also requires creating conditions for every child to achieve their full potentials. The interest for studying the quality of growing-up context was prompted also by the formation of social constructivist theory of learning according to which the child’s mental activity cannot be separated from the social and cultural context. In addition, the modern educa- tional scene is characterized also by the new ways of understanding child, as well as by consid- erations regarding the meaning of that new understanding of education. The child is seen as an active and competent being that joins the social context in a completely individual and unique biographical manner. Relying on the new pedagogical picture of the child requires conditions for becoming familiar with individual capabilities and their development, which opens the need for a learning environment that encourages the child’s curiosity and interest in the world and for the others. In the light of the above settings, this paper is aimed at understanding the possibility of providing adequate educational support to potentially gifted children in family and institutional context. When it comes to a family context, the paper particularly emphasizes the importance of favourable and stimulating family environment and providing an enriched environment necessary for the development of a potentially gifted child. The paper also highlights the undeniable impor- tance of the parental role, but emphasizes the fact that parents do not create gifted children, but only the atmosphere in which the child can express his talent. With regard to the institutional context, the paper emphasizes that it is the quality of institutional environment of which the quality of children’s experience and learning largely depends on, and points to the conditions by which the developmentally appropriate environment is characterized. In this regard, the paper points to kindergartens of Reggio Emilia as stimulating and developmentally appropriate environ- ments, which are examples of how environments in preschool institutions where learning revolves around child’s play should look like. In addition to the above, the paper underscores that the effi- cient, cooperative, partnership-based relationship between the family and educational institution makes a very important factor in the development of potentially gifted children. This perspective is supported by the research which has shown that difficulties in the child’s development and ad- vancement are often resulting from the discontinuity of experiences received by children in the family and educational institution in terms of expectations and learning support. Thus, educating and upbringing potentially gifted child requires sensitivity to specific challenges it faces and willingness to work together with other adults who work with the child. Adults need to have giftedness clearly defined, understand how it develops, and identify the implications for planning and programming educational activities.