Giftedness assumes a set of characteristics, above-average abilities, a high degree of creativity, and motivation to accomplish above-average achievements in one or more areas. Potential giftedness in children can be recognized already at an early and preschool age. Looking for gifted traits in children can provide useful information to parents, educators, and children themselves and also help them to better understand who these children are. Very often deeply intelligent children are not properly identified and therefore they do not receive an appropriately challenging education. Potentially gifted children face various risk factors that could hinder and inhibit their optimal development. This is why it is necessary to provide a stimulating and inclusive environment to prevent gifted children from becoming unsuccessful, maladjusted, and living a socially and emotionally deprived life. This paper will present a case study that can contribute to a better understanding of the effect of identification and work with potentially gifted children. In addition to the above, we want to determine what the modern understanding of potentially gifted children in early and preschool education represents, how to raise the level of support for potentially gifted children in their overall and comprehensive development, and how system support can improve the work of educational workers. To get the desired data, a qualitative method of data processing will be used. The data will be collected by observing two potentially gifted children in the regular program in Kindergarten „Sesvete", the shorter enriched program „Bis3ći< and outdoor activities.