Wide support of giftedness in STEM (Science, Technology, Engineering and Mathematics) is a relevant social necessity. Gifted students have special educational needs. Fostering gifted students involves identification and development of their giftedness. This educational fostering of gifted students also plays an important role in their personal development. Crucial areas for the fostering of gifted students are: education of teachers in identifying and development giftedness, creation of a support system to help teachers and families in the education of gifted students, and setting up high-quality school facilities for gifted students. The creation of suitable conditions for the development of students gifted in STEM is an important task for teachers. This objective involves the identification and the development of giftedness to the highest possible level. The study presents the research results of science teacher training in educational methods suitable for fostering gifted students. Design-based research was used as the main research method.