The ability to transform representations is thus crucial for successful mathematical problem solving. Therefore, a study was planned guided by the following research question: "What processes of transformations of external representations do gifted children use in their problem-solving process?" The study is associated with an enrichment program for children, aged 8 to 14, who have high interest in mathematics. The collected data consists of 13 video recordings and its transcriptions of interviews with 18 children. The results indicate that the concept of transformations in constructing one's own diagrams to gain new mathematical insights can also be applied to children. Future research has to show if and how these transformation processes can be stimulated to support new mathematical insights in problem-solving processes.