This article provides a meaningful analysis of the phenomenon of giftedness, defines various ways to identify signs of giftedness and the importance of developing children's logical thinking. Also in the process of data analysis, we are talking about the effectiveness of using the Japanese horizontal arithmetic method of calculation, the so-called "mental arithmetic" in the development of logical thinking of gifted children. In order to solve the above problems, the analysis of the history, main directions and possibilities of mental arithmetic is carried out.