The modern children grow and develop in an extremely dynamic environment. They are surrounded by a variety of information and many digital devices. The ways of processing and using knowledge, as well as the formation of specific skills, are based on the child's personal experiences and social contacts. The community responsible for the development and upbringing of the growing generation - parents, school, kindergarten, educational institutions - are confronted with the complex task of preparing children for their lives in the future. The dynamic with which all spheres of social life are developing makes it difficult to predict how to educate children today so they will be ready for the life that awaits them. Traditional learning, which has proven its importance, needs to build on so-called 21st century skills - communication skills, critical thinking, collaboration, digital literacy. It is necessary to identify important and up-to-date knowledge and skills that should be proposed to children in their current cognitive activities. Contextual competencies or so-called "soft skills" are part of the key competences for human success at every stage of its development. Under soft skills, we understand competences for: communication, tolerance, tolerance, mutual assistance, empathy, teamwork, leadership, negotiation, decision making, creativity, etc. The formation of these important personality skills starts at an early age and key factors are the family, community, educational and social institutions with which the child interacts. The modern society based on technology and information forms a digital generation of children. Technologies offer and support communication and team interaction models. To protect the teenage generation from the dangers of technology - cyber-dependence, isolation, and associal behavior - a variety of cognitive and training patterns need to be applied to seek balance between tradition, modernity and the future. Educators who work with children are directly involved in the process of their preparation for their future lives. This fact determines the importance of the professional training of future teachers. They have to be prepared to bring out the most important theoretical and methodological themes and to present them to the children in an interesting and entertaining way. This article proposes a model for the organization of cognitive mathematical activities for children from a preschool age (5-7 years), in which soft skills such as critical thinking, knowledge transfer, creativity, etc. are being developed. An interdisciplinary approach is underpinned in the model. The proposed methodological solutions are derived from work in the 2018/19 school year with students who are taught for kindergarten and elementary school teachers.