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Abstract: One of the most urgent pedagogical challenges of the system of education today is the importance of solving the problem of forming an adequate attitude to ionizing radiation in society. Its solution is an essential component of the strategy of modernization of education, both general and professional. This strategy includes the formation of an integral system of universal knowledge, competence and skills as well as experience in individual activity and personal responsibility of students as key abilities that define the modern quality of education. The scientific understanding of ambivalence of radioactivity has not practically affected public consciousness, or social attitude, or education. The article contains recommendations how to direct pedagogical efforts towards the transformation of existing theoretical knowledge into a person’s adequate attitude to reality which helps react to all sorts of influences of a complex environment. The author stresses the importance of V.I. Vernadsky’s contribution to the understanding of ambivalent character of ionizing radiation without which life activity is impossible. The outstanding Russian scholar contributed much to the formation of modern natural science theories of unity of the universe. The example of radioactivity and radiophobia in society illustrates that not only teachers of the discipline “Fundamentals of Life Safety” are responsible for the formation of an adequate attitude to danger. This complex object should be discussed in the courses of different subjects in the fields of the Humanities and the Sciences, and it is necessary to facilitate effective cooperation of the teaching staff for the solution of this problem.