The methodology of pedagogical actions within the process of moral education of personality is a part of basic, theoretical and empirical researches in pedagogy. When it is referred to moral training, it is primarily referred to the moral aspect of pedagogical actions affecting the development of personality - the formation of moral awareness as a characteristic of a certain individual’s values. Moral education of personality refers to the moral behaviour and action, the formation of attitudes and the development of moral reasonable interests, the introduction to the moral norms and demands, as well as the process of development of a personality’s moral traits. Moral capacity is expressed through the evaluation of moral acts and through moral action while being in accordance with intellectual capability and developmental logic. The educational role of school can be discussed in general or in a more specific way, depending on the extent up to which the school can contribute to the process of moralisation of individuals and the accomplishment of tasks of moral education. Primary and secondary schools in Serbia do not have moral education as a separate subject, but the curriculum sets certain specific tasks which should be accomplished through classes and all extracurricular activities. In accordance with that, this paper focuses on the problematisation of analysing the role of a teacher in moral education and personality development, as well as the analysis of the attitudes of teachers about the necessity of a separate subject or, at least, a “hidden curriculum” in schools which would refer to moral education. The factorisation of measurement variables shows that the awareness of teachers about techniques and methods of moral education and learning should be heightened, which provides a good direction towards a new research. The obtained results have helped us clarify the general problematisation of moral education, and it is believed that they will contribute to overcoming and advancing the existing situation of the school system in Serbia.