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The research problem of this paper is the competencies of teachers for the implementation of distance teaching in Music Culture. We started with the special assumptions that the research will demonstrate that there is no significant difference in teachers' assessments of their competencies for the implementation of distance teaching in Music Culture, depending on the impact of their length of service in teaching and their knowledge of ICT and participation in professional development programs in the field of ICT. The research was conducted in the first half of the 2021/2022 school year on a sample of 170 teachers who were surveyed by an online questionnaire. Data collected by the research and processed by descriptive statistics showed that there is no significant difference in the competencies of teachers for the implementation of distance teaching in Music Culture depending on the impact of their length of service in teaching and their knowledge of information and communication technologies: 𝞆²(2) = .164; p = .921 and the participation in professional training programs in the field of information and communication technologies: 𝞆²(2) = 1.839; p = .399. Based on the research results, the paper proposes a program of professional development of teachers with the aim of increasing the level of their digital competence for the effective implementation of teaching Music Culture. The skills necessary to possess this competence are: the need for ICT in everyday work; ability to search and process information through ICT; ability to access forums and other ways of using ICT and information.

Logical thinking represents an important process of reasoning and a basic skill in building students' knowledge and experience which should accompany the learning process and develop students' potential at all levels of education. The program of teaching and learning mathematics in primary education in Serbia contains a large number of topics that support the goal of learning mathematics, but there is also room for improvement. The paper deals with the possibility of propaedeutics of logic and the encouragement of logical thinking, the application of open-ended tasks in the initial teaching of mathematics. Respectively to the program contents of the mathematics class, examples of open-ended tasks are presented, as support and analog to teachers in creating teaching practice, in order to promote the development of students' logical thinking, as an important component of mathematics learning outcomes.