The self-explanation effect (SEE) has great potential in strengthening student learning outcomes. With adequate instructional guidance, this potential is even higher. Our study aimed to examine to what extent direct instruction (DI) and indirect instruction (II) in science, technology, engineering, arts, and mathematics (STEAM) education can strengthen different types of student engagement, as well as whether and to what extent the SEE can support instructional STEAM learning and enhance student engagement. The research was conducted through a quasi-experimental design. The data were collected using an instrument–the engagement scale and were analyzed using confirmatory factor analysis (CFA), one-way ANOVA analysis, and paired sample t-test. The study involved 103 students aged 9-10 years. The results of CFA showed that the adapted version of the instrument for measuring four types of student engagement–emotional, behavioral, cognitive, and agentic–represents a valid and reliable measure for these purposes in primary education. In addition the results of one-way ANOVA analysis and t-test revealed that the usage of DI and II proved to be successful in enhancing all four types of student engagement in the performance of STEAM activities, whereby the combination of the usage of DI with the SEE was singled out as the most successful strategy. As a significant practical implication, this research underlines the need to create appropriate conditions for introducing the SEE in the teaching of STEAM.

This study aims to present educators’ views on the importance of incorporating traditional music during activities with preschool-aged children to develop their socio-emotional competencies. The sample consisted of 88 educators from preschool institutions in the Republic of Serbia. The results showed that most educators frequently use traditional music in their work. Its significance for the development of emotional intelligence, social skills, and cultural awareness in children was particularly emphasized. The analysis showed that educators who regularly incorporate traditional music content report higher levels of socio-emotional competencies in children, highlighting the importance of this practice. Although the educators’ age, work experience, and place of residence did not have a statistically significant impact, regional differences were observed. Educators in different parts of Serbia assessed socio-emotional competencies in a specific way, reflecting the cultural and pedagogical particularities of those regions. The conclusions confirm the importance of integrating traditional music into preschool curricula as a way to develop socio-emotional competencies and children’s cultural identity. The research contributes to the understanding of the role of cultural heritage in the contemporary educational context, providing recommendations for further improvement of pedagogical practices.

Kurepa’s hypothesis for the left factorial has been an unsolved problem for more than 50 years. In this paper, we have proposed new equivalents for Kurepa’s hypothesis for the left factorial. The connection between the left factorial and the continued fractions is given. The new equivalent based on the properties of the integer part of real numbers is proven. Moreover, a new equivalent based on the properties of two well-known sequences is given. A new representation of the left factorial is listed. Since derangement numbers are closely related to Kurepa’s hypothesis, we made some notes about the derangement numbers and defined a new sequence of natural numbers based on the derangement numbers. In this paper, we indicate a possible direction for further research through solving quadratic equations.