Research competencies of students direction "forestry" in the context of field practices

It is obvious that the forest ecosystem is the main topic of environmental issues for the world community, requiring high scientific and professional competencies and skills for effective solutions. Scientific competencies are especially required from specialists for whom forestry is interpreted through professional orientation and affiliation. Therefore, training students in the field of "forestry" with developed scientific research competencies is becoming the dominant model of modern specialized higher education. Students should not only be professionals in solving "forest" problems but also identify new problems and generate scientifically based solutions. Therefore, the generation and development of students' research competencies is a critical task for higher education, especially in areas that require an integrated approach to research activities, such as forestry. This paper proposes a linear mathematical model and an algorithmic model that describe the process of developing research competencies based on cognitive, procedural, and practical components. The linear mathematical model allows us to quantitatively assess the contribution of each component to the overall level of competence, identifying the process component as the most dominant. The experimental data show that the introduction of a practice-oriented methodology led to an increase in research competence of 35.3%, confirming the effectiveness of the model. The algorithmic model complements the linear analysis, allowing us to model the dynamics of competence development over time. The iterative approach demonstrates that the growth rate of competencies depends on their interrelation: insufficient development of the cognitive or procedural components acts as a resistance factor for overall progress. The algorithm of adaptive competence updating makes it possible to personalize educational strategies, predict student progress, and adjust curricula. The models considered can be used to optimize educational programs, provide individual support to students, and monitor the effectiveness of training. Future research may focus on integrating machine learning methods to predict individual competency development trajectories and take into account additional factors such as student motivation and external educational resources.