Actualization, activation, and potentialization of spatial imagination in geometry among students

This study investigates the realization of spatial imagination in the independent creative development of students. It identifies learning activities as a key factor in shaping a student's thinking through knowledge acquisition. Spatial representation is defined as the ability to create, modify, and manipulate spatial images in the imagination, which is essential to solve geometric problems. Success in building models, analyzing structures, and performing practical tasks largely depends on this ability. The study focuses on the organization of educational activities for future mathematics teachers to foster spatial imagination. Three stages of developing spatial images in solving geometric problems are distinguished: actualization, activation, and potentialization. Actualization restores the existing knowledge, activation encourages its application in new contexts, and potentialization aims at advancing imagination to the level of independent creative thinking. The study emphasizes the role of creative assignments, independent activities, and problem-based approaches in enhancing learning. The integration of these stages facilitates a more effective understanding of geometric concepts and the development of stable spatial representations. Furthermore, the research introduces a theoretical model for the development of spatial imagination, based on three interrelated components: cognitive, analytical, and practical, which together ensure the transition towards independent creative thinking.