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

Gulnisa Borboeva; Gulbadan Matieva; Venera Isakova; Cholpon Mustapakulova; Gulshana Omurzakova; Gulnisa Borboeva; Gulbadan Matieva; Venera Isakova; Cholpon Mustapakulova; Gulshana Omurzakova

doi:10.3934/steme.2025037

STEM Education

2025, Volume 5, Issue 5: 836-854. doi: 10.3934/steme.2025037

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Research article

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

1.
Institute of Mathematics, Physics, Technics and Information Technologies, Osh State University, 723500,331 Lenin Str., Osh, Kyrgyz Republic; gulnisaborboeva36@gmail.com, gu-matieva@outlook.com, c_mustapakulova@outlook.com, gulomurzakova@hotmail.com
2.
Faculty of Mathematics and Computer Technologies, Osh State Pedagogical University, 723500, 73 Isanov Str., Osh, Kyrgyz Republic; v.isakova422@hotmail.com

Academic Editor: William Guo

Received: 11 March 2025 Revised: 09 May 2025 Accepted: 20 May 2025 Published: 22 July 2025

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.
- future teacher,
- visualisation,
- development zones,
- self-development,
- mathematical discipline
Citation: Gulnisa Borboeva, Gulbadan Matieva, Venera Isakova, Cholpon Mustapakulova, Gulshana Omurzakova. Actualization, activation, and potentialization of spatial imagination in geometry among students[J]. STEM Education, 2025, 5(5): 836-854. doi: 10.3934/steme.2025037

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Abstract

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.

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Author's biography Gulnisa Borboeva is a PhD, Associate Professor at the Institute of Mathematics, Physics, Technics and Information Technologies, Osh State University. She is specialized in mathematical modeling and applied physics. Her research interests include computational fluid dynamics, numerical methods for partial differential equations, and their applications in engineering; Gulbadan Matieva is a Full Doctor, Professor at the Institute of Mathematics, Physics, Technics and Information Technologies, Osh State University. She is specialized in theoretical physics and quantum mechanics. Her research interests focus on quantum information theory, condensed matter physics, and the interaction of light with matter; Venera Isakova is a PhD, Associate Professor at the Faculty of Mathematics and Computer Technologies, Osh State Pedagogical University. She is specialized in applied mathematics and computer science. Her research interests include algorithm design, machine learning, and the development of software systems for data processing; Cholpon Mustapakulova is a Master, Lecturer at the Institute of Mathematics, Physics, Technics and Information Technologies, Osh State University. She is specialized in mathematical analysis and optimization techniques. Her research interests are focused on optimization problems in various fields, including economics and industrial applications; Gulshana Omurzakova is a Master, Lecturer at the Institute of Mathematics, Physics, Technics and Information Technologies, Osh State University. She is specialized in computational mathematics and simulation. Her research interests include high-performance computing, simulation of complex systems, and computational methods in physics and engineering

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