A PRIMER ON SPATIAL CONCEPTS: INTRODUCING BASIC TOPOLOGY IN EARLY EDUCATION

This research introduces a new perspective on teaching basic topological notions in early education, guided by the directives set by the National Ministry of Education and their implementation in classroom practices. The study focuses on characterizing the pedagogical phraseology of educators when teaching fundamental topological concepts such as interior, exterior, open, closed, up, down, and proximity. The overarching goal is to shed light on the classroom practices of teachers and propose a didactic approach for teaching basic topological notions within the context of early education at the "Agropecuario Veracruz Institute". The specific objectives encompass exploring teachers' conceptions of basic topological notions, characterizing teaching practices in the Transitional Grade at the Veracruz Educational Institution in Santa Rosa de Cabal, analyzing the impact of pedagogical practices on students' understanding of basic topological concepts, and devising and implementing experiences to assist preschool educators at the Agropecuario Veracruz Institute in solidifying fundamental topological notions in their early education students. This research presents a platform for further curriculum development in the field of spatial cognition for students pursuing a degree in early childhood education, focusing on the component of spatial thinking and, in particular, the development of topological space in early education. It signifies a call to action for Colombian educators in early education, urging the construction of praxeologies that bridge the gap between everyday life and mathematical language for learning basic topological concepts. Furthermore, this study suggests the potential for a doctoral investigation in mathematics education to reshape the sequenced perspective on the evolution and learning of spatial thinking. The proposed vision encourages progression from the topological to the projective, culminating in the Euclidean, laying a theoretical foundation for the definitive reconfiguration of these postulates. Lastly, this research opens avenues for the same study to be conducted across the twelve municipalities of the Risaralda department, enabling a broader generalization and generating direct proposals to the National Ministry of Education regarding curriculum and teacher training. In conclusion, this research highlights the lack of a comprehensive and clearly defined proposal from the National Ministry of Education for teaching topological concepts, contributing to teachers' limited commitment to deepening these notions. It also reveals a surface-level treatment of topological concepts in early education, mostly confined to two-dimensional representations. Transforming classroom practices proves to be challenging due to educators' limited mathematical and didactic training, necessitating institutional and pedagogical reform. The study emphasizes the need to incorporate specific didactics, particularly in mathematics, into the training of early childhood educators, an area currently absent from their curriculum. Keywords: Praxeology, Anthropological Theory of the Didactic (ATD), Levels of Didactic, Codetermination, Didactic Organization, Mathematical Organization, Didactic Moments.