Kuhn's Epistemology and its Contributions to Understanding the Process of Knowledge Construction and Mathematics Teaching

Context: Scientific progress does not occur linearly but through revolutions that replace paradigms that no longer meet the demands of a given field of knowledge with others that address these requirements and expand the problem-solving horizon. Objective: to analyze how Kuhn's epistemology can be applied to understand the paradigm shifts that have occurred in the process of knowledge construction and mathematics teaching. Design: this is a bibliographic investigation of an analytical and interpretative nature. Scope: the study analyzed how paradigm shifts occurred in the history of mathematics and illustrated these transitions with examples such as the adoption of infinitesimal calculus and the development of non-Euclidean geometry. Data Collection: the study was based on a bibliographic review, critically describing the main epistemological themes and concepts developed by Kuhn and his respective commentators. Additionally, it systematized the implications of these paradigm shifts for mathematics teaching, with particular emphasis on the urgency for teachers to remain open to new theoretical-methodological approaches and the use of emerging technologies, such as educational software, which can provide a deeper, more dynamic, and interactive understanding of concepts and facilitate mathematics teaching. Results: the use of technology enables students to explore problems, visually verify results, and understand concepts, fostering more meaningful, innovative, and critical learning. It also helps reimagine mathematics education and build a promising future for future generations. Resistance to paradigm shifts in mathematics teaching often stems from adherence to traditional methods and a lack of proper training. Conclusions: addressing these challenges, given the need to prepare students for a constantly changing world, requires continuous teacher training, curriculum adaptation, the adoption of active methodologies, and the use of new technologies.