Homotopies in Higher Mathematics Education: The Gap between Theory and Didactics

Abstract

Homotopy theory is a fundamental pillar in algebraic topology and offers relevant applications across various scientific fields. This study conducted a bibliometric and systematic analysis of the literature related to homotopies and their integration into educational contexts on the basis of 59 documents retrieved from the Scopus and WOS databases. The results reveal an irregular temporal evolution in scientific production (1966–2024), with notable peaks in 2008, 2012, and 2013, identifying four thematic blocks: concepts, applications, history, and didactic approaches. Additionally, a key finding is the scarcity of pedagogical approaches, with only four documents identified that employ methodologies grounded in contextualized didactics and metacognitive strategies. The identified gap between the theoretical development of homotopies and their pedagogical implementation represents both a limitation of the field and an opportunity for the development of innovative didactic proposals. Further exploration of approaches that incorporate interactive visual tools, historical perspectives, and contextualized applications to facilitate the understanding of these abstract concepts in educational settings is recommended.

Received: 30 July 2025 / Accepted: 16 October 2025 / Published: 05 November 2025