Unveiling the complexities of ‘Abstract Algebra’ in University Mathematics Education (UME): fostering ‘Conceptualization and Understanding’ through advanced pedagogical approaches

Abstract

This scholarly inquiry critically examines the pedagogical aspects pertaining to the instruction and acquisition of Abstract Algebra within the realm of University Mathematics Education (UME). Drawing upon multiple lenses, including epistemological, cognitive, phenomenological, and institutional perspectives, this study investigates the formidable challenges encountered by students and delves into the intricate abstraction processes required to master Abstract Algebra concepts. Moreover, this article endeavors to shed light on the underlying rationales that underscore structural concepts while rigorously analyzing the predominant instructional practices adopted by educators in this domain. The study contends that Abstract Algebra presents distinctive hurdles by virtue of its characteristic dual movement of abstraction, namely idealization and thematization. As such, it necessitates the development and implementation of inquiry-based methodologies to foster optimal conceptualization and comprehension. However, despite ongoing research endeavors in this field, the need for further systematic investigations remains evident. Within this context, the research identifies several critical domains that demand deeper exploration. It underscores the imperative of unearthing the phenomenological foundations of Group Theory and extends this analysis to encompass Ring Theory and Field Theory. By comprehending these fundamental underpinnings, educators can derive valuable insights to inform effective instructional strategies tailored to the specific branches of Abstract Algebra.