The Dynamics of Resistance to Learning: A Re-reading of Epistemological Obstacles in Advanced Mathematics

Document Type : Expository article (original)

Authors

Mohamad Sabzi ¹

Mehrdad Nandari ²

Mohammad Ali Siavoshi ²

¹ Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz Ahvaz, Iran

² Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz

10.22067/tmsj.2025.96780.1074

Abstract

This paper addresses the question of why learning failures in mathematics occur even when learners possess the relevant knowledge and strategies. Drawing on Bachelard’s notion of the epistemological obstacle, we argue that many persistent learning failures cannot be reduced to superficial misunderstandings; rather, they stem from deep-seated, prior cognitive structures that resist new knowledge. We show that Schoenfeld’s theory of problem solving, particularly the components of beliefs and control, can be understood as a metacognitive reformulation of the same Bachelardian logic. We also demonstrate that concepts such as diSessa’s p-prims, Fischbein’s coercive intuitions, and Tall and Vinner’s concept image are all distinct forms of Bachelardian obstacles. The theoretical framework of the paper is based on the Mathematical Knowledge Architecture (MKA), which introduces five mechanisms, translation, compression, reconfiguration, coordination, and epistemic shift, as the core processes underpinning the construction and evolution of knowledge. Using this framework, an analysis of three instructional vignettes on infinite cardinality, the harmonic series, and the quotient group reveals how a single epistemological obstacle can systematically disrupt multiple MKA mechanisms. 

Keywords

Epistemological Obstacle

Mathematical knowledge Architecture

Failures of Control

Conceptual Development in Mathematics

Mathematics Education

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