Persistent Misconceptions in Algebra: A Critical Analysis of Errors with Implications for Teaching and Further Research

Abstract

This study explores the persistent challenges students face in learning algebra, with a focus on prevalent errors observed in secondary education worldwide. This study highlights the complex interplay between conceptual and procedural knowledge in algebraic reasoning through a comprehensive review of theoretical frameworks and empirical studies by influential scholars such as Kieran, Shard, Booth and Koedinger. As students transition from arithmetic to algebra, they encounter widespread difficulties, including misconceptions about algebraic notation, variable manipulation and the application of algebraic rules in diverse contexts. An analysis of global research reveals that these errors are pervasive across different educational systems, indicating universal obstacles in developing algebraic understanding. The study further identifies gaps in recent research, especially regarding targeted interventions and practical strategies for correcting algebra errors. Despite advances in educational technologies and instructional methods, effective approaches to addressing these challenges in diverse classroom settings remain underdeveloped. This study emphasizes the need for tailored instructional strategies and context-specific interventions that prioritize both conceptual clarity and procedural fluency in algebra. Concluding with key takeaways for educators, the paper outlines avenues for future research focused on innovative teaching practices and the integration of technology and manipulatives to support students' algebraic understanding.