From Mistakes to Meaning: Analyzing Struggling Students’ Error Patterns in Basic Algebra through Newman Error Analysis (NEA) Model

Abstract

This study examines the error patterns of struggling Grade 9 students when solving quadratic-equation word problems using the Newman Error Analysis (NEA) model. A mixed-methods descriptive study using the NEA model, in which data were collected from 101 learners who completed a four-item diagnostic assessment requiring the use of algebraic methods and showing their full solutions. The triangulation method through a semi-structured interview process was employed to further analyze and extract themes behind algebra difficulties. Student responses were coded across four NEA stages - comprehension, transformation, process skills, and encoding with inter-rater validation by two mathematics teachers. Findings reveal persistently high error rates across all stages, with process skills and encoding errors emerging as the most critical. Substantial proportions of students demonstrated difficulties in interpreting problem statements, constructing appropriate equations, executing algebraic procedures accurately, and expressing final answers. Notably, non-attempt rates increased with task complexity, indicating issues related to cognitive load and learner confidence. The study contributes a detailed diagnostic profile of algebraic errors and highlights the interdependence of conceptual understanding and procedural fluency. It underscores the value of NEA as a classroom-based diagnostic tool and proposes targeted instructional strategies focused on mathematical language, modelling, and solution verification.