Patterns of Students' Errors in Solving Algebraic Equations: A Newman Error Analysis of Senior Secondary School Students in Northwestern Nigeria

Abstract

Algebraic equation solving remains challenging for many secondary school students, with errors often reflecting underlying conceptual, comprehension, and procedural difficulties. This study investigated the patterns of errors committed by Senior Secondary School II (SS II) students when solving algebraic equations in Kankia Education Zone, Katsina State, Nigeria, using Newman's Error Analysis (NEA) as the diagnostic framework. A cross-sectional descriptive research design with a diagnostic assessment approach was adopted. The population comprised 4,683 SS II students, from which 130 students were selected through multistage sampling involving simple random selection of two co-educational public secondary schools and intact class sampling. Data were collected using the Algebraic Equation Diagnostic Test (AEDT), comprising six structured essay questions. The instrument was validated by two experts in Mathematics Education and yielded a test–retest reliability coefficient of .82. Data were analysed using frequencies, percentages, and a chi-square goodness-of-fit test. Sixteen specific error types were identified, with errors in tabulating values and selecting appropriate graph scales being most frequent (8.4% each). Comprehension errors were the most prevalent Newman category (27.0%), followed by transformation (26.1%) and process skills (22.8%). The distribution differed significantly across categories, χ²(4) = 37.83, p < .001. The findings highlight the need for diagnostic and formative assessment that prioritises students' comprehension and transformation of algebraic tasks to inform targeted instruction and remediation