Conceptual and Transformational Errors in Solving Non-Routine Algebra Problems: A Newman’s Error Analysis of Junior High School Students

Abstract

This study investigates the types and underlying causes of students’ errors when evaluating non-routine algebraic problems that present procedurally plausible but logically invalid solution steps. The participants were 37 ninth-grade junior high school students from East Java, Indonesia, who had previously studied basic algebraic operations. Data were collected through a diagnostic task involving an algebraic fallacy that leads to a contradictory conclusion (e.g., 2 = 3), followed by semi-structured interviews with selected students. The analysis was guided by Newman’s Error Analysis (NEA), focusing on reading, comprehension, transformation, process skills, and encoding errors. Students’ written responses were independently coded by the researchers using predefined NEA indicators, and discrepancies were resolved through discussion. Descriptive statistics were used to summarize error frequencies, while interview data were analyzed qualitatively to explore students’ reasoning. The results indicate that transformation errors were the most dominant, occurring in 48.64% of students’ responses, particularly due to inappropriate cancellation of algebraic factors without considering domain restrictions. Many students accepted contradictory conclusions such as 2 = 3 or 3 = 2 as valid, as long as the solution steps appeared procedurally correct. These findings suggest that students tend to rely on mechanical algebraic procedures rather than validating the conceptual legitimacy of each transformation. The study highlights the importance of emphasizing equivalence-preserving transformations and domain conditions in algebra instruction, especially through non-routine tasks that require justification and critical validation of solution steps.