Mapping Cognitive Breakdown in Mixed Integer Operations: A Newman Error Analysis of Secondary Students’ Problem-Solving

Resa Septiani; Dani Firmansyah

doi:10.31949/dm.v8i1.16978

Authors

Resa Septiani Universitas Singaperbangsa Karawang, Indonesia
Dani Firmansyah Universitas Singaperbangsa Karawang, Indonesia

DOI:

https://doi.org/10.31949/dm.v8i1.16978

Abstract

This study aims to analyze Grade VII students’ errors when solving mixed-integer operation problems using the Newman Error Analysis (NEA) framework. A qualitative case study design was employed to obtain an in-depth understanding of students’ cognitive processes underlying their errors. The participants were 23 students from a junior secondary school in West Java, Indonesia, selected through purposive sampling. Data were collected through a diagnostic test, semi-structured interviews, classroom observations, and document analysis. Student responses were classified into five stages of NEA: reading error, comprehension error, transformation error, process skills error, and encoding error. Data were analyzed using an interactive qualitative model involving data reduction, data display, and conclusion drawing. The findings reveal that students’ correct response rates remained below 15% across all items, indicating substantial conceptual and procedural weaknesses. Reading errors were minimal; however, comprehension, transformation, process skills, and encoding errors occurred at consistently high frequencies. The dominant difficulties were related to misunderstandings of the operational hierarchy, particularly the equal precedence of multiplication and division and the left-to-right processing rules. Cross-case analysis showed that similar incorrect answers originated from different cognitive sources, including conceptual rigidity, weak procedural fluency, limited metacognitive monitoring, and affective factors such as confusion and anxiety. This study shows that students’ errors in mixed-integer operations follow identifiable cognitive patterns rather than occur randomly. The findings underscore the importance of strengthening conceptual understanding and integrating metacognitive strategies into mathematics instruction to prevent cascading errors in problem-solving.

Keywords:

Newman Error Analysis, Integer operations, Conceptual misunderstanding, Procedural fluency, Metacognition

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