A Cognitive Diagnostic Model Approach to Developing and Validating a Mathematics Literacy Instrument on Systems of Linear Equations

Abstract

This study addresses the limited availability of mathematics literacy assessments that provide detailed cognitive diagnostic information at the junior secondary level. While most existing instruments focus on total achievement scores, few are systematically developed to diagnose specific cognitive attributes underlying students’ problem-solving processes. This study aimed to develop and validate a mathematics literacy instrument on Systems of Linear Equations in Two Variables using a Cognitive Diagnostic Model framework. The instrument was constructed in the form of complex multiple-choice items with partial credit scoring and explicitly linked to four cognitive attributes through a Q-matrix specification. The development process included needs analysis, expert validation, pilot testing with 200 students, and large-scale field testing with 960 eighth-grade students. Data were analyzed using the Generalized Deterministic Inputs, Noisy “And” Gate model to estimate students’ cognitive mastery profiles. The findings revealed that 28.54% of students mastered all four attributes, whereas 28.75% did not master any attribute, indicating substantial polarization in conceptual and procedural understanding. The instrument demonstrated satisfactory content validity and classification reliability. This study contributes a systematically developed, curriculum-aligned diagnostic tool that advances mathematics literacy assessment beyond conventional score-based measurement.