A Diagnostic Analysis of Fourth-Grade Elementary Students' Numeracy Difficulties in Solving Contextual Problems: A Rasch Model Approach and Implications for Differentiated Instruction

Abstract

Contextual numeracy is a key competency in Indonesia's Merdeka Curriculum, yet many elementary students continue to demonstrate low achievement. This study aimed to identify fourth-grade students' contextual numeracy difficulties using the Rasch Model and formulate implications for differentiated instruction. A quantitative descriptive design with a diagnostic assessment approach was employed involving 156 fourth-grade students from three public elementary schools in Bogor Regency selected through cluster random sampling. Data were collected using a 30-item contextual numeracy diagnostic test with satisfactory psychometric properties (Cronbach's α = 0.86, Person Reliability = 0.79, Item Reliability = 0.94). Rasch analysis generated Wright Maps, item difficulty estimates, and profiles of students' cognitive errors. The results showed that only 31.4% of students achieved the expected numeracy proficiency. The greatest difficulties occurred in mathematical modeling of real-world situations (logit = 1.87) and multimodal data interpretation (logit = 1.52). Think-aloud protocols identified three major cognitive barriers: misconceptions in contextual numerical operations, difficulties translating verbal information into mathematical representations, and excessive cognitive load. These findings informed the development of differentiated instructional strategies based on content, process, and product differentiation. The study demonstrates that integrating Rasch-based diagnostic assessment with differentiated instruction provides a practical, data-driven framework for improving contextual numeracy learning in elementary schools