Item Analysis of Mathematical Critical Thinking Skills Using the Rasch Model in Elementary School Students
Abstract
The validity and reliability of educational assessment instruments are fundamental prerequisites for accurate measurement of student competencies. This study evaluates the psychometric quality of a 12-item mathematical critical thinking test grounded in the Facione framework, encompassing Interpretation, Analysis, Inference, and Evaluation, administered to 49 Grade V elementary school students (n = 49) using the Rasch measurement model via Winsteps software. Four psychometric dimensions were assessed simultaneously: (1) construct validity through item fit statistics (Outfit MNSQ, Outfit ZSTD, Pt Measure Corr); (2) internal consistency and reliability (KR-20, Person and Item Reliability, Separation Indices); (3) item discrimination (Pt Measure Corr classification); and (4) item difficulty hierarchy (logit scale measures and Wright Person–Item Map). Results show that 10 of 12 items (83.3%) met Rasch fit criteria, yielding construct-valid measures for all four critical thinking indicators. KR-20 = 0.79 (Good), Person Reliability = 0.79–0.82 (Adequate–Good), and Item Reliability = 0.95 (Excellent). Person Separation (1.96–2.12) confirmed differentiation of ≥2 ability strata; Item Separation (4.37–4.61) confirmed a well-differentiated difficulty hierarchy. All retained items exhibited Moderate difficulty (logit range: −0.66 to +0.23), confirming optimal targeting of the respondent population. Two items failed due to low Point Measure Correlation (0.21–0.22) and were excluded. The final 10-item instrument meets international psychometric standards and is recommended for use in authentic mathematical critical thinking assessment.