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The diagnostic mathematics test is a critical tool for measuring students' abilities to understand and apply mathematical concepts, with the design of good test items being paramount to ensure validity. This study leverages Item Response Theory (IRT) models and Differential Item Functioning (DIF) methods to refine the construction of test items, specifically focusing on rational numbers. Engaging 929 junior high school students from three public schools in Cirebon, West Java The research utilized R Software to analyze the most suitable IRT models and investigate DIF methods. The findings underscore the efficacy of the Parameter Logistic 3PL model based on Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), -2 loglikelihood, and Standardized Root Mean Square Residual (SRMSR) values, alongside item fit, highlighting that nearly all analyzed items were suitable except one that required replacement. Additionally, the identification of items with significant DIF effects points to potential biases, suggesting avenues for enhancing test fairness and reliability. The study's broader implications extend to improving diagnostic assessment practices, informing item design in educational evaluations, and guiding future research towards creating more equitable and precise measures of mathematical understanding. This contributes to a nuanced comprehension of student abilities, offering valuable insights for educators, assessment designers, and policymakers aimed at fostering improved learning outcomes in mathematics education.
Hartono et al. (Tue,) studied this question.