The difficulty parameter's estimation of the achievement test items according to the item response theory and its logical estimation by the subject teachers

The study aims to compare the teacher's estimation of the difficulty of the mathematics achievement test items, based on the item response theory (IRT), and the rational estimation of the items by subject matter experts (SME). The research sample consisted of (500) male and female students from the first intermediate grade, and (25) specialized teachers to estimate the difficulty based on their experience in the subject. A test consisting of (40) multiple-choice items was constructed, and its data were analyzed using the Rasch model using the Construct Map 4.6 program. The study results showed that IRT estimates were more accurate and reliable in determining item difficulty, particularly the more extreme items (very easy, very difficult), compared to teachers' estimates, which tended to overestimate difficulty. There was also a high correlation between the two estimation methods (r = 0.91) and high inter-estimation reliability (ICC = 0.88), with a slight bias in favor of teachers' estimates, with the Bland-Altman agreement rate being (-0.37). This result confirms the integration of quantitative (IRT) and qualitative (SME).