Analysis of Item Characteristics in Elementary School Mathematics Reasoning Assessment Using Item Response Theory with the Generalized Partial Credit Model

Abstract

This survey-based research focuses on the analysis of item characteristics in the assessment of mathematical reasoning among elementary school students, employing the Item Response Theory (IRT) and the Generalized Partial Credit Model (GPCM). The findings are as follows: 1) Overall, the knowledge assessment items are categorized as satisfactory, with discrimination indices ranging from 0.422 to 2.401 and difficulty indices from -1.31 to 0.924 on the logit scale. A single item requires revision due to acceptable difficulty levels paired with poor discrimination. The knowledge assessment instrument provides precise information across a skill range of -2.5 to 1.7, peaking at approximately -0.8; 2) Generally, the skill assessment items are also rated as satisfactory, with discrimination indices from 0.561 to 1.554 and difficulty indices from -2.335 to 1.808. Three items necessitate corrections due to unfavorable difficulty levels despite adequate discrimination. The skill assessment instrument accurately measures abilities within a range of -3.2 to 2.6, with the most significant information at approximately 1.3; 3) Lastly, the attitude assessment items are generally good, with discrimination indices from -0.071 to 1.635 and difficulty indices from -0.588 to 1.273. Three items require adjustments due to poor difficulty levels, despite satisfactory discrimination. The attitude assessment instrument effectively gauges the range of -1.75 to 2.5 in skills, with the highest information value around 0.5. This study underscores the effectiveness of the GPCM in discerning item characteristics that are crucial for enhancing the assessment of mathematical reasoning in elementary education.