Evaluation of test item quality using discrete mathematics and measurement theory in education

Abstract

The purpose of the article is to analyze approaches to assessing the quality of test items using methods of discrete mathematics and measurement theory, as well as to substantiate the expediency of applying modern psychometric models in the education system amid the digitalization of the educational process and the growing role of adaptive learning technologies. The methodological framework of the study comprises a theoretical analysis of scientific literature, methods of discrete mathematics, probabilistic modeling, and psychometric approaches. Item Response Theory (IRT) models, including unidemensional (one-parameter, multi-parameter) and multidimensional models, as well as cognitive diagnostic models, were applied. Special attention is paid to contemporary approaches that integrate machine learning methods to enhance assessment accuracy and handle large datasets. As a result of the study, it has been established that the use of mathematical models improves the accuracy of test item quality assessment, ensures the objectivity of results, and accounts for the individual characteristics of learners. It is proven that the application of multidimensional models and advanced algorithms contributes to a more precise determination of item difficulty parameters, discrimination power, and guessing probability. It is determined that the integration of digital technologies enables adaptive testing, automated analysis of results, and increases the efficiency of educational assessment. The conclusions substantiate the expediency of using discrete mathematics and measurement theory methods to analyze test item quality. Future research prospects are identified, focusing on improving assessment models, expanding adaptive testing capabilities, enhancing the interpretability of results, and integrating intelligent systems into the educational outcome assessment process. The proposed approaches can be utilized to improve the quality of educational measurements and enhance learning outcome evaluation procedures.