Application of item response theory in the quality control of an entrance exam in a mathematics teaching course

Abstract

Learning assessment, particularly in admission processes for undergraduate courses at higher education institutions, is a crucial step and constitutes a constant challenge for these educational institutions. Ensuring quality and equity in these processes is essential to ensure that the selection process is fair and that the candidates admitted have the appropriate profile. At the Instituto Superior de Ciências da Educação de Cabinda (ISCED-Cabinda/Angola), the entrance exam for the Mathematics Teaching course is the main instrument used to select candidates with the necessary profile to face the challenges of this degree. Item Response Theory (IRT) and Multidimensional Item Response Theory (MIRT) were applied to achieve some insights about students’ abilities and quality of the main instrument of selection. The single factor analysis showed that the items were well-designed, but allowed us to identify two problematic items, suggesting improvements for the construction of future exams. The Multidimensional Item Response Analysis revealed the presence of two main latent factors of “Analytical Geometry and Algebra”, and, “Calculus and Trigonometry”, suggesting that the entrance exam is capable of adequately capturing these two core competencies for the course. In general, the results show that the test has good internal consistency and is composed of discriminative and very discriminative items and that there are items of all levels of difficulty. Therefore, there are reasons to agree that the test produces the expected results, that is, it measures the skills of candidates in the ISCED-Cabinda/Angola entrance exam.