Application of Item Response Theory to Mathematics High School Exams in Portugal

Abstract

Item Response Theory (IRT) provides statistical models that relate an examinee’s response to a test item to an underlying latent trait that is measured by the items. Unlike classical test theory, IRT models focus on the responses to individual questions instead on the total score obtained in the test. In this paper we apply IRT models to the results of the quiz part of the first and second calls of mathematics exams accomplished by high school graduating students in Portugal, in the years 2008, 2009 and 2010. We concluded that the quiz part of the first call exams had a difficulty level lower than the students median ability, whereas the quiz part of the second call exams had a difficulty level higher than the students median ability.