Bridging the Gap: Methodological Validation of a Rasch-Based Diagnostic Tool for Math Knowledge

Many students transitioning from secondary school to higher education face significant challenges with foundational mathematics, impacting academic success. This study investigates the one-parameter Rasch model within Item Response Theory (IRT) as a diagnostic tool to assess mathematical skills and identify weaknesses in this population. The aim of this paper is twofold: first, to conduct a literature review on standardized assessment instruments; second, to exemplify how a Rasch-based diagnostic instrument can assess mathematical proficiency. The literature review examined psychometrics and IRT, highlighting the Rasch model’s potential for analysing student responses. Microdata from the 2023 Brazilian National High School Exam (ENEM) for 160 students were used. Student responses to 45 mathematics items were analysed using the Rasch model implemented in R. The analysis included estimating item difficulty, visualising the distribution of student abilities, and comparing Rasch-generated scores with official ENEM scores derived from a three-parameter IRT model. The results suggest that the Rasch model provides valuable insights into mathematical proficiency, even with smaller sample sizes. These findings have implications for developing targeted interventions and support programmes, as identifying weaknesses allows institutions to improve support programme effectiveness and enhance student success and retention.