An early numeracy digital brief assessment: parametric and non-parametric IRT models

Abstract

Developing efficient and reliable tools for assessing early mathematical skills remains a critical priority in educational research. This study aimed to develop and validate a brief version of the Prueba Uruguaya de Matemática (Uruguayan Mathematics Test, PUMa), a digital tool to assess mathematical abilities in children aged 5 to 6. The test comprises both symbolic and non-symbolic dimensions, including tasks as approximate number system, counting, numerical ordering (forward and backward), math fluency, composition and decomposition of numbers, and transcoding auditory-verbal stimuli into Arabic-visual symbols. Using a sample of 443 participants and applying parametric and non-parametric models within the framework of Item Response Theory (IRT), along with correlations with TEMA-3, we generated preliminary evidence that the brief version retained both precision and validity. The resulting brief test, consisting of nearly half the original items, achieved a balanced representation of symbolic and non-symbolic tasks. These findings highlight the efficiency of digital tools for real-time data collection and their potential to enable scalable early interventions. Such advancements support personalized educational strategies, fostering cognitive and academic growth from an early age.