An Early Numeracy Digital Brief Assessment: Parametric and Non-parametric Item Response Theory Models

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 original test included 144 items covering both symbolic (66%) and non-symbolic (34%) tasks, such 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. Unlike most existing tools that require individual administration by trained professionals and lack cultural adaptation for Latin American contexts, PUMa is self-administered, culturally grounded, and suitable for large-scale assessments using tablets. 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, preliminary evidence was generated showing that the brief version retained precision and validity. The resulting shortened tests included 69 and 73 items for the parametric and non-parametric versions, yielding a balanced representation of symbolic (56%) and non-symbolic (44%) tasks. Despite item reduction, ability scores remained highly correlated between original and brief versions (r > .90), and both brief versions demonstrated strong internal consistency (α = .94). PUMa improves upon existing assessments by combining cultural relevance, group-based digital administration, and real-time data collection, offering a scalable solution for early identification and intervention. These features support personalized educational strategies that foster cognitive and academic development from the earliest stages.