# Readability Formulas for Elementary School Texts in Mexican Spanish
###### Abstract  
Readability formulas are mathematical functions that assess the 'difficulty' level of a given text. They play a crucial role in aligning educational texts with student reading abilities; however, existing models are often not tailored to specific linguistic or regional contexts. This study aims to develop and evaluate two novel readability formulas specifically designed for the Mexican Spanish language, targeting elementary education levels. The formulas were trained on a corpus of 540 texts drawn from official elementary-level textbooks issued by the Mexican public education system. The first formula was constructed using multiple linear regression, emulating the structure of traditional readability models. The second was derived through genetic programming (GP), a machine learning technique that evolves symbolic expressions based on training data. Both approaches prioritize interpretability and use standard textual features, such as sentence length, word length, and lexical and syntactic complexity. Experimental results show that the proposed formulas outperform several well-established Spanish and non-Spanish readability formulas in distinguishing between grade levels, particularly for early and intermediate stages of elementary education. The GP-based formula achieved the highest alignment with target grade levels while maintaining a clear analytical form. These findings underscore the potential of combining machine learning with interpretable modeling techniques and highlight the importance of linguistic and curricular adaptation in readability assessment tools. readability assessment; readability formulas; linguistic features; genetic programming; interpretable machine learning 2020  
formulas exist in the scientific literature [2; 3], most of them are suitable only for the English language. Limited efforts have been made to extend current English readability formulas to other languages. In particular, only a few approaches exist for the Spanish language in spite of the vast cultural and linguistic differences in Spanish-speaking countries. Furthermore, variations in dialects (regional speech patterns) and socioletal--differences in the way language is used by particular social groups, classes, or subcultures--occur across different countries. For instance, the use of \"vos\" as a second-person singular pronoun is common but not universally employed. It is worth noting that there is currently no readability formula tailored specifically to Mexican Spanish texts, despite Mexico having one of the largest populations of Spanish speakers globally, with more than twice as many speakers as any other country in the world. Readability formulas have traditionally been associated with adapting written material--primarily textbooks--to achieve more effective didactic communication (e.g., [4]). They have also been used to measure the readability of online patient education materials (e.g., [5]). While psycholinguistic research continues to advance readability assessment, recent studies have begun exploring computational approaches to this task. In recent years, techniques based on standard machine learning and deep learning approaches have been used to develop models for automatically assessing the readability level of texts [6]. Some of these works have been modeled using feature engineering [7], but currently, most of them rely on word embedding representations [8; 9] and deep learning [10; 11; 12] approaches, which have demonstrated improved performance over linguistic feature-based systems. In particular, transformer-based language models such as BERT and RoBERTa have shown strong predictive capabilities in readability assessment tasks across various languages [13; 14]. From a machine learning perspective, the readability assessment is often viewed as a classification task, where an annotated set of corpora is trained with its corresponding labels. However, these models are often considered \"black boxes\" due to their lack of interpretability.