# Readability Formulas for Elementary School Texts in Mexican Spanish
## 4 Experimental Study
### Discussion  
The experimental results underscore the limitations of traditional readability formulas when applied to Mexican Spanish educational texts. Formulas originally developed for Spanish, such as Fernandez-Huerta, Szigriszt-Pazos, and Gutierrez-Polini, as well as those adapted from other languages, generally fail to capture the incremental complexity of texts across elementary grade levels. This is reflected in their low separability scores, limited \(R^{2}\) values, and overlapping score distributions. These findings suggest that such models lack the sensitivity needed to align with contemporary curricular progression in the Mexican context. In contrast, the proposed formulas--Linear-MX and GP-MX--demonstrate clear advantages in both predictive accuracy and grade-level differentiation. The Linear-MX model achieved the highest \(\Delta_{p}\) score, indicating a superior ability to distinguish between texts from different educational stages. Although the GP-MX model slightly outperformed in terms of RMSE and \(R^{2}\), its lower separability score suggests a reduced capacity to distinguish adjacent grade levels. Therefore, while GP-MX offers marginally better regression performance, Linear-MX appears more effective for grade classification tasks. These results have both theoretical and practical implications. Theoretically, they confirm the importance of context-specific modeling in readability assessment, particularly the use of statistical and symbolic regression approaches guided by empirical data. Practically, they point to the value of tailored formulas for educational content evaluation, curriculum design, and adaptive content generation. The methodology used to construct the proposed formulas can be transferable to other languages or educational systems. While the formulas themselves are language-dependent and cannot be directly applied to other linguistic contexts due to reliance on features sensitive to language structure (e.g., syllables, sentence length), the modeling strategy remains valid. With retraining on language-specific corpora and proper adaptation to linguistic and curricular features, this approach offers a robust framework for developing localized readability tools across diverse educational and linguistic settings. Although recent large language models (LLMs) have demonstrated strong performance in a variety of NLP tasks, their applicability to readability assessment poses important challenges. LLMs typically require substantial computational resources and extensive training data, which may limit their feasibility in real-world classroom or curriculum design settings. Moreover, they operate as black-box systems, reducing interpretability and  
Figure 5: Values of the metric \(\Delta_{p}\), which quantifies the separability of elementary grade levels based on the statistical significance of post hoc comparisons using [PERSON]’s HSD test across educational grades. making it difficult to align their outputs with pedagogical goals. In contrast, the proposed models are lightweight and interpretable: the Linear-MX model is based on standard multiple linear regression, while the GP-MX model, though more computationally intensive during training, generates compact symbolic expressions with low inference cost. Regarding the relatively low \(R^{2}\) values observed, this can be attributed to the inherent complexity and variability of early-grade Spanish texts, which do not always follow a strictly incremental progression in linguistic difficulty. For example, some fourth-grade texts featured more complex syntactic structures or vocabulary than sixth-grade texts, often due to thematic content or pedagogical intent. These inconsistencies reflect curricular objectives rather than purely linguistic complexity. Furthermore, real-world educational materials frequently include non-textual elements--such as illustrations, formatting, or contextual cues--that support comprehension but are not captured by textual features alone.