Abstract:

The persistent learning gap in primary level mathematics constitutes a structural challenge across many Latin American countries. Limited access to qualified teachers, coupled with connectivity barriers, restricts opportunities for systematic, personalized support as an essential factor in helping students consolidate fundamental mathematical competencies. Artificial Intelligence (AI) and, in particular, large and small language models (LLMs/SLMs) have recently shown significant potential to support individualized learning experiences through conversational tutoring. However, most existing AI-based educational tools rely on cloud services, are trained in English, and are inaccessible in contexts with low connectivity or limited computational resources.

This study presents the design and development of an open-source AI-powered educational tutor for mathematics, based on Spanish Small Language Models (SLMs) and fully deployable locally, without requiring an Internet connection. The proposed system aligns with the Colombian national curriculum for grades 3 and 5 with Spanish-language contents, focusing on fundamental arithmetic operations, problem-solving, and conceptual understanding. Its pedagogical model emphasizes guided dialogue, immediate feedback, and adaptive scaffolding to strengthen self-regulated learning in students.

This work followed a four-stage process. First, a pedagogical and functional specification was defined, aligned with national curriculum standards and the competences assessed in national standardized tests, ensuring the tutor’s curricular relevance. Second, a Spanish instructional dataset was generated and curated from public mathematical resources, systematically organized by topic and difficulty level to support both model training and evaluation. Third, selected small language models were adapted to the educational domain through supervised fine-tuning and direct preference optimization, aiming to enhance the clarity of explanations, logical sequencing of solutions, and compliance with pedagogical style. Finally, a prototype user interface was implemented following a Model-View-Controller (MVC) architecture, comprising three main modules: lessons organized by learning stages, a conversational problem-solving space with mathematical expression rendering, and a profile section for local storage of student progress.

The results show that it is technically feasible to deploy a mathematics tutor based on Small Language Models (SLM) on local devices. The adapted models can generate explanations in Spanish that are pedagogically consistent with the targeted grade levels, while the proposed architecture proved suitable for operation in low-resource environments. The evaluation also revealed areas for improvement, particularly in step-by-step verification, in the level of granularity in feedback provided to learners, and the mechanisms for logging interactions to enable subsequent learning analytics. Despite these limitations, the prototype constitutes a replicable framework for schools and research groups seeking inclusive, low-cost AI solutions to support subject-specific education.

Keywords:

Small Language Models (SLM), AI Tutoring Systems, Low-Resource Settings, Offline Learning Technologies, Curriculum Alignment, Educational Technology, Open-Source Frameworks, Conversational Tutors, Spanish Language Models, Primary Education.