Análisis de errores aritméticos procedimentales y conceptuales que limitan el pensamiento algebraico temprano en estudiantes de octavo grado de educación media en Nicaragua

The transition from arithmetic to algebra represents a critical stage in secondary education, often hindered by cognitive and instructional barriers. This study analyzed the difficulties associated with early algebraic thinking among eighth-grade Nicaraguan students by identifying their problem-solving strategies and the underlying causes of their learning challenges. A mixed-methods approach with an explanatory sequential design was employed. In the quantitative phase, a diagnostic test was administered to 108 students. In the qualitative phase, mathematics teachers were interviewed, and a documentary analysis of the national curriculum was conducted. The findings revealed a statistically significant correlation between conceptual and procedural errors, indicating that computational mistakes stem from gaps in conceptual understanding. The study also identified the complete absence of variable use for generalization among the participants and a strong association between an arithmetic interpretation of the equal sign and failure to formulate algebraic rules. Triangulated analysis further revealed a curricular discontinuity in the transition from primary to secondary education, as well as instructional practices largely driven by the need to cover procedural content.It is concluded that the identified difficulties cannot be attributed solely to incidental mistakes but rather reflect broader challenges associated with the teaching and learning of algebra. These findings suggest a predominance of instructional approaches focused on the mechanical application of procedures at the expense of a conceptual understanding of mathematical structures. Therefore, it is necessary to strengthen teaching strategies that promote reasoning, conceptual understanding, and abstract thinking in order to foster more meaningful learning and facilitate students' engagement with increasingly complex algebraic concepts.