Comparative analysis of mathematical language proficiency in higher education: a case study among incoming and advanced semester students
DOI:
https://doi.org/10.62305/alcon.v6i4.1236Keywords:
mathematical education; mathematical language; university students; semiotic analysis; theory of reificationAbstract
Proficiency in mathematical language is a cross-cutting factor in university education within the fields of engineering and the exact sciences. This study comparatively evaluates the understanding and manipulation of this formal language between students in the leveling course (entrance) and students in advanced semesters at the Manabí Higher Polytechnic Agricultural School (ESPAM MFL). A quantitative approach with a descriptive-comparative scope and a non-experimental cross-sectional design was adopted. The simple random probability sample consisted of 100 students equally distributed into two independent groups (n = 50 per group). The evaluation was conducted using a structured questionnaire that measures four dimensions of semiotic competence: linguistic translation, algebraic manipulation, geometric comprehension, and data organization. The descriptive results indicate a lag in the leveling group, where 80% are at the lowest performance levels in algebraic manipulation. Inferential analysis using the Student's t-test for independent samples confirmed significant differences favoring the career group in all dimensions, with the widest gap reported in the operational manipulation of algebraic expressions (t(98) = -12.87, p < 0.001). It is concluded that the development of advanced structural thinking requires an explicit transition from purely instrumental didactic approaches to pedagogical scaffolding based on analogical mediation and cognitive semantics.
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