Towards onto-semiotic analysis of the university students of business sciences’ mathematical activity when solving mathematics problems of a diagnostic

This article analyzes the mathematical activity of students entering a university mathematics course for the first time, based on their completion of a diagnostic questionnaire consisting of five problems in elementary arithmetic and algebra. The study is developed from an onto-semiotic approach, integrating the analysis of mathematical practices, cognitive configurations of primary objects, and the types of mathematical connections established by the students while solving the tasks. The methodology was qualitative, based on a content analysis of the mathematical activity of students in logical-mathematical reasoning. The results show that the first problems primarily activate procedural and instructional connections, associated with prior school knowledge, which is reflected in high success rates. However, as the onto-semiotic complexity of the tasks increases, especially in the linear function modeling problem, a significant decrease in performance is observed. This decrease is explained by the need to simultaneously coordinate multiple mathematical connections, particularly those related to the articulation of representations, the construction of meaning, and the activation of procedures. It is concluded that the difficulties identified do not stem from a lack of mathematical knowledge, but rather from a breakdown in the connections necessary to reinterpret school content within university contexts. These findings provide relevant elements for the design of teaching strategies aimed at facilitating the transition from school to university level.