Onto-semiotic analysis of Colombian engineering students’ mathematical connections to problems-solving on vectors: A contribution to the natural and exact sciences
Camilo Andrés Rodríguez-Nieto 1 * , Hernán Alonso Cabrales González 1 , Jhonatan Arenas-Peñaloza 1 , Carlos Eduardo Schnorr 2 , Vicenç Font Moll 3
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1 Universidad de la Costa (CUC), Barranquilla, COLOMBIA2 Universidad de La Salle, Bogotá, COLOMBIA3 University of Barcelona, Barcelona, SPAIN* Corresponding Author


The mathematical connections Colombian engineering students activated when they solved vector problems were explored. The study was based on the extended theory of connections and the onto-semiotic approach. We followed a qualitative methodology that consisted of three stages: (1) selection of engineering students as participants; (2) application of a questionnaire with 15 tasks on vectors to the participating students; and (3) analysis of these data based on the theoretical articulation. The results show that students perform arithmetic operations with vectors, find the scalar and vector product, the norm of a vector, the angle between vectors, and unit vector based on mathematical connections (procedural, meaning, different representations, and implication), detail from an onto-semiotic point of view. However, some students have difficulty finding the angle between vectors because they misuse the norm. Furthermore, the new metaphorical connection based on mnemonics activated by the “law of the ear” is reported. The connections activated by engineering students to solve problems about vectors may have been influenced by the explanations provided by their calculus teacher, who promotes connections for the teaching and learning mathematical concepts.


This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2024, Volume 20, Issue 5, Article No: em2438


Publication date: 01 May 2024

Online publication date: 08 Apr 2024

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