Onto-semiotic analysis of Colombian engineering students’ mathematical connections to problems-solving on vectors: A contribution to the natural and exact sciences

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.