Exploring University Mexican Students’ Quality of Intra-Mathematical Connections When Solving Tasks About Derivative Concept

The quality of the intra-mathematical connections made by Mexican university students when solving tasks on the derivative was characterized. The typology of mathematical connections and the quality levels of mathematical connections were used. Interviews were conducted based on eight tasks applied to three case studies. The results showed that the quality of the intra-mathematical connections: different representations, procedural, implication, part-whole and meaning of the students, is found mostly at level 2 (consistent and argued mathematical connections) and only one student presented inconsistencies to find the correctness equation of the tangent line to the curve at a point (quality level 0 connection). Likewise, the metaphorical connection was identified when a student mentioned the metaphorical expression “the graph has no holes”, which suggests the conceptual metaphor “the graph is a path” referring to the continuity of a function. We believe that quality level 2 mathematical connections ensure understanding, and the quality level 0 mathematical connections are the reasons why students have difficulty understanding the derivative.