(untitled) (Innovaciones Educativas, 2026)
There is a disconnect between the uses of mathematical knowledge in engineering and the content covered in university mathematics courses. Therefore, this study examines how the development of a school design in which the derivative—traditionally conceived as the slope of the tangent line at a point—is confronted with an environment of uses from chemical engineering: prediction, analyticity, and trend behavior. The research is based on socio-epistemological theory and is developed using a qualitative methodology, based on an instrumental case study, which analyzes whether this design favors the emergence and assessment of uses of the derivative. The implementation was carried out with five chemical engineering students from a Costa Rican university. For data collection and analysis, unstructured interviews and the exclusion-inclusion dialectic were used. The results show that the design, under the consideration of a socio-epistemological category of mathematical modeling, allows students to move autonomously from the interpretation of the derivative as the slope of a tangent line to its reinterpretation in other engineering applications. It is concluded that the development of reference frameworks for teaching mathematics at a higher level, with the category of modeling as the central axis, makes it possible to establish a horizontal and reciprocal relationship between mathematics and reality.