Instruction process of the derivative applied in Commercial Engineering students in Chile

Abstract

[Objective] The objective of this article is to present the results of the implementation of an instructional design for the teaching of the derivative for undergraduate students of Business Engineering in Chile. [Methodology] The participants of the study are ninety students of Applied Business Calculus at a Chilean university. The methodological design, based on the tools of the Ontosemiotic Approach to Mathematical Cognition and Instruction, consider diverse ontosemiotic configurations in the situations-problems on tangents, the calculation of derivatives from rules and theorems of derivation, applications of the derivative for the calculation of maxima and minima and analysis of function graphs. In addition, it integrates ICT into various activities. [Results] The results indicate that the instructional proposal for teaching the derivative overcomes some of the student's learning difficulties, as evidenced in various research studies. In particular, the difficulties of Business Engineering students regarding the Euclidean conception of the tangent line; the interpretation of the derivative function and its geometric representation, the optimization of economic functions and the application of the derivative to marginal functions. [Conclusions] It is considered that for the effectiveness of a teaching and learning process of the derivative to occur in a specific career, it is essential that the subject programs and the trainers of future professionals incorporate the ontosemiotic configurations of the derivative, its different problem fields and contextual applications together with ICT resources in the instruction.