Teaching and learning of function optimization : the transition from one to two real variables ; L’enseignement et l’apprentissage de l’optimisation des fonctions : la transition d’une à deux variables réelles

The main objective of this research is to study the teaching and learning optimization of functions R2 in R for engineering students. To develop this, we have adopted The Mathematical Work Space model, we asked ourselves what mathematical work is done in teaching and learning about it. To address this, we started by doing an status of the situation of teaching and learning about optimization with functions of R2 in R, considering an analysis of two textbooks, interviews with professors, and analysis of tests. This analysis showed that teaching optimization with functions of two real variables is based on the use of the criterion of partial second derivatives, which is used mechanically, since it involves implementing technical knowledge without the need to explain the criterion or justify it mathematically, as a consequence of the above we studied the design implementation of tasks proposed to students on the basis of the MWS. These tasks aim to consider in the mathematical work of teaching optimization, the mathematical aspects using the limited developments of order one and two that allow us to conclude in the local study of the special points of the function, considering at the same time the cognitive aspects to complete the mathematical work with the graphical visualization in 2D for the functions of R in R, and in 3D for the functions of R2 in R. We have highlighted the advantages and difficulties in the mathematical work of the transition of functions from one variable to two real variables in the study of function optimization. ; El objetivo principal de esta investigación es estudiar la enseñanza y el aprendizaje de la optimización de las funciones de R2 en R para los estudiantes de ingeniería. Para desarrollar esto, hemos adoptado el modelo de Espacios de Trabajo Matemático, nos preguntamos qué trabajo matemático se hace en la enseñanza yel aprendizaje de este tema. Para abordar esto, comenzamos haciendo un estado de la situación actual de la enseñanza y el aprendizaje sobre la optimización de las ...