What is the maximum area of a house? A problem from the perspective of technology-oriented problem solving

This paper presents the partial results of a Master's-degree-level research project on the contribution of employing the teaching-learning-assessment methodology through problem solving using GeoGebra, in connection with the different registers of representations, in teaching and learning the maxima and minima of functions. The educational product derived from this research was a didactic booklet, developed using the online GeoGebraBook tool, composed of several applications that seek to assist in the resolution of function optimization problems. Adopting a qualitative and interpretative approach, data were collected on the solutions of an activity tested in two pilot classes, one in high school and another in an undergraduate program. In the results, we will point out the potential regarding the use of technology that favored the resolution of the problem due to the interactive approach and the possibility of transition between different representations, as well as some challenges in certain stages of the adopted methodology.