This paper presents the results of the implementation of a design focused on the resignification of the parameters of the quadratic equation (parabolas) through the context of a physical phenomenon. This design was based on an epistemology of practices framed in principles of cognitive and social constructivism, particularly the socioepistemological theory of mathematics education, based also on the model of guided discovery. Based on the students’ arguments, evidence of resignification is shown in the parameters of the quadratic equation in such a way that relationships between algebraic and graphical expressions were established. It was identified that the students’ experiences, as well as the context, were determining elements for success in the resolution of the design.

The objective of this research is to get students to mean the mathematical objects related to the second order differential equation through the context of a physical phenomenon. With the support of the physical system of the simple pendulum, the behavior of the angular position is studied in a modelling process with the help of simulators. From variational thought and language as a line of research of socio-epistemology in mathematics education, activities that promote a modelling process in a differential equations course for students in initial training for teaching mathematics are designed, implemented, and analyzed. The results of the process experienced by the students are presented, such as: familiarization of the phenomenon, use and interpretation of the simulations, construction of the mathematical model and its predictive role for decision making. It was identified that the students’ experiences, as well as the physical context, were determining elements for success in the resolution of the design.

The objective of this research was to describe the mathematical contents that are part of the mathematics programs of a Physics course at a certain Costa Rican university. In order to respond to the proposed research objective, data were collected from the mathematics study programs of the bachelor’s degree in Physics at Universidad de Costa Rica, which were analyzed through a thematic analysis, braided with documentary analysis techniques, where the ATLAS.ti computational tool served as support to carry out such analysis. The results of this research allowed describing the mathematical contents studied in this career through ten topics. Based on these results, a discussion was held about modeling situations that can be implemented in mathematics courses of this major with the purpose of strengthening the link between mathematics and physics. Among the conclusions, the educational community is left with the task of incorporating different theoretical modeling perspectives into the mathematics programs of this career that will strengthen its link with physics.