The Physical-Mathematical Working Space as a theoretical proposal to analyze the semiotic processes that are carried out during the modeling of a dampened harmonic motion

Abstract

The modeling process is very important for teaching and learning both physics and mathematics and establishes their interaction. Here we propose a Physical-Mathematical Working Space (PMWS) as an extension to the theory of Mathematical Working Spaces (MWS) because its structure allows to explain the processes that arise when such tasks are carried out. We consider that modeling the movement of a damped harmonic oscillator allows students to reflect on their own representations. We present the results of a didactic implementation based on the construction of representation, a pedagogical approach to targeted research that requires students to interpret and build representations of scientific concepts, affirmations, and processes. Since these are students in work teams to motivate scientific debate and self-reflection, the ACODESA methodology was used. On the other hand, we show elements that allow us to account for how they are activated in semiotic, experimental, and discursive genesis within the PMWS. This is the relationship between PMWS and MWS. The analysis of the data in this qualitative study on how a student transitions from understanding a physical phenomenon to its mathematical description through modelling has made it possible to propose a contribution to the theoretical framework of the MWS. He worked with a group of 14 second semester engineering students on a comprehensive calculus course at a University of Mexico City.