Collective reinterpretation of quadratic functions in the study of inclined planes: an experience with modeling and technologies in initial teacher training

Abstract

This article explores the meanings that emerge about quadratic functions and derivatives in an empirical modeling experience of the inclined plane, developed with future mathematics teachers. From a sociocultural perspective and within the framework of socioepistemological theory, it analyzes how mathematical objects—usually taught procedurally—take on new meaning when used in specific contexts. Through an action research methodology, 20 group reports prepared by the students were collected and analyzed, identifying a diversity of uses and conceptions about the parameters of the quadratic model and the derivative. The results show that, although the trajectories are varied, there is a shared mathematical practice around the quadratic and the act of deriving. This practical convergence, mediated by tools, context, and experience, allows us to understand the phenomenon under study and socially consolidate meaningful mathematical knowledge in schools.