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Artículos

Vol. 28 (2025): Publicación continua

Epistemology of graph use in parametric contexts through trajectory modeling

DOI:
https://doi.org/10.12802/relime.2025.28.e683
Submitted
June 30, 2025
Published
2025-12-19

Abstract

This study examines how university students use graphs to model trajectories when working with parametric functions without analytic expressions. Drawing on Socioepistemology, and particularly on the Functionings–Forms (Fu–Fo) model, the analysis focuses on students’ progression through the three moments of graph use. The study adopts a qualitative approach and is based on the analysis of graphical productions and discourse generated by eight students in two parallel modelling activities. Results show that students: (1) construct initial representations through spatial segmentations and numerizations; (2) justify transformations of the graph, horizontal stretches due to changes in speed and constant segments due to stops, by articulating graphical features with the phenomenon; and (3) generalize criteria constructed for one component function to adjust the other without rebuilding the reasoning from scratch. Based on this evidence, an extension of the Fu–Fo model is proposed for parametric contexts.

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