Epistemic actions during the learning of continuous magnitudes

Abstract

This research involves a qualitative case study involving task-based interviews and model elicitation  activities carried out with fifth-grade students. The results show that epistemic actions constitute  central processes in the construction of mathematical meanings about continuous magnitudes. These actions function as dynamic mechanisms that mediate students’ understanding between perception and explanation. Comparison was identified as the most recurrent epistemic action, acting as a  resource for articulating magnitude and the unit, whether standard or nonstandard, in the process of estimation and measurement. It was also evident that epistemic actions do not operate in a linear way but instead in a nested manner, integrating the processes of comparing, estimating, calculating, and iterating. These actions are culturally mediated, demonstrating that learning about continuous magnitudes combines cognitive resources with cultural repertoires. The results of the study provides an integrative framework for the design of culturally relevant tasks with didactic implications.