Exploring the convergence of sequences in the embodied world using GeoGebra

Abstract

This study addresses the embodied approach of convergence of numerical sequences using the GeoGebra software. We discuss activities that were applied in regular calculus classes, as a part of a research which used a qualitative methodology and aimed to identify contributions of the development of activities based on the embodiment of concepts, with the use of software, to the understanding of the convergence of numerical sequences and to the transition of mathematical thinking from elementary to advanced. Such activities had an exploratory nature and were constructed based on the theoretical frameworks of Advanced Mathematical Thinking and the Three Worlds of Mathematics. For the data collection were used the recordings of the computer screens, audio recordings of the discussion between students, student records in the responses of the activities and field notes of the researchers. The data were analyzed considering relations between the embodiment of the concept of convergence and proceptualization processes and axiomatization and also considering the transition from elementary mathematical thinking to advanced. The results indicate that the activities enabled the formation of the mental image that the convergence of sequences occurs when the sequence terms are approaching a certain value, and thus propitiated the embodiment of the concept of convergence and established cognitive roots for formal definition of convergence by the limit and further theoretical development. They also indicate that relations between different representations were established, which contributed to abstraction of the concept of convergence of sequences and thus for the transition between elementary and advanced mathematical thinking.