From a Neglected Concept to the Construction of Dynamic Connections Between Precise Definitions of the Limit Concept Using GeoGebra

This study explores university students' understanding of the relationships between formal definitions of the limit of a function and the limit of a sequence in terms of the accumulation point in a technology-enhanced collaborative learning environment. The participants of this study are 17 prospective mathematics teachers. The data are collected with scripting tasks, researcher notes related to questions and comments during the teaching experiment, and GeoGebra files. The teaching experiment — integration GeoGebra into the collaborative learning, scientific debate, and selfreflection stages which help the participants acquire a cultural semiotic system — is here used also to analyse how this integration method can support the dynamic connections between the limit of a sequence and the limit of a function at a point. The data show that most participants cannot understand the role of accumulation point in the construction of the connection between formal definitions of the limit of a function and the limit of a sequence. Their mathematical organization is based on the algebra of limits; however, in this teaching experiment, the use of GeoGebra's tool (such as slider tool and dragging tool) as semiotic mediators and argumentation process in teamwork and debate stages as semiotic mediation can encourage participants to make dynamic connections among the accumulation point, the limit of a sequence, and the limit of a function at a point.