We investigated how two didactical tools assist high school students in constructing knowledge about convergence and limits. The first tool is manual plotting of the terms of selected sequences, and the second, a technological applet. Student pairs worked in an interview setting on an activity designed for the purpose of this research. The interviews were transcribed and analysed using the RBC model of abstraction in context. The analysis of the interviews revealed that manual plotting supported students' development of intuition about convergence and the technological tool supported students in constructing a notion of 'as close as one pleases', thus making a step in the direction of the formal definition of limit. As a result, a structure of the elements of knowledge of the concept of convergence of sequences has been developed, the support of the tools has been evaluated and possible obstacles of the process have been identified.