In this paper we analyse the representations and the reasoning processes used by university students when exploring investigation activities during a teaching experiment in a numerical analysis course. The study aims to understand how the students' representations support their reasoning. The study follows a qualitative and interpretative methodology, based on three case studies, and uses a variety of data sources. The results show that students used both inductive and deductive reasoning but suggest the need for increased attention to two reasoning processes where students displayed noticeable difficulties - generalization and justification. Students use a variety of representations for understanding, exploring, recording and evaluating but do not use them in a flexible way in their explorations, which constrains their reasoning.
Representations; Mathematical Reasoning; Investigation Activities; University Mathematics; Numerical Analysis
