Background:
Pre-service secondary mathematics teachers’ (PSMTs) understanding and ability of constructing a proof is not only important for their own learning process, but also important to help their students to gain the ability to do proof in their future teaching. Therefore, this study is focused on and explained PSMTs’ behaviors that they revealed throughout the proving process of a proposition.

Materials and methods:
In this qualitative case study, the participants were fifteen volunteer PSMTs from a public university in Turkey. The participants were given a proposition which they were asked to think aloud and prove it on the blackboard.

Results:
In detail, PSMTs had difficulties in application of mathematical language and notations, understanding the meaning of the given proposition, knowing where to get started on a proof, using examples efficiently, using appropriate and efficient methods to construct the proof, and defining logical structures of the proposition to construct the proof.

Conclusions:
The findings of this study show that PSMTs’ behaviors and thoughts regarding the given proposition were limited.