In this paper, we report the analysis of thought processes used by Pre-Service Teachers' (PSTs') through clinical interviews as they solved an algebra task involving a linear pattern. The PST's were asked about a mathematical model they had constructed to describe a pattern problem. Our analysis suggests that conflict factors arise due to incompatibility in participants' personal concept definition and the formal concept definition of continuity. We identified how personal concept definitions of the participants differed and how this difference affected their decision on whether a graph was continuous or not.