As any ordinary person knows, the shortest distance between two points is a straight line. What, then, is the shortest distance between three points? Four points? The study reported in this article deals with the observed actions of Turkish student mathematics teachers as they were working with minimal network problems. Having analysed the mathematization processes of student mathematics teachers in computerized environment, I describe here how new mathematical relationships can be discovered from real-world situations. The results showed that using real world situations in computerized classrooms leaves the doors open for the students for decision making, experimental verification, conjecturing and even for construction of proofs.