The aim of this study was to research the prospective mathematics teachers' ability to construct a mathematical model for a real life problem and to prove these models by generalizing them to use in similar situations. The study was conducted with 129 prospective teachers determined on a volunteering basis. The data were obtained with the help of Modelling and Proof Test that were applied to the prospective teachers. In the analysis of the data obtained, the categories which emerged as a result of the classification of the model and proofs formed by the relevant literature and the prospective teachers were used. It was discovered in consequence of the study that the prospective teachers construct seven different models and presented proofs in seven different categories for proving these models. It was observed that the prospective teachers had difficulties in constructing a model for the solution of a real life problem and transition from the model to the proof.