Thanks to technological progress the world becomes more and more complicated. People stand in front of new and difficult problems that need to be solved. These are problems, the solutions of which are not universal, and cannot be learned. Many solutions require specific data that cannot be learned, as new data is part of the ongoing generation of what people might describe as "what we know". These reasons demonstrate that it is more important to focus on identifying conditions for solutions, as opposed to results--when solving problems. Teachers should focus on improving competences that are key to problem solving, and not merely on enriching knowledge structures. In this article, the author focuses on competences in mathematical modelling as a part of the set of competences that are necessary for problem solving. He first describes the process of mathematical modelling which can be divided into three phases: (1) identify the starting points necessary for a model; (2) construction of a mathematical model; and (3) verification of any model that has been constructed. He then shares his research into children's ability to carry out mathematical modelling and interprets the results. (Contains 4 figures.)