(ProQuest: ... denotes formulae omitted.)IntroductionFor Leonardo da Vinci "saper vedere", that is, knowing how to see, or having the art to see, was the key to unlocking the secrets of the visible world. Saper vedere included a precise sensory intuitive faculty as well as artistic imagination (Heydenreich, 1954) which were at the root of Leonardo's inventiveness and creativity. According to Leonardo, to understand, you only have to see things properly (Bramly 1994, p. 264). Knowing how to see is also important in mathematics. The Italian mathematician Bruno de Finetti (1967) stresses this importance in his book on "Saper vedere" in mathematics. He highlights several aspects of knowing how to see in mathematics, such as knowing how to see the easy, how to see the concrete things, and how to see the economical aspects. He also discusses in what ways knowing how to see also helps us to better recognize the meaning of general and systematic methods of mathematics represented in formulas. His book starts by highlighting the importance of reflection for learning the art of seeing.Reflection also plays a central role in Polya's Looking back stage in problem solving. Polya's heuristics also provide a language to help problem solvers think back about their problem solving experiences. As Lesh and Zawojewski (2007) point out, "by describing their own processes, students can use their reflections to develop flexible prototypes of experiences that can be drawn on in future problem solving" (p. 770). Reading Polya's heuristics and looking at the examples he gives, we can concur with Lesh and Zawojewski that Polya's heuristics are intended to help students go beyond current ways of thinking about a problem, rather than being intended only as strategies to help students function better within their current was of thinking.Lesh and Zawojewski (2007, p. 769) point out that when solving problems in complex problematic situations the abilities related to "seeing" are as important as abilities related to "doing". Schoenfeld (1985) found that individuals select solution methods to problems based on what they "see" in problem statements. Schoenfeld's data indicate that mathematical experts decide what problems are related to each other based upon the deep structure of the problems, whereas novices tend to classify problems by their surface structure (p. 243). Krutetskii (1976) found in his research that one trait of mathematically able students was to strive for a clear, simple, short, and thus "elegant" solution to a problem (p. 283). He also mentions that "a striving for simplicity and elegance of methods characterizes the mathematical thought of all prominent mathematicians" (p. 283-284). Krutetskii also describes how all the capable students, after finding the solution to a problem, continued to search for a better variant, even though they were not required to do so (p. 285). In contrast, average students paid no particular attention in his experiments to the quality of their solutions if there were no special instructions from the experimenter in that respect. Krutetskii observed that capable students "were usually not satisfied with the first solution they found. They did not stop working on a problem, but ascertained whether it was possible to improve the solution or to do the problem more simply" (p. 285-286).In this article we will focus on learning the art of seeing the easy, by using an example of a problem posed to future secondary mathematics teachers. De Finetti indicates that it is often difficult to see the easy things, that is, to be able to distinguish, in the complexity of circumstances present in a problem, those that are enough to formulate the problem or that allow one to do the formulation as several successive steps that can be carried out easily.The problem presented below was posed as part of a modeling course. Lesh and Doerr (2003) point out that from a modeling perspective, traditional problem solving is viewed as a special case of model-eliciting activities. …