The importance of problem solving to the development of science has inspired many education researchers to design teaching strategies centered in this process. However, scientific problems are significantly different from the ones of everyday life once they require specific kinds of reasoning and tend to be structured in mathematical language. Taking into account that Mathematics structures physical thought, this paper criticizes the naïve function commonly credited to Mathematics as a mere tool and the artificial distinction between the scientific and mathematical aspects of a problem. Considering that the Mathematics used in Physics is semantically different from the one taught in maths’ classes, we propose a categorization which allows us to distinguish technical skills – the ones related to the capability of dealing with specific rules and properties of mathematical systems – from the structural skills – which are associated to the capacity of employing the mathematical knowledge for structuring physical situations. To exemplify some aspects of the latter, we present a discussion about the use of trigonometric functions in Physics’ problems.