In this paper, I focus on the so-called structural account for the effectiveness of mathematics in physics. After presenting such an account, I take into consideration some difficulties related to it. Part of these difficulties can be settled, but some critical aspects remain. Particularly, the structural account needs to be integrated in order to account for those mathematical representations that seem to play an active role in making new discoveries and to foster new advancements in scientific research. I will try to provide the required integration by offering a new version of the structural account, in which a major role is played by a certain number of pragmatical and contextual elements. The resulting account is in a better condition to make the applicability of mathematics less mysterious and miraculous than it is often presented.