Educators often argue that students should engage in activities such as conjecturing, proving, and deductive reasoning. The underlying principle is that learning mathematics means doing as mathematicians do. However, "mathematician" implicitly refers to a pure mathematician at university. "The aim of our paper is to critically question the logic model underpinning these premises in order to suggest which aspects of mathematicians' practice could be salutary for students in schools and university and which are not." We argue that aligning learning with these practices might not meet the broader educational goals of pragmatism and vocationalism. We show that activities attributed to pure mathematicians are largely ignored by biologists, engineers, and physicists and in workplace settings. In contrast the practices of professional modellers are highly valued. We argue that such practices are desirable for learning to use and apply mathematics. Next, we illustrate the suitability of practices from studies of professional modellers and applied mathematicians for classroom learning using empirical data. We conclude that the interpretation of mathematicians' practice to be emulated must be broadened to include professional modellers' practices to better serve meeting educational goals for more students.