In this paper we discuss epistemological aspects of the mathematical modeling process motivated by an analysis of the component 'reality' in this process. Descriptions of the mathematical modeling process inspired by the applied mathematics as scientific method of research are presented, focusing on the reality to be modeled, which leads us to a deeper analysis of this component of the process and subsequent epistemological analysis, differentiating the initial reality from a pseudo-reality, the latter being the object of the knowledge. This leads us to a re-reading of the above-mentioned process, based on conceptions of the philosophy of science such as realism, structuralism and empiricism, which is adapted to the study of mathematical situations considered as the initial reality to be modeled, allowing a semi-empirical vision of the mathematics whose consequences for Mathematics Education are discussed.
Mathematical Modeling; Epistemology; Reality; Pseudo-reality; Mathematical experience
