Resumen

The research related to critical and reflective dimensions of mathematical modeling isseeking identity, definition, and objectives. As well, it is developing a sense of its own nature andpotential for research methods used in order to legitimize pedagogical action. It is necessary to discussthe importance of philosophical and theoretical perspectives found in critically reflective dimensionsof mathematical modeling. As well, the importance of a virtual learning environment that helpsstudents to develop critical-reflective efficiencies has become increasingly important to enable the exploration of theories related to critical mathematical modeling, distance interactions, and transactional distance by using long-distance technologies. These interactions are triggered by lessons placed on platforms, which are virtual learning environments (VLE) and that enable the use a combination of technology, teaching and the learning of specific content. By developing discusión forums and video conferences, professors and tutors are able to analyze interactions enabled by these tools, which contributed to the reflective developmentof the elaboration of mathematical models in the VLE.