Logic and deductive thinking as well as formal and precise language characterize mathematics as a powerful tool in scientific and technological development as it offers conceptual elements that represent reality phenomena. Thus, teaching mathematics in higher education aims at developing forms of behavior or cognitive competency related to the formalizing, organization, logic reasoning, and elaboration of models to represent the properties of situations by means of mathematical concepts. Knowledge of behavioral analysis, and more specifically the concept of behavior, seen as a complex interrelation with the environment, may help find out what kinds of behavior need to be developed when teaching mathematics in order to prepare engineers to deal with a reality that is strongly affected by advances in computer science and technological development, and to achieve significant results. From information gathered from twenty-two subjects that work in mechanical engineering, mathematical behaviors that mechanical engineers need to show in order to successfully deal with daily routines in their professional environment have been partially identified and characterized. Analysis and interpretation of data also indicate that it is necessary to examine and clarify the relationship among: phenomena; phenomena representation; mathematical phenomena; mathematical language; cognitive competence for dealing with phenomena; cognitive competence for dealing with phenomena representation; cognitive competence for determining teaching conditions that enable the establishment of relationships; cognitive competence for evaluating to what extent one is able to establish relations with his/her professional environment; and mathematical behavior necessary for the proposition of a kind of teaching technology for teaching the establishment of relations with the environment having the "mathematical knowledge" as a starting point, that is, for teaching mathematical behaviors. (Contains 24 references.) (Author/ASK)