Towards a full integration of physics and math concepts: The path full of traps

Both mathematics and physics concepts have been closely interrelated since their formal beginnings in ancient times. Moreover, from a historical perspective, it is possible to identify how physics advanced as more complex mathematical ideas were available. In fact, it is hard to separate them either in or outside a classroom. However, in the classroom there are many instances that the teaching of one subject obstructs or creates barriers for the other. After five years of teaching a physics and math integrated course for freshman undergraduate students, a series of inconsistencies have been identified between both subjects. These inconsistencies can be perceived as traps that create conflicts between the concepts, interfering with students' learning. The instructors teaching the integrated course are aware of those problems and they are authentically concerned about what to do to create awareness for these conflicts that make learning and understanding harder for students. Moreover, they have some suggestions as to what to do or how to address those inconsistencies, so the teaching and learning of both disciplines (physics and mathematics) is improved. In this study, the authors present some of these inconsistencies that arose while working in an integrated physics and mathematics course for first year undergraduate students (mostly kinematics and differential calculus). Some of the inconsistencies come from language, other from the framework of reference, and some others from the applications. As concluding remarks, the authors aim to provide some ways to alleviate that tension. The main objective is to have series of works focusing in the inconsistencies while searching for suggestions to mediate them and improve conceptual relationships that promote a better understanding for students.