Towards full integration of physics and math concepts: Words versus meanings

Mathematics and physics concepts have been closely interrelated since their formal beginnings in ancient times. Moreover, from a wide variety of perspectives, it is possible to identify that the understanding of physics progressed as more complex mathematical ideas became available. In pedagogical practice, there are many instances where the teaching of one of these disciplines might obstruct the understanding of the other; this problem, combined with the difficulty of teaching them inside or outside a classroom, produces a ripe opportunity for educative improvement. After a significant experience of teaching an integrated physics-math course for freshmen undergraduate students, a number of inconsistencies were identified and previously reported. One of those inconsistencies is a trap rooted in language, and it creates worrying cognitive conflicts that interfere with students' learning. Specifically, the use by teachers of different names for the same concepts or ideas (perhaps because they look to relate specific concepts to everyday language) might be helping misconceptions to prevail. In this work, the authors focused on the analysis of terms like mass, force, and torque. To do this, they analyzed various research sources and texts to identify the roots of different names for similar concepts and their uses, and they considered the consequences of differing terminology and meaning to the construction of complex thinking. Raising awareness about the inconsistencies of terminology in mathematics and physics and the resulting consequences is the primary objective of this study. This work was motivated by an authentic concern to facilitate the learning and comprehension of these subjects by students. Accordingly, the authors issue a call for action for a transformation in the teaching and learning of physics and mathematics through reflection on better use of terminology in these fields, so that the terms are negotiated between the disciplines, which results in precise descriptions of what is being taught, free of inconsistencies, confusion, and conflict.