Permeating countless strong and central arguments in classical mechanics is an understanding that emerged with the advent of possibility that the Earth might be moving without our sensing it.  The understanding is that uniform motion, unlike acceleration, is not a thing to be sensed at all.  The perspective, experience and measurements of two uniformly moving observers are all equivalent—even if the magnitude and direction of the two motions are distinct.  Neither the Earth nor any sun is characterized by inherent velocity or by an inherently preferred status on the stage of space and time.  Ever since Einstein re-directed our attention in 1905, we refer to such equivalence as Galileo’s principle of relativity.  The principle makes no reference to quantity.  Impediments to student comprehension of this physics centerpiece cannot be reducible to struggles with numerical computation nor symbolic manipulation.  My studies seek to assess and improve the mental models we hold regarding the fundamental principles associated with relativity.