Standard pedagogical practice gives primary importance to bar lines and counted beats, usually quarter notes. By emphasizing this visual convenience much is lost -- so much that no one has bothered to tally the resulting destruction.
The student is bound to lose interest as soon as he or she can count to three or four.... What else is there to do?
Arithmetic, in other words, is not the point.
This loss of interest is coupled with lost curiosity about entire centuries full of magnificent music rendered unbearably tedious by predictability.
When tone comes first rhythm is enlivened the way the hand of the sketcher is enlivened when producing a rough draft.
Let's hear it for rough musical drafts rather than starting off with the student painting, as it were, eyelashes.