While doing my undergrad work at the Hartt School of Music, I played in the Hartt Jazz Band whose director was Al Lepak (also the percussion teacher).
Whenever the trumpets and trombones fell apart on some complex rhythm, Al would simply look up, unlit cigar in his mouth and say in that gravelly voice, "Guys, guys, it's ba-um"
Ba - pick-up
Um - downbeat
Of course his other saying was "Guys, guys, it's um-ba"
It still amazes me how this simple advice worked instantly to fix our counting errors.
Extending this idea a bit .....
I seem to perceive rhythm differently than some of my students and (maybe) most people. I see most rhythms as pick-ups to downbeats (BA-UM or maybe BA-BA-BA-UM, etc)
Think of the excerpt from La Gazza Ladra:
A common rhythmic error is to leave the top note early, thus starting the run too soon.
Instead of perceiving the beginning of that run as "1&2&BA", I think of it as "BA-BA-BA-UM"
Over time, I've learned to know the "feel" of three pickups to a downbeat.
In other words:
You can count a rhythm by relating it to
or to what follows
For what it's worth, it worked like a charm in one lesson today.
PS Just like Tabuteau numbers if you're familiar with them.