Yes, my 12 year old shih tzu does this, especially when frustrated. She'll offer up everything she knows, then run to her mat and started barking at me.
My 10 month old Bouvier also does this, though usually only when confused (like when I'm starting a new behavior with him). Usually runs through a sit, down, go to mat, kennel, nose touch, etc. Then stares at me with sad eyes.