A One Button Game: multiple players behind the same screen, each one only has a single button.
You’re all walking a stairway together. (Left to right, higher and higher until the top).
Your button just makes you take the next step.
Reach the top with the best score, not necessarily first.
(A kind of “smell the flowers” metaphor in there?)
This mechanic is so simple because the actual game will be more complex. Like, maybe you’re collecting letters or numbers, maybe there’s some even harder mechanics going on. That will be the educational component of this one.