My grandma has this game! I wanted to buy my own!
You turn them all over and put them into piles of 10. Separate the piles according to the amount of players.
Each player takes it in turns to flip over their top tile on the pile on the right hand side. The aim is to build up six piles from 1 to 20 in the middle.
If you turn over a tile and someone has a tile a number higher or lower (e.g. you flip over a 17 and someone else has a 16 or 18) you pass your tile over to put on their tile. The first player to get rid of all their tiles wins.
The game you're searching is probably "Up and Down Donkey" (page 8 in the PDF)
It was used in math classes, and got sold commercially one time. Several rules existed to play with these tiles ;)