What it teaches
Sorting, and the fact that it can be done with one repeated move. Swapping neighbours is bubble sort performed by hand, and a child who does it a few times has done a real algorithm before ever meeting the word.
The screen says how few swaps the row needs, and that number is exact: the fewest swaps any sorting can take is the number of pairs that start out the wrong way round.
How it works
A row of towers appears, each one as tall as its number. Tap two that stand next to each other to swap them. A tap on two that are not neighbours is refused and says why.
The Watch button runs bubble sort in front of the child, a step at a time: the pair being looked at goes one colour, and the pair it decided to swap goes another, because looking is not swapping and that difference is the algorithm. A fresh row is dealt afterwards, so the answer to the solved one is worth nothing.
What to look for
Four towers is a puzzle and seven is a genuine one. The counter showing how many pairs are still out of order is the thing to point at: it goes down by exactly one on every useful swap, and not at all on a wasted one.