which other countries? that's certainly not the case in Germany. you might see some proofs in geometry, and maybe some informal derivations of things later on,

which other countries? that's certainly not the case in Germany. you might see some proofs in geometry, and maybe some informal derivations of things later on, but "induction" is a university level thing (it's possible that some kids that focus more on maths in school see this kind of stuff earlier, but it's definitely not a universal experience).