not a teacher
This will have some regional variations.
A general term for this is "to flirt with".
He tried to flirt with Mary the first time he saw her at a party.
She likes flirting with the boys in her class.
Where I live, a common term for what you describe is "to chat up".
I saw a group of boys trying to chat up the girls in the mall.
At parties he spends most of his time chatting up the girls.
Student or Learner