cut (one's) teeth
To gain experience with something, especially at a young age (when one's teeth would be coming in). Oh, I cut my teeth on those kinds of equations! Give me a challenging problem for a change! Jen may be young, but she cut her teeth at a prestigious journal, so her perspective and expertise will be invaluable to us.
cut teeth
[for a baby or young person] to have new teeth emerging through the gums. Billy is cranky because he's cutting teeth. Ann cut her first tooth this week.