Today I read a very impressive story called Lessons by Otter Girl. The premise is that Jenny and the Tenth Doctor have found each other again, and are traveling together on the TARDIS. They're doing what you might expect: wandering, having adventures, and getting to know each other. Each of the 24 chapters is a separate vignette of lessons taught and lessons learned.
Jenny has so much to learn. She's Gallifreyan, and she has the Doctor's genes, but she doesn't have his training or experience. She's not a Time Lord (or Time Lady, if you prefer), and she's aware of that, sometimes painfully aware. She wants to learn everything, she wants to do everything, and she wants to please her father. Sometimes the last bit seems the hardest.
The Doctor has lessons of his own to learn. It's been a long, time time since he was a father. Now he's faced with a brilliant, moody, impulsive adolescent will all of his curiosity and half his self-control. One funny but touching chapter has the Doctor and Sarah Jane Smith discussing the trials and tribulations of raising a genius clone.
The lessons cover a wide range of topics, from "How to escape from a dungeon where you are shackled to the wall (and how you could have avoided being there in the first place)" to "how to drive a vintage combustion-engine Earth vehicle". There are lessons in how to grow a TARDIS, how to speak Gallifreyan, and the use of a yo-yo as an aid to sensing time.
I don't think I'm committing any spoilers by saying that the most important lessons learned here are those of family, and respect, and love.
A small disclaimer: I did some beta-reading for Otter Child on one of her other stories. Also, she borrowed -- with permission -- a MacGuffin from one of my stories. The chapter it appears in is beautifully written, which is entirely due to Otter Child's writing. She could have used a dozen other devices, and the scene would work as well.
Go and read. And if you enjoy -- and I believe you will -- leave a review.