What a cool thread Lillian!
I haven't read others, but will when I'm done.
Some examples that stand out how my children have learned something just because they were interested in learning about it:
DS15 has always (even while still in ps) been interested in war/military history and weaponry, and has always searched out information (even reading encyclopedias as leisure reading) on that topic.
He's also a big lover of golf, and a huge fan of T. Woods. He has searched out lots of information on golf and golfers.
I still chuckle over his library book selections. One of my favorite, which shows how eclectic his learning desires are, was a while back. He had 32 books; the selection was from Hitler, small engine repair, golf, football history, Sophia Loren (sp), silent films, Calvin and hobs, super hero comics, ancient weaponry, and solar electric toys.
This year has been the year to learn 16th century England, which also leads to all over 16th century history. He joined the cast of our state Ren faire, and it being a faire that tries to focus on education-entertainment, he needed to research his character and other aspects of Elizabethan history. Needless to say, I've learned a lot along the way as well. The younger 2 also joined in on the learning, and it became a family affair. Not only did we all have a blast with this, but we all had a blast while learning. I can't imagine having had to work around a work schedule, school schedule or even a school at home schedule and get all that we had to do done without going insane. My hats off to all that did do it, I'd not have done so well.
DD9, when she was just over 6 was looking over my shoulder as I was looking at a picture of a caterpillar that was being discussed on a message board. She said, "Oh no, you don't want to touch that one, it stings you and it hurts". It was a "white caterpillar" and it does have that very effect. I asked how she knew this and she replied, "I read it in one of my bug books".
She wished to learn how to play the piano. Well, we can't afford a piano or lessons, so I got her an inexpensive keyboard and found an online free lesson plan and she taught herself how to play and read music from that. Sure she won't be a concert pianist, but she enjoys playing music.
She taught herself how to read because she wanted to know how to. I went to read with her D|ck and Jane one day when she was 5, and she picked up the book and read it to me as if she'd been reading all along, even the harder words she read smoothly and understood what was going on. She then, in turn taught herself how to read cursive...then later how to write. All because she wanted to know how to do it. She's now teaching herself how to write in cursive, because she wants to.
She's also searching out ways to improve her spelling, all because she wants to be able to spell better.
This is also the child that at age 5 put the tv on closed caption, just so she could read the sub-titles. She also puts dvd's on different lang. modes so she can watch them in another lang.
She teaches herself math concepts, just for giggles and kicks. I'm always in search of interesting and child friendly math concept reading materials for her, since she learns best by reading or watching and copying.
For longer than the past year, she's been into the brain. This child will go on and on about the brain. The other day, we were out in the heat all day, and I wasn't feeling too "with it" on the way home. She goes on how my cerebellum affects balance and on and on about the brain and why I'm feeling the way I'm feeling because such and such affected my brain in this such and such way. She has asked to see a real live brain, I've yet figured out how to accomplish this one.
There's a lot more on her, but I'll move on.
DS5 isn't reading, yet, but that hasn't stopped him from learning about things he wants to know about. He LOVES dinosaurs, has since infant hood, it seems. He may not be out there reciting the different dinosaurs and their purposes, but he knows about them and enjoys learning about them. He also enjoys and has searched out information on various topics, I can't think of off the top of my head...oh yea space stuff. He's, on his own, learned mental math. I'm not sure how or when this happened; he just the other day came up to me as said 4 and 6 is 10. Later on he was asking for something, and I said he could have 5, and he said that he wanted more. SO I said he can have 10 more after lunch. Without hardly any hesitation he said, "Then I get 15 total, OK!". Somewhere along the way he's learned how to tell time on the digital clock and he's now trying to learn on a reg. clock. He also said that he wishes to learn to read this year, so we'll see how that goes. He also likes to measure things and loves things about Knights.
OK, there really is so much more, but I'll stop for now.