My girls are 3.5 and 2. I love them and love seeing them learn. I have boatloads of experience with kids and have taught preschool so I do feel equipped to teach them. And seriously with a quick google search I can get anything else I want or need.
For school we live. Sharing, reading, taking turns, colors, counting, abc's, sharing, getting dressed, doing puzzles, sharing, reading books, chores and sharing.
The two big ones are reading and sharing. Lots of both.
We count everything. Name what color it is. And if one of them shows an interesting we run with it.
Today my oldest asked about where the sun is. So I found a solar system diagram online and we talked about it. That lead to talking about the moon and why we can only see it at night. I love running with these things with her! Watching her figure out that we live on a planet was really neat. She doesn't totally get it of course but for a three year old she's starting to. I hope we can continue letting her lead her education as much as possible.
I've let her lead much of her development. Potty learning was 100% her lead. We talked about it lots and one morning she said no more diapers. She's had maybe 5 accidents since then. That was just after her 3rd birthday. She co slept with us until she wanted to be in her own bed when she was about 18 months old. Not once did she come back in with us. She knows what she needs and wants and I only want to encourage that strength!!