Our days are like ommmward's; I'm also home educating autonomously.
Here was today, for example:
Dd1 (13yo) went out on her paper round while dd2 (7yo) watched very early Donald Duck cartoons on YouTube. She's quite interested in how and why the style of animation has changed over the years - both the appearance of the characters and the method of production. Mostly I was doing housework but we chatted about the cartoons some too. She also asked how coins are produced so we found a video about that.
Then I took dd2 to a toddler music class which she still enjoys, while dd1 stayed home and worked on the desk she is restoring, in between chatting with pals on Facebook. Quick swoop through the library on the way to take both to their routine doctor appointments. Read some books and did some drawing in the waiting room.
All three of us went to our friends' house for the afternoon. On the way, dd2, who has mild learning difficulties and particular delays in maths, for the first time recognised written numbers over ten. Did she ever!! She suddenly began to rattle off all the numbers of the numerous buses we saw on the way and read the numbers on the timetables on every bus stop: 700, 19, 400, X90, 31. (739 foxed her though, LOL!) It's lovely to see something coming together which she's learned through daily life and asking her own questions, rather than by being drilled. She was tremendously excited and pleased with herself.
She's quite interested in the local area, constantly asking about which buses go where and why and when, how the town grew up, why certain materials and building methods were chosen for various buildings, which businesses have gone bust recently and why, and what sorts of people live in the different areas of town. Such discussions are frequent as we are out and about.
At our friends' house we watched a film, made pancakes and discussed the eating habits and work ethic of our different cultures. The two families include people of three different nationalities.
Once home, I chucked dd2 in bed and told her a few poems while dd1 practised a piano piece on the keyboard. She's recently discovered that she could figure out the basics of playing the keyboard with no formal instruction, which came as a delightful revelation to her. She asked me to refresh her memory about how to read music. She has dabbled in this a few times but has never become proficient at it because she hasn't used it enough. Not a problem. When she has a use for it, it will stick. Then Dd2 went up to bed.
And me, I came onto Mumsnet where I read a thread on which people who don't home educate are decreeing knowledgeably that children whose parents let them learn whatever they like are neglected educationally. They might as well tell explorers who've personally sailed around the world that the earth is flat because... well, obviously it is, you can see for yourself that it must be flat, how could it be otherwise, don't try to wind me up with your silly stories.