There are many divergent beliefs on the methods of homeschooling out there. Many who homeschool, and most who do not homeschool, are in favor of formalized lessons and schoolwork: i.e. every day you "have school" and do worksheets, lessons, and exercises. There's explicit explanations of concepts and explicit learning sessions.
My "philosophy", if you can call it that, is much more informal. Right now it's pretty easy for me: She's 5, so she'd be in kindergarten. I'm not trying to maintain grade-level parody or anything: if it takes her longer to do something it's not a big deal, and if she's beyond a topic, I'm not going to force her to practice something just because that's what her peers in school would be doing. But… I do look at the local school district's curriculum as a rough guide and to make sure I (eventually) cover all the bases.
Looking at the curriculum also helps me keep things in perspective. I think about what she'd be doing if she were in public kindergarten… Making a macaroni picture. Identifying the letter A. Counting 1 to 20. Singing the ABC song. Having story time. etc. We do all those, and we are well beyond them in most cases, so I don't worry if we don't have a formal 15 minute lesson on writing, reading, spelling, addition, or subtraction every day, or even every week.
I'd love it if my daughter would spontaneously start loving to do worksheets. If she'd like it, I'd sit with her for a few hours and practice math or writing or reading… but that's not the case most days. Some days it is, but that's not everyday, just every once in a while. I could force her by offering punishments, or bribe her with stickers, toys, praise, or the promise of a fun activity later, but I think that's a bad path to follow. If I go down that path now, there's probably no turning back. I want her to enjoy learning, I do not want it to be a chore she gets through because she want to avoid a negative, or chugs through merely for a disconnected reward. I want her to get better at writing because she wants to write a letter to her Grandpa. I want her to get better at math because she wants to figure out how much money she has, or to figure out how to cut that triangle, or to play Monopoly, or a million other things. I want her to want to read and understand history, culture, science, religion, and art because, well, it's interesting.
If I force her to sit and do math worksheets or practice writing, that applies an external motivation rather than her own internal motivation. With external motivation, there's a very real chance she'll never gain internal self-motivation, or she could even end up disliking the learning process completely.
So I often suggest worksheets. I often suggest silly educational games. I often suggest many educational things, but I don't force them: I just suggest them in the same way I might suggest walking to the park or reading a story. Sometimes she wants to, many times she doesn't, but it works often enough that I declare it working. And in my own secret evaluations of "where she is", everything is going swimmingly.
Now, since I'm so fond of lists of guidelines I try to follow, here's a nice bulleted list of guidelines I try to follow in our education, at least while she's young (now until around 7 or 8 or so):
First, the things I am not doing:
- No visible "curriculum"
- No forced schoolwork
- Minimal division between "classes" or "subjects"
- No (visible) grade levels
- No (visible) grades (A, B, satisfactory/unsatisfactory, etc)
- No rewards for schoolwork
- No "textbooks"
- No pressure to perform
- No pressure to "advance"
Now, the things I am doing:
- Plenty of activities where reading, writing, and math are implicit
- Lots of play
- Lots of interactions with kids of all ages
- Lots of interactions with adults
- Plenty of field trips
- Plenty of outside time
- Lots of play
- Plenty of art
- Some crafts (i.e. art a final goal in mind)
- Plenty of music
- Lots of stories
- Lots of play
- Introduction of diverse ideas
- Lots of reading (by her)
- Lots of reading (by me)
- Lots of history stories
- All explicit "schoolwork" is strictly on a voluntary basis
- Discovery and experimentation
- Did I mention lots of play?
- Trying things out
- Sneaky school
As she gets older, I want to slowly begin formalizing things a bit. When she's 7 or 8 or so, "lessons" can start to be more explicit. I think a 7 year-old is much more capable of "doing school" than a 5 year old. In fact, in Finland (ie the best schools in the world), official school does not start until age 7. There are many pre-school activities available before then, but zero grades, zero competition, and no pressure. That sounds like a plan to me.