My daughter will be 3 this summer, and I am very excited that she is asking questions and wants to learn things. My dream is coming true -- I can teach both children the same things, but on different levels simultaneously. It's a very cool concept. So right now we are doing animal classification. My daughter is just completely adorable with the sudden intense interest she has taken in mammals. It came up some time ago that a giraffe is a mammal and has "nursies." Well nursies are her favorite thing in the world, so she immediately took to mammals. I appreciate that Usborne animal books usually have photographs of the mammals nursing their young, so this is something we've pointed out at every opportunity. We also like the Charlotte's Web animated movie that shows the pigs all clamoring to get a teat! So Elisabeth is just very excited about mammals. When we cuddle before bed, she's been asking me each night "Can you ask me some questions about mammals?" So I ask her, "Is a duck a mammal?... Why not? ... Do birds have fur? What do they have instead? What do fish and reptiles have instead?" etc.
My son is almost 6 years old (would be finishing kindergarten in public school) and has completed all his first grade coursework; but it's not always so simple to classify learning. One thing I love about homeschooling is the flexibility. In math, for instance, he has completed 2nd grade and is working on skills from 3rd and 4th grade and above (multiplication, area and perimeter, measuring angles with a protractor). We do whatever he is interested in, or whatever comes up (i.e. finding a protractor at the store) without worrying about what level it fits into. Ahhh the FREEDOM!
We are following the "What Your __ Grader Needs to Know" books as a loose guide and a benchmark of when he's completed a grade. I think these books are great, but the social sciences are way advanced in these books so I hold him to everything except that. A six year old can move along at his own pace with math or reading, but it takes more maturity to get into certain historical topics. So that is something we're not pushing right now. What we are doing for history is using Abeka's 1st and 2nd grade readers on the United States, which I totally recommend, as well as the Living Scriptures "Animated Heros" video collection which has different movies for different historical figures, such as presidents, scientists, philosophers, etc. We watch 3 of them right now but I think that's enough to handle without confusing him. He isn't picking up on these facts as quickly as he does with math; there is a lot of rote memorization as far as who people are and what they did. I just think he needs more maturity in that field. So he can tell you about the Wright brothers, George Washington, and Columbus. It was even a mistake to watch those two last videos the same week; he would get them mixed up and it has taken a lot of review and discussion to get it straight!
Another reason I love homeschool is that we put our own spin on it, coming from our own culture and lifestyle. This is something you cannot escape; anybody who teaches anything is going to teach from their paradigm or worldview. School is not objective; teachers are still subjective people. Even textbooks are not objective; it is not a thing, it is merely a medium of communication from the group of people who wrote and compiled it. People are subjective, and your child is always learning from people, including their beliefs and prior influence (This could be as serious as the hominid or as casual as Pocahontas; none of it is 100% fact). So who do you want them to learn from? Do you send them to a different religion to teach them scripture? Or do you make sure it's coming from your family's worldview? I'm not even saying that other teachers would teach something wrong. But it wouldn't be complete or wholly accurate, compared to somebody from his own family and culture teaching the same thing.
For example, we are LDS (Mormon) and in our ancient scriptures we have prophesies of Columbus and the formation of America as the "Promised Land." We have revelation about why America was kept secret; why it was discovered; who the Lord wanted to lead; etc. This is all very pertinent to us in terms of U.S. History. The Book of Mormon, for other reasons as well, is a crucial reference for History as well as politics.
Another example is animal classification which we are now learning. We teach the commonly accepted classification because that's what it means to be educated; however we can also teach the caveats such as these classifications are not objective; some people made them up the best they could with their understanding. The divisions are based on evolutionary theory which we don't agree with. We remain open minded that some revisions will most likely happen in the future, and when God reveals the objective truth to us we may be in for a few surprises.
Anyhow, I had recently posted an update about my son not being excited about piano anymore. He is still playing and taking lessons, and does enjoy it, just not with reckless abandon. He writes his own music which usually actually is harmonious, and he is advancing very well through his Suzuki piano course. It's a great opportunity for him to have some structure and formality with that; I am very pleased.
To sum it up, I would say homeschooling has been an adventure, complete with difficulties, and is definitely a growth experience for all of us. I have been very humbled as not all my ideas work, and usually it just comes down to doing things their way. That's what parenting is all about! (What, you thought God sent you kids for you to teach them???) Very humbling indeed, and puts us in our place as the Lord's servants.
Of course it would be easier to send my children to school and let somebody else raise them. But frankly, I am their mom, and raising them is my job, thank you very much. They are going to be spending time with me, not with a stranger 6 hours a day. Their memories are going to be about each other, not with random folks they won't keep in touch with. Their influence and world view will come from home, family, church. That's what it means to me to raise my children.