D.K.
Radical unschooling is just that, radical! Some swear by it and some swear that it creates basically naieve adults that have no knowledge of anything outside of their own sphere. These are opinions of course. What you need to realize is that there are as many ways of homeschooling as there are homeschooling families. There's no one right way to do it, and there's no law against combining different philosopies and approaches to customize the experience for your own family. In fact, no matter what they use, most homeschoolers will tell you that THAT is the primary benefit of homeschooling. Customization.
If you're considering doing "both" by which I assume you mean some school-at-home and some unschooling, then what you are really trying to put together is what is known as a "classical" education, which is what I chose for my kids. I feel that it combines the best of all worlds. It's also a time-honored method of childhood education with a fabulous track record. Most of the founding fathers of our great nation were educated at home, by their parents in the classical style. It created the great free-thinking, but deeply ethical and principled men that made our wonderful nation possible. It is the traditional approach to educating children and it's tested and true.
What I do might look like unschooling (not radical by any means, but mild unschooling) to most people. My son and I explore what interests him and I use these things to broaden his education in all subjects. I don't believe that education can be divided up into arbitrary "subjects" when the world is obviously a wonderful conglomerate of every "subject" in every way, and compartmentalizing it invalidates the value of the whole. My son and I have what I call "conversations" that cover practically every subject in one shot and often involve sketched diagrams or handwritten lessons and explanations along with some more formal practice with things like math.
For example: we were reading Amy's Eyes by Richard Kennedy (a WONDERFUL book by the way) and there was mention of Scurvy. My son asked what that was, so I explained that it was a disease and what the common causes and symptoms were. I didn't know too much about it though, so we looked it up online and we learned a TON of stuff. We learned about Hippocrates and the Hippocratic oath (Hippocrates was the first to "discover" or "categorize" scurvy.) Of course we couldn't talk about Hippocrates without talking about ancient Greece and the roles of the physicians and philosophers of the time (history). We also learned that a vitamin C deficiency is the main cause of scurvy and why it was most common among sailors (health). We learned about modern food preservation techniques (science) and we spent some time rooting through the pantry looking at preserved foods that could fend off scurvy (some reading and health again). Next time we were in the store we ran some math problems to see which was most cost effective: buying preserved foods rich in Vitamin C, or buying fresh fruits and vegetables (which also led to a lesson in fractions, decimals, percentages, division and multiplication when we got home). We wanted to know which foods have the most vitamin C, so we looked that up too and found out that strawberries have a TON of vitamin C. We made sure to talk about it again the next time we were picking strawberries for my annual several batches of strawberry freezer jam and talk about how likely it is that the jam I make every year contributes to our super healthy constitutions all winter long (I make enough jam to last at least a year every spring). etc... etc...
This is one example of many things that were going on at that time. During that time period we were also learning about vulcanism (which started with a discussion about Hawaii which is where my son was born), which led to a discussion of tectonic plate action, which lead to a discussion of the solar system (because of the volcanoes that have been discovered on other planets and moons and us speculating about how they might have been formed), which lead to a discussion of astrophysics (my personal favorite hobby), which lead to a discussion of theory v. fact and the scientific method, which lead to a discussion of what empirical evidence is and where it is found (mainly in the fossil record) which lead to a discussion about geology and so on....
My son is only 8 years old.
So no, we're not working out of a text book or a pre-packaged curriculum, which some would consider "unschooling" but I do not believe that we are unschooling because we are constantly learning, day in and day out and there are a few more formal type lessons in there for the more technical stuff. It is a classical approach to education in which the parent is a "facilitator" in a child directed education. I offer my experience, knowledge and research skills and we learn together about what he's interested in. Of course I bring up a lot of things that he hadn't thought of, but that's my job.
At any rate, I'm not too sure where I was going with all of this! lol! Maybe I'm just trying to give you something to chew on. Of course, the most important thing is to observe your children closely and do what helps THEM the most.
Best of luck! I think you're making a fantastic decision with benefits that are going to resonate in your family for generations!
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Edit: Oh yeah, and my FAVORITE part....how much do you think my 2yo is picking up just from "contamination"? Isn't that GREAT to think about? :)
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And I'd also like to disagree with the previous poster. You don't have to "stick to a schedule" or "plan lessons". I certainly don't. We spend less that 3hrs. a week on formal "lessons", the rest of the time is spent in daily life, allowing the world to teach us the things we need to know. I'm very relaxed. I let my son watch TV and play video games, he stays up very late for an 8yo, but he sleeps late too, so he's on a good sleep schedule, it's just not what most people consider "normal" since it's shifted around to later than most kids his age have. Don't be afraid to shuck labels and think outside the box. Also, my son has plenty of "extra-curriculars". They are out there and you don't have to send your kids to government school to get them.
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And yet ANOTHER edit! lol!. In regards to socialization, please read The Socialization Trap by Rick Boyers. The reason most homeschooled children have a hard time with "peer interaction" with government schooled children is that government schooled children are not learning real world socialization techniques, so homeschooled kids find it hard to relate to them. Government schooled children are in an artificially narrow, age segregated environment all day and are basically raised by their peers. Most kids graduating these day (most, ladies, not ALL) don't even know how to talk to someone that isn't their own age. I've seen it time and again with my own two eyes! I want better for my kids. Read the book, it'll open your eyes. My son has no problem holding a respectful conversation with anyone that will talk to him. THAT is real socialization!