We homeshcool and maybe I can shed a little light here. A child seems to learn a lot better when they are interested in a subject. For instance, our daughter is nuts over the prairie days and settlers. You can let her take off on this subject and bring in aspects of each traditional school subject in relation to this topic. For example, reading is accomplished by reading materials related to the subject. History is a given - but so is civics and geography. You can teach math using this as a backdrop in creating examples. You can teach literature by using books about the period in history. Grammer and spelling can be taught using examples from this area of interest.
The idea is to break down the structure and give a little more freedom to teach what needs to be learned by using areas of interest of the child. Another type of unschooling that we have used in unit studies. We used the Little House books as a basis for unit studies. Once again, we were able to teach a variety of subjects using the books as a backdrop.
I hope this makes sense. But, it has been very effective for us to use a curriculum for each child that has a lot of room for what interests each child. It's just easier to teach an interest kid.
Unit studies are wonderful, sounds like you have a great program. I would not call it unschooling, tho, for you have set goals for your kids and provide structure, within which your children choose their interests. Otherwise you have Summerhill all over again, with all the tomfoolery that provides. To me unschooling smells of 'We did not teach our kids any religion; we want them to choose their own,' which I believe is abusive.
Good explanation. Sometimes this is called "emergent curriculum", letting the child direct which way to go according to his interests. I'm sure you've found it is more work for the instructor! :) But a very rewarding way to learn.
That sounds like what they do with 'integrated curriculum' in the public school. I thought folks home schooled to get back to the basics. If you want this new age teaching, why not just leave them in public school?