OK I read the comments so far, and I'd like to add my direct, first-hand knowledge of Home Schooling, as two of my three children were home schooled for at least part of their elementary education.
Unlike in many other nations, in the United States, it is perfectly legal to decide that you do not want your kids to attend school, and that you will teach them what they need to know yourself.
The United States of America is, after all, 50 "states" which used to mean "countries" - as a result, there is no national standard for what must be taught and how (this is also true of "regular" schooling).
As a result, "homeschooling" isn't one way of doing things, indeed the only thing that we can say for sure that is common for all who home school their children is that they have decided to not participate in the institution of facilities-based learning.
There is a strong correlation in the USA between home schooling and deeply conservative, typically Christian, families. For the most part, they have opted out of the school system because of a perceived conflict with their religious values - for example, many "Young Earth Creationists" do not want their children exposed to science curriculum that they see as conflicting with their belief system, and so they opt to teach in a manner that is consistent with their worldview.
However, while there is a correlation between strongly conservative religious views and homeschooling, it is not a domination of the home school movement. There are also ample secular (non-religious) home schooling families, my family was included in this group. In the group, there is also a feeling of dissonance with the public (and often private) school concept itself - in short, "schooling" is the problem, not education.
John Taylor Gatto wrote extensively on the subject of schools - he was a former teacher and had very passionate feelings about the failings of schools:
His central thesis might be best expressed from
this essay:
"Do we really need school? I don't mean education, just forced schooling: six classes a day, five days a week, nine months a year, for twelve years. Is this deadly routine really necessary? And if so, for what? Don't hide behind reading, writing, and arithmetic as a rationale, because 2 million happy homeschoolers have surely put that banal justification to rest. Even if they hadn't, a considerable number of well-known Americans never went through the twelve-year wringer our kids currently go through, and they turned out all right. George Washington, Benjamin Franklin, Thomas Jefferson, Abraham Lincoln? Someone taught them, to be sure, but they were not products of a school system, and not one of them was ever "graduated" from a secondary school. Throughout most of American history, kids generally didn't go to high school, yet the unschooled rose to be admirals, like Farragut; inventors, like Edison; captains of industry, like Carnegie and Rockefeller; writers, like Melville and Twain and Conrad; and even scholars, like Margaret Mead. In fact, until pretty recently people who reached the age of thirteen weren't looked upon as children at all. Ariel Durant, who co-wrote an enormous, and very good, multivolume history of the world with her husband, Will, was happily married at fifteen, and who could reasonably claim that Ariel Durant was an uneducated person? Unschooled, perhaps, but not uneducated." Indeed, we were strongly aligned with John Taylor Gatto personally and for several years - my son and middle daughter both have several years of early education years in home schooling, and while they are now all at the public school, we do not regret our decision.
As far as testing goes, as I had mentioned before, each state has its own laws pertaining to home schooling, where I live, the child was required to keep a journal and pass an assessment of skills on an annual basis, but no "certificates" or anything is issued. For secondary school (high school), if a home schooled child wants a high school diploma, they must pass a "General Equivalency Degree" test (GED)in order to demonstrate that the core skills required of that school district have been met. Other states have different rules. Some states have no particular requirements at all.
Within the homeschooling household, however, there may be no testing at all - in fact, there may be no classes, no curriculum, no specific direction. Adults and others with more experience simply give instruction as the child shows interest and that instruction is led by the interests of the child. This approach - called "unschooling" by many seems anti-intuitive, but I know a few families who not only have "unschooled" all of their children, their children are incredibly smart, competent and accomplished in what we could call "classic" academic skills.
There's more to be said later. Scurrying off to a meeting now.
