'Radical' means "to go to the root."
And there is a movement within the movement of homeschooling that wants to get 'radical'.
In American society this word normally connotes a negative idea of rank anger and irrationality. But in this series of articles about an up and coming sub-movement within homeschooling, it will not be used in such a derisive sense. I struggled with finding a suitable adjective or even a noun, but I think 'radical' works best because when rationally examined, the word dovetails with the movements goals: to return to the supposed root of Western Civilization educational methodologies--homeschooling.
The other usage of 'radical' involves a relatively extreme commitment to a particular cause--which describes the leaders of this movement because they believe homeschooling (and other derivatives) is either demanded by the Bible or the best option that fulfills the Bible (not all who think homeschooling is the best option are radical as I define it in this post).
The word can also denote advocating drastic change. The leaders of this movement are not interested (as displayed by their actions) in presenting or propagating their views piece-meal. They want change and they want it now.
Why this much ink for a single word? Because being labeled is no fun and some people will react negatively to the word. But labels are necessary for those who wish to be disassociated from differing views. This tripartite definition--the historical, moral and urgent elements--may not set well with some, but it is my humble attempt to understand this unique approach to Christian education. I will try to only label this theoretical position and not the people.
Now to the point: Radical homeschooling is the doctrine that homeschooling is the sine qua non of biblically based parenting.
In other words, homeschooling is commanded by the Bible:
"Of course, my prayer is that every family would homeschool from birth. If that's not you, my prayer is that you will homeschool from now on. It may require difficult changes. It may require the awkward work of repenting to your wife and to your children for how you have abdicated your responsibility." (p.133, When You Rise Up)
" 'Therefore thou shalt love the LORD thy God, and keep His charge, and His statutes, and His judgments, and His commandments, always'" (Deut. 11:1). This is why we should homeschool. God commands parents to teach their own children God's law, and we must be obedient." (p.9, Homeschooling from a Biblical Worldview)
In fact the about page of Vision Forum asserts: the "modern classroom…is a distinctly Greek and pagan approach to education."
One of the more influential homeschooling leaders, the founder of the NCFIC (family-integrated church group), clearly stated his position a few years back:
"Our reasons for home educating are not preferential, but principled, being derived from God’s Word.... Wrong educational methodology can lead a child to Hell…" Doug's blog, Oct. 8, 2004
Is this his personal opinion? (As though that could be divorced from his public efforts.) Fortunately, this sentiment has been stated and rather boldly at the parent website, Vision Forum's about page:
"Most men are gripped by fear. They fear the loss of job security. They fear the unknown. They fear the opinions of others. This fear prevents many fathers from beginning home education — the educational approach most consistent with both the methodology and goals of education as articulated in Scripture. This fear prevents other fathers from making lifestyle changes which will allow them to spend more time walking beside their children, as God commands...Methods are not neutral. The rise of the home education movement is not merely a response to the failure of government education; it is an affirmation of a distinctively Biblical approach to both the methods and the objectives of Christian education."
The author boldly declares homeschooling as the "most consistent" approach to the Bible. Naturally, Christians would not settle for the second most consistent approach of anything in the Bible. Who would not want to spend "more time walking beside" their children--as God commands? Vision Forum is about homeschooling. It is about more, but it is in the business of propagating homeschooling as the Biblical approach. This statement is further amplified in a radio interview:
“Home educators, almost by definition, have turned their heart to their children [Mal. 4]… So, there’s been a revival that’s taking place in the heart of these homeschool families. And this revival works itself out to the local church...our prayer: every Christian in the world is in a family integrated church. And there should be nothing but that, but you know what that is going to lead to? That’s going to lead to people homeschooling! And vice-versa; they play off of each other. Because when you understand the importance of discipleship you move in that direction…” 
Clearly the speaker's prayer (and goal?) is to make every church in the world--not Reformed, not Dispensational, not Baptistic--but a family-integrated, homeschooling church. Why? Because homeschoolers "almost by definition, have turned their heart to their children." Homeschooling is a revival.
A clear and unequivocal statement, such as, "God commands homeschooling," is not needed because it is the warp and woof of this movement.
This unique approach to education presumably allows for exceptions to homeschooling (presumably because I have not actually found any such evidence), yet a biblical command is a biblical command, exceptions notwithstanding. If this is a message you wish to follow, dear reader, then by all means join the organization and help them make their point loud and clear. But I hope in this continuing series to demonstrate that, in spite of some of the laudable goals of RH, its view of the history of Christian education is mistaken and its understanding of key elements of Christian nurture is misguided.
Soli Deo Gloria
 Phillips quoted from “The Family-Integrated Church Movement,” interview, Generations Radio, sermonaudio.com, June 12, 2006.