I found a link and posted it on these forums once, recently when I said the top five percent of the nations High School Graduates was composed largely of Home School Grads. People, understandably find it difficult to understand how unqualified people can do a better job than accredited and licensed teachers but the answer is simple.
Most people from the industrial nations leave basic education with a Fifth Grade Education level stuck in their heads. The evidence is easily view in the writings found in the Commercial Newspapers, both in print and published on the WWW. These are composed for the masses and they read at the Fifth Grade level.
So why can the paid teacher not do better? First there are the Teacher's Unions forbidding them going the extra mile. And then there is the Class Size.
When mom teaches it is much closer to and sometimes is a one on one instruction. But you say, they have not even been to college.
My granddaughter is a licensed teacher but refuses, after the required year of teaching in a public school to, ever teach in one again, there was so much back biting from the union members when she moved toward the obviously intelligent but falling behind.
And then; Yes, the mother, almost always ceased learning when she dropped out or graduated High School but as she receives or downloads her child's lessons, she studies first: Both are being educated and mom wants her baby to excel and to rise above the masses.
There is much that is positive to be said about Home Schooling and not so much to the negative.