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If that's not an enfringement upon freedom of choice
Freedom of choice for who though? The parents or the children? Because it's the children's rights that are the real concern here, and children have a right to a free and appropriate education.
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we home schooled out two children from 2nd-5th grades.
Personally I don't have much beef with homeschooling your children through 5th grade as long as you do a good job of it. Beyond that I would have a problem with it almost regardless of your qualifications. However, there is (currently) no way to distinguish which parents who are homeschooling their children are qualified, and which place their children in a borderline abusive situation.
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We're discussing home schooling/private schools vs public education,
And I have already plainly stated why private schools perform better-- parental involvement in the child's education being the primary factor. This is common knowledge to educators. Children who have parents involved in their education almost always outperform their peers. You're comparing the averages, but if you compared student to student under those variables, I assure you there would be no significant difference between public and private schools.
And fyi, private school teachers are often payed less than or equal to their public school counterparts, and they're generally not more qualified either.
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Let's agree, at least, that private schools, dollar for dollar educates more efficiently than public schools, be that in terms of test scores, college bound freshmen percentages, or class size.
Class size is an important factor. It really should be legislated that there be at minimum one teacher and one classroom to every 20 students. However, the fact that there is not and that private/home schooling has a better teacher:student ratio is a good example of how class stratification affects children where it should affect them the least.
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Bill Gates was a genius too and made gajillions.
Probably not the best example anyway. His gajillions were at least as much a result of theivery (or we'll just say... capitolistic opportunism) as genius.
Allow me to reiterate the key point here:
If you are involved in your child's education, it won't matter whether your child goes to public or private school. If anything, they'll probably be better off in the public school because of the exposure they'll have to a demographic of children and families that they need to know about.