Do home-schooled children suffer from any negative discrimination when it comes to college applications?
We have a 10th grader who is looking at colleges. We have been to visit a few places, private Catholic and non-Catholic and public. All of them are very open to homeschool students. Some of them, in fact, voice a preference for homeschooled students because they have better study skills than their public school counterparts. Homeschool students are often very goal oriented and are more well rounded.
Is it difficult to keep the children educated in math and science at a level comparable to their public school peers?
Our 5th grader is one year ahead of his peers in math and he is studying science that he is actually interested in. When we pulled him out of public school in 3rd grade, he was still doing simple addition problems. He was being timed in math problems, so he could do them really fast in order to pass their tests. However, he was incredibly bored. When we started homeschool, we enrolled him in a math grade ahead and he caught on really quickly. This year he is doing well. He will probably be ready for algebra by 7th grade.
On the other hand, our 10th grader, who was in public school through 9th grade has struggled with geometry since day one---it's taken him over a year to grasp the concepts. And this was an "advanced" math student in high school.
We have had the same experience with science. Our 10th grader struggled through chemistry. He probably couldn't tell you anything useful about it. Yet he was a "super" public school student.
Our 5th grader chose his curriculum this year---flying creatures---he has learned so much. A lot more than he would have learned in public school.
Science in public school is pure propaganda so your children will be convinced of evolution and the non-superiority of humans.
What about children that attend private school at traditional chapels?
I don't know any children, personally, who attend an SSPX school. I do know of a few families who have moved to be near the SSPX school for their children. However, I do not know what their education is like.