I home schooled two of my children. The oldest went on to the young scholar program which partners colleges with high school students. He was the one of four students in the chemistry class to get an A. He also tested out of required math classes. The younger child went back into the public school system this year because of changed circumstances at home. She has been accepted by Johns Hopkins University to become part their special program for the top performing 95% elementary students in the world. She was also recommended by her school to attend a leadership conference for promising youth to be held for one week in Washington D.C. This honor is because of her intelligence, maturity, and leadership abilities.
Home schooling done correctly, using excellent text books, field trips which include museums, science museum, historical sites and the like, reinforce lessons. My 5th grade daughter just had a history question to be answered in essay form. She was the only one who could accurately name the generals at the Battle of Gettysburg. Most students thought President Lincoln fought there and didn't know that he actually delivered the Gettysburg address at the consecration ceremony of the cemetery.