As a teacher for 37 years, and a parent of three children, I'm convinced that the problem with being too involved in your children's education is that your children risk being too dependent on your help. They start thinking that without parental help they can't achieve. By high school age, many of my students who had had hovering parents went on strike, and did little or nothing.
The critical job for parents is to install a love of reading in their children. That is a more precious gift than a Harvard education.