My oldest is only 6.5, so maybe it's different with an older child, but we have found it truly wonderful to have outside learning opportunities for our kids. Usually 4 days/week, they have at least one outside class. They take a homeschoolers' art class, creative movement, piano lessons, swimming, and sewing for homeschoolers. It really helps give structure to our days (we plan to do math and piano practice, for example, before leaving for swimming), and, frankly, on the days when we don't have *something* doing outside, we tend to stay in the house all day, and get cranky with each other. Also, some of these skills (like sewing) are things that the "schooled" friends aren't getting, so my kids get to exhibit mastery over some things, instead of feeling that the school kids are smarter than they are.
Mama to four great girls: 14 , 12 , 7 and 4