These children do best studying topics that interest them for extended periods of time. One gifted homeschooled boy became fascinated with trains. His family visited train shows, watched movies and documentaries about trains, and exhausted the library's supply of train-related books. This lasted almost a year. Although his "train period" was several years ago, the boy still remembers everything he learned, and is a walking train encyclopedia. He then chose to learn about World War II (after watching a documentary) and later, astronomy and physics. When my homeschool group attended a physics demonstration at a local college, this boy astounded the professors with his knowledge and questions (he was 11).
Gifted kids are often bored in school. Their quick minds are unable to comprehend why they are so bogged down with meaningless busywork, while they must rush through those subjects that do interest them. Many gifted programs do little to remedy this problem, and often involve nothing more than adding more difficult, meaningless busywork. Your son may not be motivated because he simply finds the material and presentation boring.
Parents of gifted children often find it difficult to make the transition from a schooled environment to homeschooling. They are not able to trust that their kids can and will learn on their own. You might want to try including some basics (spelling, math, reading), then let your son explore and learn on his own. I would definitely give him lots of space during the first year of homeschooling, and carefully observe how he learns and what his interests are. Turn off the TV, put away the Gameboys, and visit the library, museums, farms, historical societies, and other activities in your neighborhood or state. One homeschooled girl became fascinated with history after visiting a living history farm, and began to volunteer there. She became more involved, participated in and organized programs, and just received a scholarship based on her activities and interest in history. Gifted Education Comes Home: A Case for Self-Directed Homeschooling by Lisa Rivero explores the many benefits of homeschooling your gifted child.