Matthew Series -The Canaanite Woman

As Jesus continues into Gentile territory, a local woman comes to him in need. Jesus' first response is to reject her request and ignore her completely, and when she persists he explains that it's not right to take the children's bread and toss it to the dogs. But what does Jesus mean by these actions and how do they help clarify his mission? And just as puzzling: why, ultimately, does he agree to her request? What does this act (and the miraculous feeding that follows) indicate about the future of the Jesus movement?