The pioneer girl in this painting is playing the Game of Graces, a popular activity for young girls during the early 1800s. Originally invented in France, it was called French Hoops. Considered a proper game for young ladies, it was designed to develop feminine grace.
Graces is played with two people. Each person gets two dowel rods. One of the players takes a wooden hoop and pulling apart the two rods sends the hoop into the air for the other player to try to catch. The winner is the player who is first to catch the hoop ten times.