Wiktionary
square scooter
n. A square plank made from plastic or wood which is attached to four swivel casters at the corners.
Wikipedia
Square scooter
A square scooter or gym scooter is a square board made from plastic or wood with a swivel caster at each corner. It is primarily used in American Physical Education classes, particularly elementary or middle school. They came into great popularity across the United States in the late 1980s and early 1990s.
The scooter is ridden simply by sitting on it and using one's legs to pull or push it in any given direction. Some models feature hand guards on the side of the board, where it is often held. These scooters are used for a variety of games and activity, including variations on dodgeball and soccer.