One may not ride a regular two-wheeler bicycle, because this is a weekday activity (22:8 above). Even if a bicycle has training wheels, one may not ride it. However, small children may ride tricycles, because tricycles are only used by small children, and there is a significant difference between tricycles and bicycles. Therefore, riding them is not considered a weekday activity (above, 22:8 and n. 4).
Some allow children to ride scooters and wear skates on Shabbat. According to them, just as children may run on Shabbat, they may use scooters and skates. Opposing them are those who feel that while children may run on Shabbat, that permission is limited to unassisted movement. In contrast, using equipment that makes one move faster and more effectively is considered a weekday activity.
Even though those who are lenient here have an opinion on which to rely be-di’avad, it is proper to be stringent, since the stringent opinion seems more compelling. Just as the widespread practice is to refrain from riding bicycles because this is a weekday activity that clashes with the spirit of Shabbat, it is similarly inappropriate to use scooters or skates on Shabbat. Additionally, by our limiting small children to simpler games, older children will learn to dedicate Shabbat to Torah and to rest.