Summarize:

Most autistic children engage in unusual motor movements – they jump, spin, twist their fingers, flap their arms, walk on their toes, and make strange faces. Like self-injurious behaviors, these motor movements are self-stimulating, but they are not harmful. Stimming helps children control their emotions, focus on tasks, prevent meltdowns from sensory overload, and feel good. (Tapping pencils, pacing, playing with hair, and tapping feet are all examples of stims that neurotypicals engage in too.) Never scold or mock your child for stimming, because this will harm their self-esteem and make coping more difficult. It is okay to casually let your child know that a stim looks odd. However, don't pass judgment or try to stamp it out of them. The stim may be very important to them. Let them choose whether it's worth the effort to redirect it or not, and give them your full support either way. If you spend lots of time engaged in playful interactions with your child, they will stim in moderation. Teach your child new games, and try to introduce imaginary play. Children who constantly stim are probably in need of more activity.  Trampolines, exercise balls, tree-climbing, swimming, recreational sports, and going on walks can help hyperactive children get the stimulation they need, so they can sit calmly during school. Keep plenty of fidget toys around. Your child may not sit still, but mild/moderate fidgeting can be enough to help them focus. Talk with teachers and aides to ensure that your child's peers learn good social skills and don't bully your child for being different. Autistic children should never be afraid to stim. Your child may enjoy playing with a doll's hair or fidgeting with a tangle. This allows your child to choose when they want to stim conspicuously, and when they prefer to stim in ways that don't attract attention. Encourage your child to explore with different stims so that they can choose the ones that are most comfortable to them.
Recognize that stimming, or unusual motor movements, are a normal and healthy part of the autism spectrum. Teach your child that stimming is okay, and that everyone stims to some extent. Offer plenty of stimulating attention. Make sure that your child's peers understand stimming. Provide toys for stimming.