Why are behaviors like spinning in an office chair, pacing, and fidgeting good for helping a person think?

I only recently learned about this, so don’t consider me an expert, but I believe it’s the same reason why stimulants are used to treat ADHD. The brain needs a certain level of excitation in order to concentrate on something, and if that level is not reached, you will consciously or subconsciously do something to increase that stimulation.

Only part of your brain is involved in higher functions like problem solving, so those other parts need to do something. Make sense?

Let’s off nervous energy I would think. Some people are more fidgity than others.

I believe it may be similar to white noise, which frees part of your mind so you can concentrate on the issue.

Sort of like what @YARNLADY said; once some areas of your brain that get in the way of creative thought are occupied otherwise, the creative areas are free to spawn answers to the problem. I find when i am trying to think on the spot that moving my eyes about in numerous spontaneous directions helps me out.

I believe it has to do with evolution. Physical movement is important in the evolution of higher intelligence. It is very natural for humans to “fidget/move while thinking”. I’m having trouble putting it into the right words. So, I searched the web and found this is closest to what I’m trying to say, although not as close I want ..lol:

“Step back a half-billion years ago, to when the first nerve cells developed. The original need for a nervous system was to coordinate movement, so an organism could go find food, instead of waiting for the food to come to it. Jellyfish and sea anemone, the first animals to create nerve cells, had a tremendous advantage over the sponges that waited brainlessly for dinner to arrive.
After millions of generations of experimentation, nervous systems evolved some amazing ways of going out to eat. But behind all the myriad forms of life today, the primary directive remains. Movement. In fact, a diminished ability to move is a good measure of aging. Inflexibility heralds death, while a flexible body and fluid mind are the hallmarks of youth.”
Source

When I’m thinking about something that’s more complex at home, I tend to have a tennis ball in my hand. It has helped my studying over the years as well.

I wonder if rhythmic activity has a calming effect, the way that rocking a baby does.

I do this!
The wife hates it when I’m on the phone because I can’t sit still and end up pacing up, down and roundabout. She also know when I’m thinking because my knee shakes like crazy or when watching TV I fiddle with the TV remote battery compartment (she has since cellotaped all these down so I don’t break anymore)

I find that meditation brings my thought process forward and allows me to think without restraint. There are studies on the brain wave patterns and when you are in Alpha it is far more creative then in Beta. You can with meditation change the brain wave pattern and go into the creative stage. Hypnotism can take you into the Alpha or Delta stage where suggestion is tremendously strong. If you get to the subconscious then you can really begin to find answers to lives questions. I would imagine that some can do the same thing with movement.

It helps you focus. Somehow, movement helps you screen out other stimuli and you can just focus on what you want to think about. I guess it’s like meditation, as @Summum says. You are stilling your linguistic mind, which allows you to access your non-linguistic mind—which is generally where most of the problem solving happens.

The brain works better with physical exertion. which is just one reason I do not understand why or even how parents tolerate conventional education systems