In a college biology class, I was learning about the difference between mitosis and meiosis. If you have learned this concept yourself, you know it can be very confusing to keep the movement of the chromatids straight at each phase of the process. As I wrote last year, images are helpful, but because it is dynamic process, they were not helping me see how things moved from on phase to another. The professor knew this, so he had us all stand up. We began in a clump at the center of the room (cell). As we moved into prophase, metaphase, anaphase, and telophase, he had us move toward partners and away from other groups until we finally had split into two classes (daughter cells). He was taking advantage of movement for encoding.
Was it because we were a room full of kinesthetic learners? Nope. At the time, because I didn't know learning styles were a myth, I would have called myself an auditory learner, but experiencing the motion of each phase did help me encode each one better than words alone (or even words with images) would have. I would like to point out, though, that the movement alone wouldn't have been helpful without explicit explanation coming first. The movement helped cement the learning, but it did not teach mitosis to me.
Gesture has become all the rage, but there is still much research to be done on its effectiveness. As with a lot of things in science, the results of experiment are very specific to content and context. So, the conclusion seems to be that some types of gesture help some kids learn some content. Given that there is zero cost to implementing it and it will help a bit with engagement, I say it is worth trying. It can be as complex as the "dance steps" we did for mitosis. It can also be as simple as having students hold up a circle with their hands to indicate a zero.
Content which involves relationships in three dimensional space benefit from use of moving the body to represent those relationships. Mitosis is one example, but as a physics student, I was taught the "right hand rules" to help with analyzing the relationship between electrical current, magnetic fields, and force. Each pair of those has a perpendicular effect on the third one. Unless you are already quite familiar with this topic, that explanation was probably confusing. It will help if you see this picture, but nothing helps as much as students twisting their hands to the orientation of the set up described in the problem. One only needs to walk into the test on this chapter and see students silently doing that exact thing to know how much it helps.
Since the research is fairly new, there are a wide variety of hypotheses about why it works and no solid conclusions. Some have posed that it provides an offload to working memory. If I can hold the number 3 that I'm going to need in a second in my hand, I don't have to hold it in my brain. I've done this without meaning to while teaching cycle classes. If I know we are going to increase tension 6 times, I'll have four fingers resting on the handlebar, so I can tell my class, "This one is number 5 of 6." If an anatomy student is pointing at her own femur while rehearsing proximal and distal attachments, she won't have to look back at a diagram to remember which part she is dealing with. The gesture might serve as a physical mnemonic device, reminding you of the thing it symbolizes. Like I said, the research is too new to have drawn any meaningful conclusion about the mechanisms just yet.
We all know the power of muscle memory for physical activities, like dance and sports. Muscles are meat, so they don't actually remember, but a well myelinated pathway from repeated practice is how we make learning permanent.
If you want to implement this is your classrooms, start slowly. There is no need to insist that every piece of content have a motion or gesture, and the research doesn't support that anyway. I would suggest the use of movements and gestures will only be really helpful if they are natural. If you have to think hard to come up with a gesture and force it to fit, it will likely not be beneficial.