I can't say it's a reliable thing. Not enough that I chew gum as a habit. Can be an interesting thing though! It certainly doesn't make me less fluent and does feel like it helps sometimes.  I think the advice comes from this dude https://itotd.com/articles/4074/demosthenes-stones/ "The story is this. Demosthenes lived in Athens from 384 BCE to 322 BCE. As a young man, he suffered from a speech impediment—which may have been a stutter, an inability to pronounce the “r” sound, or both. He designed a series of exercises for himself to improve his speech. According to legend, he practiced speaking with stones in his mouth, which forced him to work very hard to get the sounds out. When his diction became clearer, he got rid of the stones and found he was able to enunciate much more effectively than before. He also practiced reciting speeches while running and speaking over the roar of ocean waves to improve his projection. These strategies must have worked, because Demosthenes achieved fame as the greatest orator in ancient Greece. He is best known for his passionate speeches urging the Greek citizens to defend themselves against invading Macedonian king Philip II." There is more to the story that needs historical context, like his later death is a tragic one but was due to the events of his time. Other philosophers suffered the same faith back then.  Have also had religious folks share this story with me. Found this snippet on google https://forward.com/culture/142439/did-moses-have-a-speech-impediment/ " [Exodus 4:10], Moses initially resists being God’s messenger because of his speech, saying: “Please, O Lord, I have never been a man of words…. I am heavy of mouth and heavy of tongue.” From this the rabbis concluded that Moses was a stutterer, which a story in the midrash attributes to his having burned his tongue on hot coals as an infant. " Edit: I included the last part because of this ancient fascination of stuttering and the belief that it was only a mechanical problem. I think that is where the talking with gum/candy/pebbles in mouth comes from. People just trying to explain speech oddities I think. Maybe others have an easier time thanks to gum I will be curious to read here!