After 28 years in the field of education I retired. I got rid of most of my notes and lesson materials, but I still remember a few things about stuttering. More boys than girls stutter, and more boys take it to adult life than girls. Out of many SLPs I have worked with, I didn’t meet one that was gifted in solving this mystery. Also, I learned that low functioning students could not easily or could not grasp a way to manage their speech. Younger students with speech errors have a fear of reading aloud in their classroom. It helps when we express this to the student’s teacher.
Via conversation, try to distinguish which vowels or beginning or middle of words are hardest through reading. Choose a story he or she wants to read and have them read to you. Have her correct sentences as she reads with a model and then without a model. If you can identify any words or sounds with a pattern, I can copy off paragraphs to read with multiple sounds of the word(s) in them. I did keep a speech book.
If you can find a pattern during conversation have her/him tap the table with a finger (for each word) when she slowly repeats (corrects) the words in the sentence. The plan is once they can successfully tap out each word in a regular pattern for some time, then he or she will be able to tap secretly under the table and then later perhaps on a knee, on or under a leg in a more private manner anywhere the student goes.
As far as I know, no one has proven a scientific reason for why people stutter. I did work with a few students who said that when they are excited (happy) or anxious they stutter more, but that is only my experience.
I hope this helps.