I know that question sounds confusing, but let me explain.
Alice was walking down the street when she met John. Instead of saying, "John, please listen to me.", Alice speaks as if she is John, "Will I listen to Alice, please?" Its not third person, because in third person it would be "John, please listen to Alice."
At home, if Alice wants to know if her son has finished his homework, she looks at her son and asks, "Did I do my home work?"
Alice's husband Bob comes home and to enquire if Bob has gotten the eggs, Alice asks, "Did I get the eggs?"
Alice when teaching her 3 year old daughter how to write the letter 'E' says, "I will draw three horizontal lines and then a vertical line to the left."
Alice wants to go to the movies, so she asks Bob, "I shall get two movie tickets when I come back from work tomorrow."
What kind of speeh is Alice using? It's not third person. It is more like Alice is assuming that she is the person she is addressing and speaks like she is them. And why do some people talk like this? I have noticed that this most common among teachers. "To produce this chemical compound, I shall add this base to this acid", " To integrate this function, I shall do a partial fraction decomposition", etc. They speak as if they are the student.
What is this form of speech and why do some people speak this way?