The way to start writing a research paper on this excellent short story would be to identify one central theme or meaning depicted in this tale that you feel confident enough to write about. The main theme, arguably, is that of coming of age, as the speaker goes through an experience where he allegorically attends the school of life and reflects on the different struggles and aspects of learning that he went through in order to become old. Of course, the allegory of this tale relates school to life, and thus the action of the protagonist in attending school and what he learns whilst at school becomes incredibly important. Note, for example, how the speaker describes his initial enjoyment in school and what it was like:
We submitted to the facts, and this submission brought a sort of contentment. Living
beings were drawn to other living beings, and from the first moments my heart made friends
with such boys as were to be my friends and fell in love with such girls as I was to be in love
with, so that it seemed my misgivings had had no basis. I had never imagined school would
have this rich variety.
Even after the protagonist realises that there is more to "school" than simple pleasures and enjoyments, and he learns to anticipate and cope with "dust-laden winds and unexpected accidents," it is clear that he is still learning and still advancing through being exposed to the various situations he faces at school. The story focuses on school as an allegory for the different stages of life, and the protagonist therefore moves from a state of innocence, where school is about play and enjoyment, to a position of facing the difficulties of school, and then accepting that life is made up on nothing more than "exertion, struggle and perseverance." It is only at the end of the school day that the protagonist realises that his whole life has been squashed into one school day, and the grandfather that he has become has learnt the lessons of life from this single day in school. Your research paper then could explore the way this allegory works and how Mahfouz uses a day at school and the various things that the protagonist learns to mirror the different stages of life, and how he navigates these different phases.