It is surprising to learn that teaching Torah on Shabbat should be restricted in any way. Nevertheless, our Gemara quotes a baraita according to which tinokot lo korim ba-tehilah be-Shabbat, ela shonim be-rishon – children should not be taught to read a new section on Shabbat, although they can review something that they have already learned.
The typical method of teaching that was practiced in Talmudic times was that the teacher would teach a passage to his students and review it with them until they were able to read it on their own. They would also add explanations appropriate to the age of the student. After the children learned how the passage should be pronounced properly, together with its explanation, they would review it over and over again (shonim be-rishon, shonim ba-sheni) until they learned it by heart. Only then would they continue on to the next passage. We can well understand that the very first interaction with the passage was the most difficult one, while subsequent review sessions – even the very first one, i.e. shonim be-rishon – became easier and easier.
Although Tosafot suggest that the reason to restrict an initial presentation of a lesson on Shabbat is because of a concern with oneg – that the child will find the lesson tedious and will be upset on Shabbat – the simple understanding of the Gemara is that our concern is with payment: the salary that the teacher will be paid for his work on Shabbat. If the teacher is getting paid for teaching proper pronunciation of the pasuk, the main “work” is getting the student to grasp the basics of the passage – i.e. the first presentation – while subsequent repetition is merely review. (There is another opinion that the teacher is getting paid more for his babysitting). Rashi suggests that the point of the baraita is to allow the first review, which is permissible and would not be considered to be payment for work on Shabbat, but certainly subsequent review would be permitted, as well.