Nathan and Sean were in the same math class. Their teacher returned the tests she had graded. When they saw their grades, Nathan
smiled, but Sean looked unhappy. The teacher said that many students had received low grades, and she hoped they would study more for the next test. Sean looked unhappy when he saw his test grade, so we can conclude that he most likely did not do as well as he would have liked. What does the teacher believe?
The teacher's expectations from what she said to Sean is that if he studies for the next exam he will do better. Therefore, she believes that it is necessary to prepare and study to obtain good grades that satisfy both the student and the teacher. This reasoning is applied in all subjects, not just mathematics.
This is a common pronoun hence one has to use a capital letter for a pronoun. Those are the name for things like the names of the cities or schools , general terms for common things.