The teacher writes ON the black board. The word IN means inside, examples You put water in a glass. You put the letter in the envelope. We found a present in the box.
The teacher writes on the blackboard, The box is on the table. You type on your keyboard.
Anyway to answer the question, that is the most efficient way to show the entire class the problem and answers and for some people seeing something visually as well as hearing it helps them to learn quicker.
Because it's easier for some people to interact with the teacher visually. If you work out a problem and get the answer, they can understand how they got that answer. They can also ask questions about the problem. Why was it worked out the way it was? Where did that 2 come from? Why did that positive change to a negative? Sometimes she's not giving the answer. It's just a example. That must be why you're failing English class.