A ratio is a way of expressing the relationship between one quantity and another. If there is one teacher to fifty students, the teacher/student ratio is one to fifty, and the student/teacher ratio fifty to one. If a very dense but wealthy prince were being tutored by fifty teachers, the teacher/student ratio would be fifty to one, and the student/teacher ratio would be one to fifty. As you can see, the order in which the numbers are compared is important.
If you are campaigning for more individual attention in the classroom, you want a higher number of teachers, but a lower student/teacher ratio.