In my country it is very common for courses to consist of two types of classes: lectures primarily focus on theoretical aspects of a topic and then after each lecture comes a corresponding “practice” class which covers practical aspects of the material from the preceding lecture, such as how to use it to solve exercises. These latter classes can be taught by the same professor or, quite often, by graduate students.
Is there a term for this kind of classes? If you are from another country, how can I concisely explain to you what these classes are for? How do I indicate in my CV that I was a teacher of such a “practical” part of a course?
As a person responsible for “practice” classes you have to plan them on your own (it is generally assumed that the topic of each class will be the same as that of the preceding lecture, but it is not a hard requirement and sometimes you might need to deviate); explain techniques and practical considerations; prove theorems (yourself or engaging the students) which didn’t fit into lectures because they were not required for the theoretical narration but rather have practical implications; solve exercises or have students solve them with your hints; etc. You are also responsible for designing and grading homework assignments, projects, tests.
In essence, professor “outsources” part of the course to you and then in the end gets your input about each student’s performance in it. The primary purpose is to divide students into smaller groups (of around 15 or less), each assigned to a separate teacher, so that each student gets more personal attention.