When an entity isn't associated with **many** other entity **at the same time**, should I still use many-to-many association?

For example, I understand that Author-Book relationship is a many to many, An author can write many books, a book can be written by many authors. This holds for all time.

Consider this situation. A Batch has many students at one particular time. If a student fails, he should move to the next junior batch. In other word, **A student cannot belong to more than one batch at the same time**. In this case, is this a many to many association? 

**Alternative Solution I thought:**
I was thinking about putting two columns in students table. `initial_batch` and `current_batch`. I can get the student's Batch history, by checking the gaps between current and initial batch, because of the rule **A student must drop to the next immediate batch**. Also, `batch.students` exists with a `has_many` association in rails. So, I think that would not be a big deal.

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By Batch, I mean batch of students get admitted in the same year.