Final answer:
Professor Quirrell taught Muggle Studies before Defense Against the Dark Arts, not concurrently with it. Therefore, none of the options (Potions, Transfiguration, Charms, History of Magic) are subjects that Quirrell held teaching positions for at the same time as Defense Against the Dark Arts.
Step-by-step explanation:
The student has asked what other class Professor Quirrell taught besides Defense Against the Dark Arts in the Harry Potter series. Professor Quirrell is first introduced in Harry Potter and the Sorcerer's Stone as the Defense Against the Dark Arts teacher.
However, there is no mention in the books of him teaching another subject at the same time as Defense Against the Dark Arts. Before taking on the Defense Against the Dark Arts position, Quirrell was the Muggle Studies professor, which is not one of the options provided in the question.
If we look closely at the options given, we find that none of them are subjects that Quirrell taught besides Defense Against the Dark Arts during the same time period. As such, none of the options - Potions, Transfiguration, Charms, or History of Magic - are correct, given the context that they are asking about concurrent teaching positions.
Therefore, based on the information available in the Harry Potter books, the correct option for what other subject Professor Quirrell taught before becoming the Defense Against the Dark Arts teacher is none of the options listed, as he previously taught Muggle Studies.