http://www.privatewriting.com/types-of-essays.html

This might help.

Thanks cat, that helps at least a bit.
Still, I'm wondering which term is used best when (English) students are taught to discuss a certain topic by giving arguments to support one side only. It cannot be something only German students have to learn, can it?

In England most examination questions are "open" - that is, it is up to the student whether he/she approaches the subject matter from a "linear" or "dialektische" standpoint, though the latter would be the norm. If a "linear Erörtung" is required this would be clear from the wording of the question. For example: "Discuss the reasons for the outbreak of World War One from a German perspective".

This is why this phrase is difficult to translate into meaningful English.