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The answer is: It's up to you, and it depends on the context. I normally wouldn't chime in on academic writing, since we have experts here in APA and MLA, but this question seems to involve none of...
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#2: Initial revision
The answer is: It's up to you, and it depends on the context. I normally wouldn't chime in on academic writing, since we have experts here in APA and MLA, but this question seems to involve none of the usual academic style guides. To back up a little: What are often called "footnotes" are, in academic writing, meant to do one of a couple of things: (1) Clarify a point without interrupting the flow of the main text, or (2) serve as a mechanism for citations. (i.e., the citation will be in a footnote.) But this is how footnotes are used when following an academic style guide or departmental style sheet. In the context of your class, much depends on whether the essays your students are generating are on academic topics or a personal ones. In an academic context, having "additional thoughts" in footnotes could be seen as extraneous and amateurish. However, in a personal essay written for a class, "additional thoughts" might do well in footnotes. (Some writers have used footnotes in this manner in fiction.) Finally, keep in mind that conventions used in other languages may not be relevant in English, and you might decide to be firm with your students if these essays are on strict academic topics. But I assume these are not theses or academic papers for publication, where the formatting of citations and footnotes/endnotes is rigidly defined. Being close to the material, you can use your judgment to set guidelines for your students. (If you do decide to allow this, I suggest letting your students bound for academia know about how footnotes are used in strict academic contexts.)