Ethics of "recycling" assignments I can't think of a better title, feel free to edit.

I'm retaking a course at university, and the basic assessments are very similar; if I can assume that I'm studying effectively, could there be any issues with modifying my assignments to fit the new criteria, and effectively resubmitting them?

From my perspective, this cannot be collaboration or collusion, but it could be defined as plagiarism, at least by a computer. I don't see why I would have to reference my own work here if it is adapted from previous writings, is it therefore sensible to assume that there will be no complication from an ethical perspective?

I'm also interested in the general concept for academia - would I have to reference my previous writings, and if so, how?

Edit: Let me clarify that this particular case is not a significant assignment, but rather a small "checkpoint".
You need to ask your professor. Opinions about this may vary substantially from instructor to instructor. In additional a lot of can depend on the nature of the assignments (are you writing a paper on a topic of your choice, or proving a theorem that has been assigned to you, for example?). 

When writing scholarly papers, you should always cite your own work if it is relevant enough that you would have cited it had it had a different author. Furthermore, if you re-use any figures or substantial amount of text from a previous paper, you need to be careful to indicate this very clearly lest someone complain that you are committing self-plagiarism. (No judgement implied here; my own views on the issue of self-plagiarism are complicated and probably go beyond the scope of the question.)