There is a grammar inconsistency or glitch relevant to the previous queries. On another exercise in this lesson "Một đôi giày" and "đôi giày" were both included in a multiple choice question as being correct for "A pair of shoes". In yet another exercise "đôi giày" is translated as "the pair of shoes". I suggest reporting this issue until it is resolved. ;-p
With "một" it should only be translated as "a..." or "one.." but without it - well - Vietnamese just doesn't use articles, so it could be translated either way depending on context. For this course, with a classifier and without "một" it is usually translated as "the...", but what constitutes as a classifier for this word? Is "đôi" a classifier, or should there be another word in front of "đôi giày"?