In the following sentence:
虽然练习做 ( ) 很多，但是我还是不懂。
We have a small discussion with our teacher. Which one should be used in the bracket and why?
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It should be '得'
In "做 (得) 很多", '得' functions as an "(degree/extend) particle" that indicate the degree or extend of the verb.
'很多'(a lot) is the degree or extend of the verb
得 (particle that indicate the degree of the verb)
多(a lot); 少(little) [degree]
得(particle that indicate the degree of the verb)
快(fast) ; 慢(slow) [degree]
Some people using 的 instead of 得 in this role because the two words sound similar.
Look at the follow sentences, and you can see 的 and 得 are not interchangeable
'要做' means 'need to do'
'要做的' means 'things need to be done'(pronoun)
'要做的(事)很多' means "a lot (of things) to do"
得 = (particle that indicate the degree of the verb)
It means "need to do a lot"
In this context 得 should be used. It works as a degree complement, and takes as a form of "verb + 得 + adjective". The phrase after 得 expresses the degree of the adjective.
So in this case,
, where 得 expresses the degree of "做" is "很多".
You shall also refer to this question, which explain the difference betwen 的, 得, and 地.
得 is probably ok, but I would use 了 or 过 for this context. It would become 虽然练习做 了（or 过）很多，但是我还是不懂。
得 is used for leading a degree complement, while 了 is used for the completion of a verb.
Logically, putting 了 or 过 as a completion is more appropriate I think. The logic is that although you have done(了) lots of practices, you still can not get it.