Incorrect spelling


Incorrect spelling, explanation: improvment is incorrect because in the case of this word the e is not dropped and it looks more like it has more to do with improv (improvisation) rather than improve. What is more, is that the e between two consonants cannot be simply removed for no reason.

Correct spelling


Correct spelling, explanation: improvement is a noun derived from the verb improve. The noun-creating suffix -ment is added to change the grammatical function of the word, but it does not in any way change the word, as it is generally more comfortable for the speakers not to have too many consonants together.

Definition of improvement:
1. An upgrade; an act of making something better
The new equipment in the office has been a huge improvement for our comfort at work.
I think that there is still some room for improvement.