Hi WarriorLite,
You're right--"improvement" is better than either of those. However, there is a significant difference between the two forms you posted. When you see an article (a, an, the) in front of an -ing word, then it is always a noun. Without the article, it may be a verb or modifier (although it could still be a noun, as in "Surfing is fun."). What you might notice, though, is that in correct GMAT usage, "ing" is not used to form a noun if there is an actual noun that could be used instead.
Thus, we see usages such as "a doubling" and "the splitting," because there are no such words as "doublement" or "splitment." "Double" and "split" can be nouns, but they denote things, not the events that "a doubling" or "the splitting" describe. (Notice the difference between "This action brought about a doubling of our profits" or "The dinosaurs witnessed the splitting of the earth's crust" and "He looks like my double" or "There is a split in my pants.") When there is an actual event noun rather than just an -ing adaptation ("improvement," "transmission," "production"), we use that. We would not want to say "I thank
Manhattan GMAT for the improving in my score," "Unsanitary conditions lead to the transmitting of disease," or "I watched a documentary on the producing of that movie." Notice that you can say "on the making of that movie," because there's no such word as "maketion."