However, the usefulness of mother tongues should not be dismissed prematurely, as each mother tongue has its advantages.

Which word is the closest in meaning to the word "prematurely" in the above sentence?

1)initially 2) childishly 3) impulsively 4) early

Whenever you need to know synonyms for words, use http://www.thesaurus.com.

Go there and enter prematurely, and let me know what you discover.

It means early. But looking at the context of the sentence, "impulsively" seems to fit the sentence better than "early". The answer given in the answer key is option 3. I chose option 4 originally. Can someone explain? I'm confused.

I would have chosen 4, too, but you're right that in the context of that sentence, 3 makes better sense.

I got this question from an assessment book. Is the answer key wrong? Typo error?

Without a sentence (context for the word), 4 is the best synonym for "prematurely."

HOWEVER, in this particular sentence (the context for the word), 3 makes better sense.

Words taken out of context leave a whole lot of options open. (This is why I'm impatient when a student posts 2 lines out of a long poem and is supposed to come up with an interpretation! The ideas have to come from the whole poem or at least the whole stanza, not just 2 lines.)

Below is the entire passage. The word "prematurely" is from the third paragraph.

Some of us are brought up in an English speaking environment, while others are brought up in Mandarin speaking families. This heavily shapes the language that we are most proficient in. A common observation is that many often struggle with their second language.
While the government's stand on bilingualism may be unpopular, it does have its merits. Firstly, English was and will continue to be the undisputed lingua franca. Without a solid grasp of English, Singapore would suffer in terms of foreign investments. Many multinational corporations originate from Western countries where English is the medium of communication. When such firms shift their operations to another country, they employ a sizeable number of employees from the local workforce. If the local workforce is incapable of speaking English, a language barrier would be created. This serves as a disincentive when multinational corporations decide where to outsource their operations to.
However, the usefulness of mother tongues should not be dismissed prematurely, as each mother tongue has its advantages. Singapore is surrounded by many countries where Malay is their first language. Having a language in common with one's neighbours would certainly do no harm to international relations. Another development over the past forty or so years is China's rise to become one of the biggest economies in the world, making the Chinese language useful when dealing with Chinese firms.
Though people from English speaking backgrounds may find it challenging to learn Mandarin and vice versa, we should not throw in the towel, for our problems do not exist because we lack the aptitude, but simply because we need more practice and exposure to the language. All we need to do is leave our comfort zone and spend more time engaging others by using our weaker language. Yes, the road to being bilingual can be likened to an uphill battle, but it is a process that is richly rewarding.

Yes, it still is something of a toss-up between 3 and 4, right?

Literally, it means "too early" or "too quickly" in that sentence in that paragraph. However, since "too early" is not a choice, "impulsively" is better.