In the first place, let's(let us) take our attention on(take attention on? that's weird... pay/turn/draw attention to is fine) the premier(former) perspective which states that we should do one thing at a time and then turn to another. This approach will really help us to(help someone do something is just fine. help someone to do something is démodé) devote all the energy on(devote somebody to OR dedicate something to, so you should choose either devote ourselves to OR dedicate all the energy to) one thing, as well as focus (on) all the outside material(what's outside material?? I didn't get it...) at the same time. Taking(Take) science research as a typical instance,(There should be a period instead of a comma.) since(Since) energy (resources) is(are) limited, scientists nowadays have no alternative but to concentrate their limited energy on one research within a certain period of time, otherwise(otherwise is an adverb, you cannot use an adverb to connect two sentences), their working period would be so long that other people(who is other people?) would probably achieve the final result in advance. (Take science research for a typical instance. Since the world is in short of many kinds of energy resources, scientists are trying their best to make full use of the resources, which means they have no option but to tackle one problem at a time, or it is next to impossible to achieve the goals they have planned.) The fact that subjects are becoming more and more intricate just demonstrate(s) that it is a trend that this world requires the capacity of doing one thing at a time in order to avoid energy dissipation.
On the other hand, with the tremendous speed(Good word!) of the modern world, there are growing opportunities appeared in front of us. However, just as the saying goes: "Time waits for no man". If we always do things one by one and permit no interrupt(interruption) at all, we would lose a fair proportion of chances. Also, some tasks really demand (objects cannot demand anything. try require) us to complete a serious(C'mon, dude, it's "series"!!) work at the same time. For instance, (the) IBT(iBT...) preparition(preparation), which includes listenning, speaking, reading and writing, requires us to prepare for them at the same time.(Try to express the same idea without using the same words. You can say "And, preparing the TOEFL iBT is the exact same situation where we have to study listening, speaking, reading and writing in a row.") Lacking any part of them, we cannot obtain high marks in the test. Therefore, the ability of doing a serious(SERIES!!!) of things simultaneously is no doubt of great significant.
In sum, based on the demonstration(s) (gave/showed/listed) above, it is partial to say that either do one thing or do many things at the same time is better, since both are (the) essential capability(capabilities) that this modern world calls for and hence training ourselves on both aspects("respects" is more frequently used) is necessary, as well as promising.
Advices:
1. Your logic is good enough. But I think you do need to make your sentence structure more complex, and by that, I don't mean you need to write long sentences. On the contrary, short but meaningful sentences are advisable.
2. I believe you will have time to check your typing mistakes while you are taking the real test, so, just pay more attention to the mis-spelled words. You can type a word in a wrong way, but you cannot do it in another way. i.e., it is okay if you type "serirs/seriws/serios" instead of "series", but you cannot make it "serious".
3. It seems that you are not dealing with prepositions very well, adverbs either.
4. You used a lot of fantastic words, as well as phrases, good. Keep on doing that!
5. Pay more attention to the verbs. Make yourself cleared with them, so you will know which can be used to describe an object and which can be used to describe a person.