Well, there are many schools of thought when it comes to ESL learning. Now, I had studied these briefly in my education classes in college, but as my focus wasn't ESL, but rather general education, I'm a little fuzzy.
What we (Native English Teachers) should ideally be doing is a type of immersion program. We offer no supplemental (mother tongue) instruction, and speak only in English. This is compared to a 'sink-or-swim' approach. This has its benefits in that it forces students to quickly adapt and learn, but this is not true immersion. In the one hour that we have with them, students need to learn English in order to understand us, but outside of our classroom there is no external pressure to learn, so this isn't so much sink-or-swim as it is taking a bath. (HOLY RUN-ON SENTENCE, BATMAN)
(EDIT: This approach is the direct method. Thank you, Wikipedia)
Then, our co-teachers, in their regular classes, offer instruction in the mother language while teaching basic vocabulary and phrases. This is very academic, so in my opinion there is not much 'learning' happening here. Rather, this is an exercise in rote memorization. And although this highly technical style of learning teaches the mechanics of language, there is little art to it.
Now, in my first job as an elementary school NET, I utilized a little Korean. The only times I used Korean were to explain the rules of games (after I first said them in English), or to teach more advanced grammar. Slowly, but surely, with continued prompts, my students learned English and I could teach grammatical terms and content in all English. By the end of the year, I was explaining how to parse sentences in English and my students understood me.
This is because our minds create a bridge between terms. If someone who has never seen a donkey before is shown a donkey and told that it was a donkey, there is no prior knowledge for that person to build off of. However, if we were to explain this this animal (the donkey) is a cousin of the horse (which they are familiar with), then a bridge of knowledge can be created that links this new information to old information, thus helping to solidify its place in his/her brain.
It's the same principle. In order for ESL students to learn English, they cannot have vocabulary thrust upon them, that's why we use pictures and body language to convey our message and lesson.
But, if a NET were able to further create a bridge, by providing students with the Korean word/translation side-by-side, students can create a rock solid foundation with which to learn English. Also, a NET who is proficient in Korean can share cultural knowledge and provide a more appropriate translation.
EX.
A friend of mine stated, "Bah, humbug!" When a mutual Korean friend attempted to translate, he found that the word 'humbug' meant '사기' (fraud, or con). Of course, Koreans do not have the cultural knowledge of Ebenezer Scrooge, so a literal translation does not convey the feeling of the phrase. A NET who is proficient in Korean can provide a more appropriate translation and vice versa.