It is sometimes known as First Language (FL), Native Language (NL) or Arterial Language. Note that it is NOT always the language spoken by your mother!
It is usually the language learned in the home thus a bilingual child may well have two MTs.
A student's MT is of interest to teachers especially when it comes to what is known as MT influence. This is when the MT interferes with the learning of a second language later in life.
For example, a student growing up speaking Greek in the home could say in English class:
* I must to go!
This is a direct translation from the Greek where must is followed by the full infinitive (the infinitive with to).
Πρέπει να πάω!
In addition there is the issue of false friends here - words which look and/or sound very similar in the student's MT and English but which have very different meanings.
Should you use the students' MT in class? This is a debate which has gone on for many years and will undoubtedly continue to go on.
On one side of the argument is the idea that when a child learns a language they "pick it up" by being constantly exposed to it. To replicate this kind of situation in the classroom means banning all languages except English. Thus, it is reasoned, the student will, by being exposed to English only start to think and speak in English without any interference from their MT and achieve a greater understanding and better command of English since they are learning as a native speaker would.
The other side of the argument is that using the MT can be both time saving and ease understanding. For example, if you had to explain when we use the perfect tenses it may make a lot more sense to explain this using the students' MT and know that everyone in the room understands fully what you are saying than possibly explain in English and have half the students not quite sure of what you say.
With vocabulary, too, there can sometimes be obvious advantages in translating words or phrases into the students' MT: it's quicker and makes for better understanding. Teachers are often witness to the situation where they spend five minutes explaining a word in English only to have one member of the class realize its meaning, translate into the class' MT and then everyone writes the translation down. If the teacher knew this word in the students' MT, should they have just translated it for them?
But what do students think? One study suggests that students appreciate it if the teacher speaks their MT, however the more advanced they are in English the less they think their MT should be used in class.
If you do use the students' MT in the classroom, there are boundaries to be considered. It shouldn't be allowed to take over and as a teacher you should consider carefully when you can allow this. Tactics here could include: