In our country, we are learning English as a foreign language, not as a second language. We teach English by using our mother tongue in some situations. Is it acceptable?
Whether or not you use the student's native language when teaching a foreign language depends mainly on two factors:
- the "distance" between the target language (here English) and the native language, and
- the theory of second language acquisition you subscribe to. (In discussions about such theories, the distinction between foreign language and second language is not very important.)
The distance in my first point refers to linguistic relatedness. For example, since English is a Germanic language, teaching English to native speakers of another Germanic language is typically easier than teaching it to native speakers of a very different language, e.g. Chinese, Japanese, Turkish or Finnish.
There are many kinds of theories about how a foreign language can or should be taught. Throughout history, there have been many methods and theories, including methods that relied on translation and methods that stressed the importance of using the target language only. There is a selective overview in a related question: What are the main foreign language teaching methods?
Methods that use only the target language for teaching the language are known as "direct methods"; these have been discussed in the question What are the advantages and disadvantages of direct methods (using only the target language)?.
It is definitely acceptable to use the student's native language. In the end, the deciding factor is what works.
The benefits of using the native language may depend on the learner's goals.
One such case is teaching industry-specific vocabulary to learners who are not very advanced in the language, but require it for professional purposes. It is often more efficient to use native terms that the learner is already familiar with.
For example, a nurse learning a foreign language with the purpose of starting a job abroad will likely find it more efficient to learn complex medical terms through their native equivalents instead of through definitions/usage in the target language (although the latter will surely be useful and even necessary as practice).