My class is composed of international high school students coming from different countries and backgrounds. Hence different skills and needs. Our lingua franca is English and it is important to note that, in my school, no student (and actually, except for the English teachers, no teacher) is a native English speaker. They have intensive training in English, so after three years, they are fluent in English.
My question is about maths in English language for freshmen (around 15 years old teenagers): coming from environments with different expectations and emphasis on English education, their level vary greatly, from students that speak with ease to almost mute students.
My question: some students asked me to use a dictionary during examination. There is no policy about this in my school; how should I consider that demand?
My current answer was: electronic dictionaries/translators are forbidden, since I cannot check whether they can use it to cheat or not. I allowed a handwritten piece of paper (precisely, A5 paper, both sides) with two columns, one with English words, and the other with their translation in the language they want. No sentence or formula is allowed. The idea is that, by actively writing their own dictionary, they will memorize vocabulary. It also help them to analyze the course material and extract the important notions from it.
Is there any smarter way to deal with this situation? I have a limited sample to test the method but it seems to work. I would be interested in other ideas to improve the efficiency of learning mathematic terminology in English.
For example, is teaching the use of logic and set theory symbols in a more extensive way than the usual textbooks do a good idea? My intuition is that, if they deeply assimilate logical symbols, relying this assimilation to their mother language, I could use more symbolic notations in class, and they will interpret symbols in their own language. In a sense, they will develop a “mathematics-mother language” dictionary instead of a “Mathematics English-mother language” dictionary. The risk is that, if they have troubles understanding these notations, the accumulation of it will slow down their understanding of other notions.
The question is not exactly about Math Education per se, but I believe there are maths-specific answers.