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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.

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  • $\begingroup$ Not only logic and set theory have extensive symbolism. You could try learning notations for all sorts of math. You can mix them too (use logic and set theory symbols to express an algebraic answer.) It may be possible to make a test entirely notation. $\endgroup$ – PyRulez Apr 23 '15 at 10:47
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If possible, you should poll department members on this: whatever policy you come up with, you and the department will have to answer for it. If they can't help you, then take the time to register your actions with the administration (cover your work-related behind).

If you have a somewhat free hand and understanding/permissive administration, you might try the following: crowd-source a cheat sheet. Have several students submit the phrases and the one or two languages ahead of time, and then compile and handout for the exam the result. If something is lacking, allow them a 3x5 notecard (or whatever is appropriate) to account for discrepancy, but ideally everyone uses the same cheat sheet. If some of them turn in their part two weeks before the exam, that should give enough time to produce and show them the sheet before the exam. Bonus: you can use this with few modifications for next class. You can try a competition format, use the results to analyze student understanding, or spin this several ways for your and the class benefit.

Gerhard "Isn't Crowd-Sourcing A Great Idea?" Paseman, 2015.04.23

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