I am giving some lectures on a calculus course in Norwegian. My Norwegian (or, rather, Scandinavic) is good enough to do so mostly without resorting to English, but I would, of course, like to improve.

In particular I have problems in understanding questions from the audience; big reason being, I suppose, that I can not anticipate what they are asking and so understanding the question is much harder. But sometimes spontanous explanations I want to give during the lecture also stumble and I have to use non-native expressions or resort to English. Sometimes, notation also causes problems, as discussed here: Resources for reading mathematics out loud in different languages

What are best practices for preparing a (fairly traditional) lecture in a language one is not yet fluent in, given a large undergraduate calculus course as the specific context?

As per the usual Stack exchange best practices on subjective questions, please base your answer on personal experience or sources you cite. See https://matheducators.meta.stackexchange.com/a/41/2083 and especially the linked blog post.

  • $\begingroup$ A thought from a non-teacher: this could be an opportunity for students to practise expressing mathematical ideas in clear language. For example, one student might have a question that's hard for you to follow. Another student might be able to interpret the question into easier Norwegian . . . Also, is "Kan du si det som om det var skrevet på bokmål?' an option? (I'm guessing' "på finsk" probably isn't .) $\endgroup$ – timtfj Jan 24 '19 at 17:23
  • $\begingroup$ @timtfj Asking for bokmål might be a good idea; speaking with foreigners does not come naturally to many people, it seems. Though dialects have not been a problem, thus far. $\endgroup$ – Tommi Jan 24 '19 at 19:35

When I first started teaching in Spanish I wrote my lectures out in full before every class, something I would never do in English (my native language). This required consulting textbooks written in Spanish and speaking to other teachers to find out what is standard usage and mathematical terminology. Such consultation is essential. Since mathematical terminology mostly comes from English, French, and German there sometimes are not native Spanish expressiosn for technical terms. Dictionaries rarely are useful for finding out what is correct mathematical usage. Much mathematical terminology in Spanish originates in French usage rather than English usage.

When actually giving class, it is important to write everything that one says on the board. If students struggle with one's accent, at least they can read what one writes. For this it is of course important that what one writes be more or less correct grammatically and orthographically. For this one sometimes has to write lectures in far more detail than one would in one's native language.

Something I have encountered frequently is that theorems are known by different names in different cultures. The (some) theorem expressing the dimension of the space of solutions of a system of linear equations in terms of its rank is known as the Rouché-Frobenius theorem in Spain. It is called differently in other countries (in the US it doesn't usually get given a name). One needs to learn these local customary names and terminology. It helps for communicating with students. Otherwise what happens is that students know some theorem as Bolzano's theorem and don't realize the professor is talking about Bolzano's theorem because he calls it something else.

If one teaches at the university level, for example calculus or linear algebra, one needs to familiarize oneself with what is taught at the high school level. Terminology used in primary education is often peculiar, highly regional, and quite different from "professional" use. For example, in Spain what most (?) mathematicians would call "convex" is called "concave up" in high school, where students are taught to speak of "concave up" and "concave down". Teaching without awareness of such issues one can generate a lot of confusion.

I found that explaining math in a second language obliged me to use a simpler, more colloquial language than I would use in my native language. My experience was that this often was positive from the pedagogical point of view. For example, I found myself explaining Cavalieri's principle in terms of presliced loaves of bread. It's a helpful metaphor I continue to use now.

When giving exams, or any graded exercise, it is absolutely essential to have a mathematically competent native speaker proofread them carefully. I once (unknowingly) wrote a problem whose meaning changed materially depending on whether como/cómo had or lacked an accent mark.

Finally, the difficulty of teaching in a second language will not last long. There is probably no better way to improve at speaking and writing a language than by giving classes in that language.

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Since you seem interested in experience in a similar situation, I will share my experiences.

I moved overseas two years ago. The biggest help to thinking about math in a foreign language (in my case Hebrew) was to watch videos of professors teaching math in that language. I was lucky enough to find a coursera course given in Hebrew which really helped me to start to think about math in Hebrew. You might be interested in this article from the Independent which discusses how bilingual people process math differently in different languages. It will emphasize the importance of learning to think about math in foreign language. If you can't find a Coursera course or open university course, there is always youtube. The bottom line is that you don't want to think about math in English and translate to Norwegian - you want to start thinking about math in Norwegian.

I have also spent time reading math books which helps with the thinking, but created a different problem - that I often mispronounced words. This is very common. As a high school student I took a class at a local college with a non-native professor. He mispronounced words and none of us were comfortable asking, so we all got lost. I suggest that you tell the students that this is not your native language and you might mispronounce a word and ask them to correct you and/or ask if your pronunciation isn't clear. This will make them more sensitive to your predicament and perhaps more helpful

Good luck.

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    $\begingroup$ On the embarrassment about asking ppoint: I think explicitly asking the students "How do I pronounce this word?" early on might help overcome that. $\endgroup$ – timtfj Jan 25 '19 at 3:00

I have given lectures numerous times in Russian. The main hurdle at first was notation, since books never discuss this. Ahead of time I thought of a lot of the notation I would need (how to pronounce all the Latin and Greek letters, integrals over a space with respect to a measure, a mapping from one set to another, a congruence mod m, a quotient space, a dual space, etc.), wrote it all down on a sheet or two of paper, and with a couple of native speakers (more than one at the same time is useful to check their agreement!) went through all of it. Later if new notation came up I checked with native speakers before the lecture.

I prepared lectures thoroughly at first, and asked a native speaker to read them and correct errors. After doing this long enough, eventually I did not feel the need to have someone go over my notes in advance, but I might check with a native if there were some new technical phrases I was unsure about.

Like you, I was concerned at first about not understanding questions from the audience, but this was not a problem since if I could catch half the words in a question then I often could tell what they wanted to ask, and if I did not understand the question after 1 or 2 tries they asked me the question in English! One student by default always asked his questions in English (even if I stuck to Russian when replying). In your case, don't all students in Norway already know English?

Sometimes, in a smaller class, I was corrected by a student (e.g., when using the Russian for "remind" instead of "recall") or the students gave me tips about a simpler way to say something (analogous to "m halves" instead of "m divided by 2"), but there were never any problems with them understanding me language-wise. It is much easier for a native to understand their own language with some errors than a foreign language they are not used to (I did have students not yet used to understanding rapidly spoken English). As long as you have generally good knowledge of the grammar and can pronounce things mostly correctly, there shouldn't be a problem. But make sure to figure out how to say all the notation you need!!

The experience of lecturing definitely got me over the hang-up of being afraid to make mistakes when speaking in all settings, although I don't feel like it improved my comprehension of Russian in a comparable way since people on a train platform, say, tend not to be discussing unramified extensions of $p$-adic fields.

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Make a list of all relevant keywords in that particular language, and do two things with it:

  • Learn it by heart, and try to find out how those words are pronounced.
  • Make a copy of this, which you put on the desk before you while you are giving the lecture. It must be readable while you're standing up (use bold font and the size should be large enough (take a font size so that your page is just filled completely)).

At the beginning of the lecture, tell your audience that this is not your mother's tongue, you are trying your best but you might make mistakes while pronouncing local words (generally people are very understanding about this, especially when they belong to smaller language communities, like Scandinavian ones).

Once you are giving the lecture, when somebody asks you a question about such a word, always be sure to repeat the question. While you do that, take a peek at your list in order to be sure that you understand the word correctly. (This also gives you some time to think about the answer)

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  • $\begingroup$ A list written in big words might help, though I know most mathematics words well enough to not need that, it seems. It might increase confidence in any case. Communicating my skill level is done already. $\endgroup$ – Tommi Jan 24 '19 at 19:32
  • $\begingroup$ Also, is the answer based on experience in a similar situation? If so, how did it work? Adding this would improve the answer. $\endgroup$ – Tommi Jan 24 '19 at 19:34

KISS: Keep it simple, s...

Use small simple words versus trying for exact translations of the most complicated long words. Follow the text closely. Work example problems.

I think if you follow this course, you will avoid opening up communication challenges that would occur if you emphasize abstractions or the most fancy technical terms (not just in the immediate lecture. It's not just you spewing stuff out (but even there, I would worry that a translation may be imperfect) but in your inability to engage in discussion about most tricky abstract things during discussion because of adding language barrier to the other issues.

Take an approach of "three quarters of a loaf is better than none" and "perfect is the enemy of better". Go in and give them a solid problem solving hour that helps them with their homework. This will be time well spent.

P.s. I hope these are not the same students who you are also trying to push more proofy non-proofs onto (separate question). If so, you are really borrowing trouble.

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  • $\begingroup$ Is the answer based on experience as a teacher or student in a similar situation? If so, did the students increase the abstraction level when it was tried? (The other question is the same course. I was being conservative and following the book, there.) $\endgroup$ – Tommi Jan 24 '19 at 19:30
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    $\begingroup$ In learning languages I've noticed, though, that technical words are often more obvious than everyday ones. Different languages often use the same word with minor adjustments (spelling, endings etc) to fit the language. And if one of those comes up, you know unambiguously what it means! So long technical words might sometimes be easier. $\endgroup$ – timtfj Jan 24 '19 at 19:49
  • $\begingroup$ @timtfj, as with all rules of thumb, there are exceptions. E.g. the anglophone world and the francophone world disagree on whether zero is a positive number / nombre positif. $\endgroup$ – Peter Taylor Jan 25 '19 at 8:49
  • $\begingroup$ @Peter Good and alarming point! Though I mean really that technical concepts might well use more recognisable terms than everyday ones—since the terms are likely to have only a technical meaning and to be shared between languages. $\endgroup$ – timtfj Jan 25 '19 at 12:54

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