# Multilingual classroom

Having pupils of many different native languages, and many languages in general, has been getting quite common in Norwegian classrooms, too. In many other countries this has been reality for a long time. In any case, a quick classification of what to do about this:

1. Go monolingual.
2. Allow pupils talking to each other in other languages, but otherwise monolingual.
3. Name some object in several languages or otherwise allow explaining concepts in several languages.
4. Use the different languages as a strength and use them to bring forth new mathematical ideas.

Number four is the ambition here.

# Polygon, an example

• In Finnish, monikulmio, with moni- referring to many and kulmio to a collection of corners/angles.
• In Swedish, månghörning, with mång- referring to many and hörning to corner.
• In Norwegian, mang(e)kant, with mange meaning many and kant meaning side. Also polygon.
• In English, polygon is Greek to most natives and also my students (and everyone else), but there are many angles there, even if most language users do not know about it.

Of these Norwegian has the interesting feature of counting how many sides there are, as opposed to corners or angles. This is a mathematical distinction encoded in the language.

Another common, but kind of trivial, example is the number system, with 72 being anything from 70+2, 2+70, $$2+ (4 - 1/2) \cdot 20$$ to 60+12 in some European languages, doubtless with more diversity available.

# The request

I would love to have more example of where different languages express the same concept in mathematically distinct ways, like polygon above. Ideally the concepts are relevant at school, and thus also in teacher education.

• I live in Belgium and I can tell you that, from the moment you accept another language to be used in your class, you won't be able to stop the multilingual flood which will tsunami you. Therefore, how difficult and unnatural it might seem, consider the usage of just one language in your classroom. Commented Jun 6 at 9:22
• Russian for set, множество, means multitude. Russian for odd, нечетный, means not-even. Are these the kind of examples you are looking for? Commented Jun 7 at 0:36
• Off the top of my head I can think of many examples between Chinese and English. The word for polygon in Chinese also refers to sides and not angles. Fractions are read with the denominator first. An interesting one is that equations are called 方程, fangcheng, which roughly means “rectangular array,” for historical reasons that are explained in the link. Commented Jun 7 at 0:41
• @user58697 I think the word for odd being not-even is common in a lot of languages, it's also true in German and French, my guess would be that English having a special word is the exception. Commented Jun 7 at 13:22
• @quarague The words for odd in English, Swedish and Icelandic all come from the same word in Old Norse. Greek also has distinct words for odd and even. Outside of Europe, Arabic does as well, and Chinese and the languages it influenced too. Commented Jun 8 at 0:36

When I introduce the concept of an antiderivative in my calculus class, I mention that in my native German, it is called a Stammfunktion (stem-function, with "stem" as in "source", "original"), and claim that both words describe the concept well.

Likewise, I mention the German word for continuous is stetig, cognate to English steady, another good word for the concept.

• Compare with primitive for antiderivative, occasionally still used in English and certainly used in Dutch, where one refers to a primitieve or a primitieve functie and the verb form is primitiveren.
– J W
Commented Jun 8 at 17:37
• Interesting that the German word for continuous is stetig, cognate to steady, as continuous functions can be wildly oscillating and not steady at all in the normal sense, at least, of the English word. This isn't meant at all as a critical remark by the way, just an observation. I would gladly be better informed about the thinking behind the steadiness of continuity. Is it because there are no sudden jumps?
– J W
Commented Jun 8 at 17:56
• @JW, I'd think that the cold fact that most continuous functions are not "steady" does not invalidate the "intention" of thinking of steadiness. :) Commented Jun 8 at 20:27
• @paulgarrett: Fair enough. Anyway, generally curious about the thoughts behind terminological choices, at least when they have been recorded or failing that, can be inferred or even just surmised.
– J W
Commented Jun 8 at 21:18