New "Math" skill in German
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A number of new skills have been added to the German tree. I was glad to see "Math" as one of them, but it only has the one lesson, and only introduces three operators (plus minus gleich). I use maths on a daily basis, and Germany's employment market is very inclined towards technical skills, so I see this as a bit of a wasted opportunity. How about including the following: division and multiplication, raising to powers, how to express decimal fractions and statistics (samples, averages, etc.) as these all come up time and time again. I know that this could be regarded as an "optional" skill, but given that a lot of people now want to work in Germany, rather than just visit, and this is the vocab people need.
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Division: Division (just german pronunciation) but in real life people say: 5 geteilt durch 5 = 1 instead of 5 dividiert durch 5 = 1 (but both are correct)

Multiplikation: multiplication but people say: 5 mal 5 = 25 instead of 5 multipliziert mit 5 = 25

Exponenten are your raising to powers. B^e  Basis hoch dem exponenten: 2 hoch 3 = 8

Brüche: fractions  Zähler / Nenner  2/3  2 Drittel. The Nenner uses for the most part the system "number"tel  VierTEL, FünfTEL, s SechsTEL, .... ZehnTEL, .... hundertsTEL. Some exceptions: 1/2 = ein halb, 5 / 2 = fünf halbe, 1/3 = ein Drittel, 6 / 1 = sechs

average = Durchschnitt
tbh a real math skill would certainly help in other languages as well, because I can't help you with the rest. ...
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All well, but consider that the fractions are written with a capital letter (they are nouns, after all). So it would be zwei Drittel, Viertel, Fünftel, Hundertstel, fünf Halbe, etc.
That is not true. According to Duden (http://www.duden.de/sprachwissen/sprachratgeber/grundzahlenundbruchzahlen) you only write the fractions capitalized if they are use as a substantive (Ich sah zwei Drittel des Films  I saw two thirds of the film) or they are joined with a noun (Zweidrittelmehrheit  Two thirds majority). Otherwise fractions are not capitalised and written separated.
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According to the source you mention (and to my knowledge) you always write the fractions with capitals except if they are used as an attribute.
So if you want to say "The result of this equation is 2/3" you would write "Das Ergebnis dieser Rechnung ist zwei Drittel." Which is how I understood the numbers given in the original posting.
You are right of course, that if we are eating half a chicken, this would be "Wir essen ein halbes Hähnchen", as the fracture is used like an adjective in this case.
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I agree. All languages should have this. I really struggle with numbers in all my languages (I don't struggle with math in my native language so it's not anxiety about that). Even though I have them memorized, when I'm reading to myself and I see a figure or a year, I conceptualize it in English every single time. Same with dates. I will read "Ein Jahr hat 12 Monate" as "Ein Jahr hat TWELVE Monate" even though I know the word is zwolf. Doing math problems seems to be a good way to get out of that habit. Maybe there are lessons on Memrise, but Duo is better for this because they can vary the questions more.
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I think this goes for everyone who has learned 2+ languages.
Most people only feel comfortable to count and use numbers in their native tongue. It is very hard, if not impossible, to train away the instinct to use your "native numbers" completely.
Adding to terms kunstkr1tik stated:
 Statistics (Statistik):
 Stichprobe (sample), eine Stichprobe ziehen (to sample, in the sense of random sample, otherwise regular sampling is "abtasten").
 Zufall (Chance), Zufällig (randomness), Verteilung (distribution), Normalverteilung / Gaußverteilung (normal / gaussian distribution), Wahrscheinlichkeit (Probability), Zufallsvariable (random variable).
Personally I think most terms you can easily learn on your own. As you have seen from these operators, most words in math have a root in latin or greek and you will readily recognise them (Funktion, Variable), and if you have had any linear algebra you already know most of the specific terms ;).
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A "math help" website in the target language is perfect for this.
It'd be good for Duolingo to include some basic terms (plus, minus, add, subtract) for each language, but I respectfully disagree that thoroughly teaching math vocabulary is something Duolingo should do. Duolingo is an amazingly effective general introduction to a language, and teaching specialized vocabulary would be counter to this. It's effective as a general introduction precisely because it does not dwell long on any subject. The Food skill teaches the word apple, but not enough words to follow recipes. The Politics skill teaches the words crime and lawyer, but not enough to discuss a courtroom hearing.
Additionally, while the format is great for a general introduction, it's not great for thoroughly learning a subject, particularly something that requires as much structured learning as math. I have yet to even be able to count to 20 from a Duolingo course. "One, two, three," "He won a thousand dollars," "Seven, eight, nine"... I'd rather not have to try to relearn math in this fashion to progress through a tree.
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It could be added as an optional skill we equip with lingots though. I'm not sure if there are additional skills that aren't showing up in the store at my current level, but it kind of bothers me that there's 3 slots and only 2 skills available for purchase.
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Probably a lot of that was considered, but in the end they had to make the cut somewhere. The tree can only be so long and teach so many words. But I agree that the German "Math" skill is a little bare and maybe could have been fleshed out a bit more. I think it would have been a great place to introduce some useful geometrical terms like Viereck, Dreieck, Winkel. Durch and mal also would have been good additions, but I think that other contexts for those words are already taught elsewhere, so the duolingo structure may not allow them to be reintroduced.