"Die," "Das," "Der," and "Den"
Is there any good heuristic for judging when 'tis appropriate to use these articles? I continue to get tripped up by this.
Die: Feminine and plural (most nouns ending in -e are feminine)
Der: Masculine (most nouns are masculine) and dative/genitive feminine and genitive plural (http://german.about.com/library/blcase_sum.htm)
Das: Neuter (no real way to tell, but most nouns beginning with ge- are neuter and also nouns ending in -lein/-chen)
Den: Masculine accusative and plural dative (refer to above link)
I hope this helps in some way :)
I'm afraid it is terribly confusing for non-native speakers. (By the way, while it comes natural to me in my native German, I have exactly the same kind of problem trying to learn Russian.)
One problem is that there is no general rule for the genders of nouns. General advice for learning it is to always memorise German nouns complete with the definite article. This hardly takes more mental effort than memorising just the nouns.
The other problem is that der and die switch roles for some gender/case/number combinations. E.g., whereas in nominative singular (subject case) we have der Mann, die Frau (this is what you should memorise), in genitive singular this becomes des Mannes, der Frau and in nominative plural it becomes die Männer, die Frauen. The only thing that helps with this problem is practice, practice, practice.
Fortunately, both problems are not very critical in the sense that native speakers are used to non-native speakers getting it wrong all the time, and it doesn't really hinder communication. Unfortunately, Duolingo has no mercy if you get an article wrong.
The normal method is to learn the gender of a noun along with the noun by learning the noun complete with its definite article, e.g.: der Mann, die Frau, das Kind. It's only a little bit harder than just learning the nouns.
The other thing is understanding how the definite articles change for the three grammatical genders with the other three cases. This is totally systematic, though the system doesn't really make sense.
Unfortunately, you need to get a table and learn how it works. (Alexinireland posted an explanation that contains such a table.) Which article you need depends on the following information:
- the case of the noun (nominative, genitive, dative, accusative)
- whether the noun is in singular or plural
- the gender of the noun (only if the noun is in singular).
Or you can use the following, which has all examples in the order nominative / genitive / dative / accusative.
- Plural: die Menschen / der Menschen / den Menschen / die Menschen
- Singular feminine: die Frau / der Frau / der Frau / die Frau
- Singular masculine: der Mann / des Mann(e)s / dem Mann(e) / den Mann
- Singular neuter: das Kind / des Kind(e)s / dem Kind(e) / das Kind
This system is totally chaotic. The only regularity I can see is that feminine singular is almost like plural, and neuter singular is somewhat similar to masculine singular. Also accusative is almost like Nominative.
These complications do not have a purpose. They just happened accidentally during language change. At some point they will disappear. In English and Dutch this has already happened. (They used to have the same complicated system.)