I want to memorize this table with it’s meaning. Not Verbatim in any way, I would like to be able to recall instantly the correct cases for sentences. Do you have any sugge
sted methods of memorization?
I would make a story between the meaning in German and English.
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The prepositions you mention are all two-way prepositions; that is, they are able to support both the accusative (direct object) and the dative (indirect object) cases.
Notice that whenever an action involves motion, it receives the accusative; when there is only a state of being or a location without motion, it receives the dative. This is the most important rule. (There are edge cases, like “Ich schwimme in dem = im Schwimmbad”: “I swim in the swimming pool”, in which motion exists, but it is within the swimming pool itself, and therefore receives the dative.)
As for the articles themselves, they receive the following transformations:
Accusative: das → das; der → den; die → die; die (plural) → die
Dative: das → dem; der → dem; die → der; die (plural) → den
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