Learn Hardcore German: Während des Trainings untersuchte der Trainer unsere Technik genau. - During practice the coach examined our technique carefully.

Während is one of a handful of prepositions in German that govern the genitive. When you use während to mean “during,” you must put the noun phrase in the genitive. Hence des Trainings (genitive singular of das Training) rather than dem Training (dative).

What’s the difference between saying während des Trainings and beim Training?

Beim is a contraction of bei dem and takes the dative. So beim Training (“at/during the training”) is a perfectly natural, slightly more colloquial alternative. Während des Trainings (genitive) is a bit more formal or written, but both mean roughly “while the training was going on.”

Why does the finite verb untersuchte come before the subject der Trainer?

German is a verb-second (V2) language. When an adverbial phrase like Während des Trainings opens the sentence, it counts as the first element. The finite verb must then occupy the second position, so untersuchte precedes the subject der Trainer.

Why is untersuchte in the simple past (Präteritum) instead of Perfekt?

In German narrative or written descriptions of events, the Präteritum (simple past) is preferred for verbs like untersuchen. In spoken everyday German, you might hear hat untersucht (Perfekt), but in a written report or story, untersuchte is more common.

Why is genau placed at the end of the sentence?

Genau is an adverb of manner (“precisely,” “thoroughly”). German word-order for adverbs of manner is flexible, but they often appear after the object to put emphasis on how the action was done: […] unsere Technik genau.

Why does Training get an -s ending in des Trainings?

In German, neuter (and many masculine) nouns add -s (or -es) in the genitive singular. Even though Training is a loanword, it follows this pattern, so you get des Trainings.

Could I express the same idea with a subordinate clause, like Während wir trainierten?

Yes. You could say:
Während wir trainierten, untersuchte der Trainer unsere Technik genau.
Here während introduces a subordinate clause, so the verb trainierten goes to the end of that clause. Both forms are correct; one uses a noun phrase in the genitive, the other a full subordinate clause.

Why is Technik feminine, and why is the possessive unsere used?

Technik (technology/technique) is a feminine noun in German, so its article in the accusative would be die Technik. A possessive pronoun replacing die must agree in gender and case, yielding unsere Technik for “our technique” as a direct object (feminine accusative).