Learn Hardcore Danish: Læreren arbejder på sit kontor. - The teacher works in his/her office.

So Læreren literally means the teacher.
You would only say Lærer by itself in things like job titles, headlines, or lists (e.g. Lærer søges = Teacher wanted), not in a normal sentence like this one.

Why does arbejder mean both works and is working?

Danish has only one present tense form, and it covers both the English simple present and present continuous.

Læreren arbejder på sit kontor.
= The teacher works in his/her office.
= The teacher is working in his/her office.

Context decides whether it is a general habit or something happening right now. If you really want to stress that it is happening right now, you can add an adverb like lige nu (right now):

Læreren arbejder lige nu på sit kontor.
= The teacher is working in his/her office right now.

Why is the preposition på used? Why not something that literally means in or at?

Danish prepositions do not match English one‑to‑one. With many places, Danish uses på where English might use in or at.

In this sentence:

på
- kontor → in/at (the) office

A few common place-nouns that often take på:

på arbejde = at work
på kontoret = at/in the office
på skolen = at school
på hospitalet = at the hospital

So Læreren arbejder på sit kontor. is naturally translated as The teacher is working in (or at) his/her office, even though på literally means on in many other contexts.

Why is it sit kontor and not hans kontor or hendes kontor?

Danish has a special set of reflexive possessive pronouns (sin / sit / sine) used when the possessor is the subject of the clause.

sin / sit / sine → his/her/its/their own (referring back to the subject)
hans / hendes → his / her (referring to someone else, not the subject)

In this sentence, the subject is Læreren (the teacher), and the office belongs to that same teacher. So you must use the reflexive form:

Læreren arbejder på sit kontor.
= The teacher works in his/her own office.

If you said:

Læreren arbejder på hans kontor.

this would normally mean:

The teacher is working in his office (some other man’s office, not the teacher’s).

Similarly:

Læreren arbejder på hendes kontor.
→ The teacher is working in her office (some other woman’s office).

Why is it sit kontor and not sin kontor?

The choice between sin, sit, and sine depends on the grammatical gender and number of the thing possessed, not the person owning it.

sin → with common gender singular nouns (en‑words)
sit → with neuter gender singular nouns (et‑words)
sine → with plural nouns (both genders)

Here, kontor is a neuter noun:

et kontor = an office
kontoret = the office

Since kontor is an et‑word and is singular, you must use sit:

sit kontor = his/her own office

If it were an en‑word, you would say sin:

en bil → sin bil (his/her own car)
et kontor → sit kontor (his/her own office)
bøger (plural) → sine bøger (his/her own books)

Could the sentence also be Læreren arbejder i sit kontor?

Native speakers overwhelmingly prefer på sit kontor here.
I sit kontor is technically possible, but it sounds odd or foreign in this context.

The usual pattern for this meaning is:

arbejde på kontor / på sit kontor / på kontoret

Use i when you really want to emphasize being inside something as a physical space:

i rummet = in the room
i bygningen = in the building

But with workplaces like kontor, skole, arbejde, the idiomatic choice is på:

Læreren arbejder på sit kontor. ✔
Læreren arbejder i sit kontor. ✖ (strange in normal usage)

Can I change the word order and say Læreren på sit kontor arbejder?

That word order is not natural standard Danish. The neutral order in a main clause is:

Subject – Verb – (Objects) – (Adverbials)
Læreren – arbejder – på sit kontor.

You can move the adverbial på sit kontor to the front to emphasize it, but then the verb must stay in the second position (the V2 rule):

På sit kontor arbejder læreren.
= In his/her office, the teacher is working.

So acceptable word orders include:

Læreren arbejder på sit kontor.
På sit kontor arbejder læreren.

but not:

Læreren på sit kontor arbejder. (ungrammatical in standard Danish)

How do you pronounce Læreren and arbejder?

Approximate pronunciation (standard Danish):

Læreren: [ˈlɛːɐ̯ʌn] (very roughly: LAIR-uhn)
- æ like the vowel in cat, but a bit longer
- the r softens the vowel; the final -en is weak, almost like -n
arbejder: [ˈɑːˌbɑjɐ] (very roughly: AR-bye-uh)
- ar- like are
- -bej- sounds like bye
- final -der is weak, often like -uh or -er but very reduced

Danish pronunciation is quite reduced compared to the spelling, so listening to native audio will help a lot.

Why is Læreren capitalized but not the other nouns? Aren’t nouns capitalized in Danish?

Danish does not capitalize all nouns like German does. Only:

The first word of a sentence
Proper nouns (names, countries, cities, etc.)

So in:

Læreren arbejder på sit kontor.

Læreren is capitalized only because it is the first word. If it were in the middle of a sentence, it would be:

… at læreren arbejder på sit kontor.

Can I leave out på sit kontor and just say Læreren arbejder?

Yes, grammatically that is fine:

Læreren arbejder.
= The teacher works / is working.

However, without the adverbial på sit kontor, the sentence is less specific. It just says that the teacher is working, without saying where. Adding på sit kontor gives more information about the situation.

So both are correct:

Læreren arbejder. → The teacher is working (somewhere, not specified).
Læreren arbejder på sit kontor. → The teacher is working in his/her office.