Learn Hardcore Finnish: Tyttö oli ylpeä, kun opettaja kirjoitti arvosanan todistukseen. - The girl was proud when the teacher wrote the grade on the report card.

on = is (present tense): tyttö on ylpeä – the girl is proud (now)
oli = was (simple past): tyttö oli ylpeä – the girl was proud (then)
on ollut = has been (present perfect): tyttö on ollut ylpeä – the girl has been proud

In a narrative about a finished event in the past (the teacher wrote the grade, the girl felt proud then), Finnish normally uses oli, not on ollut. So oli matches kirjoitti (also past tense) in time.

Why is ylpeä not inflected to match tyttö? Shouldn’t it change form?

Ylpeä is an adjective used as a predicative (what the subject is), after olla:

tyttö on ylpeä – the girl is proud
tytöt ovat ylpeitä – the girls are proud

In Finnish:

Attributive adjectives (before a noun) agree in case and number:
- ylpeä tyttö – a proud girl
- ylpeät tytöt – proud girls
Predicative adjectives (after olla) usually stay in the base form in the singular:
- tyttö on/oli ylpeä
  The adjective only clearly changes in the plural: tytöt ovat ylpeitä.

So tyttö oli ylpeä is the normal pattern: singular subject + base-form adjective as predicative.

Why is there a comma before kun in Tyttö oli ylpeä, kun opettaja kirjoitti arvosanan todistukseen?

Kun opettaja kirjoitti arvosanan todistukseen is a subordinate clause introduced by the conjunction kun (when).

In Finnish punctuation, a main clause and a following subordinate clause are normally separated by a comma:

Tyttö oli ylpeä, kun opettaja kirjoitti…
Kun opettaja kirjoitti…, tyttö oli ylpeä.

Both orders are possible, but in both cases a comma is used between the clauses. This is just a standard rule of Finnish punctuation with kun, että, koska, etc.

Can I also say Kun opettaja kirjoitti arvosanan todistukseen, tyttö oli ylpeä? Is there any difference?

Yes, that version is perfectly correct:

Tyttö oli ylpeä, kun opettaja kirjoitti arvosanan todistukseen.
Kun opettaja kirjoitti arvosanan todistukseen, tyttö oli ylpeä.

The meaning is essentially the same. The difference is in emphasis:

Original word order highlights the girl’s feeling first, then gives the situation.
Starting with Kun opettaja kirjoitti… puts more focus on the circumstances first, then states the result (she was proud).

Both are natural. Word order in Finnish is fairly flexible and mostly affects emphasis, not basic grammar.

Why does opettaja not have any article like a or the?

Finnish has no articles at all—no equivalent of English a/an or the.

The bare noun opettaja can mean:

a teacher
the teacher
just teacher in a generic sense, depending on context.

In this sentence, opettaja is understood from context as her teacher or the teacher (the one relevant in the situation). If you need to be more explicit, you could say:

hänen opettajansa – her teacher
luokanopettaja – the class teacher, etc.

But normally opettaja alone is enough.

What form is kirjoitti, and how does it relate to the verb kirjoittaa?

Kirjoitti is the imperfect (simple past) form of kirjoittaa (to write), third person singular:

hän kirjoittaa – he/she writes / is writing (present)
hän kirjoitti – he/she wrote (past)

So opettaja kirjoitti = the teacher wrote.

The sentence keeps both verbs in the past: oli (was) and kirjoitti (wrote).

Why is arvosanan in the form with -n? What case is that and what does it express?

Arvosanan is the genitive singular of arvosana (grade, mark).

Here, arvosanan functions as a total object of kirjoitti:

opettaja kirjoitti arvosanan – the teacher wrote the (whole) grade

In Finnish, a complete, bounded action taking a full object typically uses the genitive for the object in the past tense:

Opettaja kirjoitti arvosanan. – She wrote the grade (finished).
Opettaja kirjoitti arvosanaa. – She was (in the process of) writing a grade (ongoing, not completed).

Because the idea here is that the teacher completed writing the grade into the certificate, arvosanan (genitive) is used.

What case is todistukseen, and what does the -een/ -seen type ending mean?

Todistukseen is illative singular of todistus (certificate, report).

The illative often answers “into where?” or “to where (inside)?”. For many words, its ending is -Vn (vowel + n), often written with a double vowel in spelling:

talo → taloon (into the house)
koulu → kouluun (to school / into the school)
todistus → todistukseen (into the certificate / on the certificate)

So kirjoitti arvosanan todistukseen literally means wrote the grade into the certificate. Idiomatically: wrote the grade on the report card.

Why is it arvosanan todistukseen and not something like todistukseen arvosanan? Does the word order matter?

Both word orders are grammatically possible:

opettaja kirjoitti arvosanan todistukseen
opettaja kirjoitti todistukseen arvosanan

The difference is in emphasis and flow:

arvosanan todistukseen: focuses first on what was written (the grade), then where (into the certificate).
todistukseen arvosanan: focuses first on where (into the certificate), then what.

In this sentence, putting arvosanan before todistukseen is slightly more neutral and common, but both are acceptable.

Why is it tyttö oli ylpeä and not something like tyttö oli ylpeänä or ylpeästä tytöstä?

Tyttö oli ylpeä follows the standard subject + olla + predicative adjective pattern:

tyttö – subject (nominative)
oli – verb
ylpeä – predicative adjective (base form)

Alternatives like:

tyttö oli ylpeänä – can exist but means the girl was in a proud state / proudly (at that moment), often more adverbial or descriptive of manner.
ylpeästä tytöstä – means from/about the proud girl (elative case), and would not fit with oli here.

So for a straightforward the girl was proud, Finnish uses tyttö oli ylpeä.

What exactly does kun mean here, and how is it different from koska?

In this sentence, kun means when (introducing a time clause):

kun opettaja kirjoitti arvosanan todistukseen – when the teacher wrote the grade into the certificate

Kun is used for:

when (time reference)
sometimes also as / while, and colloquially sometimes because.

Koska mainly means because, expressing a reason:

Tyttö oli ylpeä, koska opettaja kirjoitti arvosanan todistukseen.
– The girl was proud because the teacher wrote the grade into the certificate.

Your original sentence with kun focuses more on time (at the moment when the teacher wrote it), though depending on context, listeners may also understand a causal nuance.

Why is there no word for her in opettaja? How do we know it’s her teacher?

Finnish often leaves out possessive words if the owner is obvious from context.

Literally, the sentence only says opettaja (teacher / the teacher). We understand it as her teacher because the only person mentioned is the girl, and in a school setting “the teacher” is naturally her teacher.

If you want to make the possession explicit, you can say:

hänen opettajansa kirjoitti arvosanan todistukseen
– her teacher wrote the grade into the certificate.

Here hänen = her, and opettajansa has the possessive suffix -nsA (her teacher). But in everyday language, just opettaja is usually enough.

What does arvosana specifically mean? Is it a grade, mark, score, or something else?

Arvosana is the common school term for a grade / mark given for performance:

A number (like 9/10), a letter (like A, B, C), etc., depending on the grading system.

In this context, opettaja kirjoitti arvosanan todistukseen naturally means:

the teacher wrote the girl’s grade on the report card / in the school certificate.

Why is tyttö in the basic form and not something like tytön or tyttöä?

Tyttö is the subject of the sentence, so it appears in the nominative case, which is usually the base form:

tyttö oli ylpeä – the girl was proud

Other forms would change the function:

tytön – genitive (of the girl), used for possession or as an object in some structures.
tyttöä – partitive, used for partial objects, some expressions of feeling, etc.

Here we just need a simple subject (the girl), so nominative tyttö is the correct form.