Learn Hardcore Portuguese (Brazil): A opinião do professor é importante para mim. - The teacher's opinion is important to me.

If you said only Opinião do professor é importante para mim, it would sound incomplete or wrong in standard Portuguese. In most cases like this, you need the article.

What exactly does do mean in do professor?

Do is a contraction of the preposition de + the article o:

de + o = do (of the / from the)
de + a = da
de + os = dos
de + as = das

So:

do professor = de + o professor = of the teacher / the teacher’s

In this sentence, de is used to express possession or relationship, similar to the English ’s in the teacher’s opinion.

Why is it do professor and not de professor?

Do professor refers to a specific teacher you and your listener can identify:

A opinião do professor = the (known) teacher’s opinion.

If you say opinião de professor (without the article), it sounds more like:

“a teacher’s opinion” in a general sense, or
“the kind of opinion a teacher gives.”

But in this sentence, we usually mean the teacher we have in mind (e.g., my teacher in this context), so we use do professor.

Does professor mean “teacher” or “professor” in Brazilian Portuguese?

In Brazil, professor is used for:

school teachers (elementary, high school),
language teachers,
and also university professors.

So professor often just means teacher, not necessarily someone with a university title. Context tells you which kind of teacher is meant.

To say “my teacher,” you would often say:

o meu professor (male)
a minha professora (female)

Why is it para mim and not para eu?

After prepositions (like para, de, com, por, em), Portuguese normally uses the “object” pronouns:

eu → mim
tu → ti
ele/ela → ele/ela (same form)
nós → nós, vocês → vocês, eles/elas → eles/elas

So:

para mim = “for me / to me”

Para eu is only acceptable when followed by a verb in the infinitive and when eu is the subject of that verb, for example:

É importante para eu entender.
“It’s important for me to understand.”

But standing alone (without an infinitive after it), you should use para mim, not para eu.

Could I say por mim or a mim instead of para mim here?

Not with the same meaning.

para mim = for me / to me (natural and correct here)
por mim often means “as far as I’m concerned / on my part”
e.g. Por mim, tudo bem. (“As far as I’m concerned, it’s fine.”)
É importante por mim would sound strange or mean something like “it is important because of me / on my behalf,” not the intended sense.
a mim is used after certain verbs that take a (like dizer a, dar a), and usually for emphasis:
Diga a mim. = “Say it to me.”
É importante a mim is grammatically possible but very unusual and sounds stiff. Native speakers would say para mim.

So in this sentence, para mim is the natural and idiomatic choice.

Can I change the word order, like Para mim, a opinião do professor é importante?

Yes. Both are correct:

A opinião do professor é importante para mim.
Para mim, a opinião do professor é importante.

Putting Para mim at the beginning emphasizes “for me / in my view” a bit more, similar to English:

“To me, the teacher’s opinion is important.”

The meaning stays the same; it’s just a matter of emphasis and style.

How would the sentence change if I’m talking about a female teacher?

You change o professor (male) to a professora (female), and the contraction adjusts:

de + a professora = da professora

So the whole sentence becomes:

A opinião da professora é importante para mim.
“The (female) teacher’s opinion is important to me.”

Nothing else in the sentence needs to change.

How would I say “The teacher’s opinions are important to me” (plural opinions)?

You need to make opinião and importante plural, and use the plural article:

As opiniões do professor são importantes para mim.

Breakdown:

As – plural feminine definite article
opiniões – plural of opinião
do professor – same contraction (the teacher is still singular)
são – plural of é (“are” vs. “is”)
importantes – plural of importante
para mim – unchanged

For a female teacher:

As opiniões da professora são importantes para mim.

Why doesn’t importante change for masculine or feminine nouns?

Adjectives in Portuguese fall into patterns:

Adjectives ending in -o usually have masculine/feminine forms:
bonito / bonita, técnico / técnica
Adjectives ending in -e or a consonant usually have one form for both genders, and only change for number (singular/plural):
importante / importantes, feliz / felizes

Importante ends in -e, so:

singular: importante (masculine or feminine)
plural: importantes

That’s why we say both:

A opinião do professor é importante.
A opinião da professora é importante.

with the same importante.

What does the accent in opinião do, and how is the word pronounced?

In opinião, the ão has a nasal sound and carries the stress:

Spelling: o-pi-ni-ão
Stress: last syllable (-ão)
Rough pronunciation in Brazilian Portuguese:
oh-pee-nee-OWNG (with a nasalized “own” at the end)

The ã with o (ão) is a very common nasal ending in Portuguese, as in pão (bread), não (no), coração (heart).

Is there a more informal way Brazilians might say this?

Yes, in informal speech and writing, Brazilians often use pra instead of para:

A opinião do professor é importante pra mim.

You might also hear a shortened form for professor:

A opinião do prof é importante pra mim. (very informal)

Pra is extremely common in speech and casual text messages. In more formal writing (essays, official texts), para is preferred.