Ο δάσκαλος μιλάει ελληνικά πολύ αργά στην τάξη.

Word by word:

• Ο – the (masculine singular, nominative)
• δάσκαλος – teacher (male teacher)
• μιλάει – speaks / is speaking
• ελληνικά – Greek (the Greek language)
• πολύ – very
• αργά – slowly
• στην – in the / in (literally to the, feminine singular)
• τάξη – class / classroom

So literally: “The teacher speaks Greek very slowly in the class.”

μιλάει (miláei) is:

• Present tense
• 3rd person singular
• From the verb μιλάω / μιλώ = to speak

So μιλάει means “he/she speaks” or “he/she is speaking.”

In this sentence it agrees with ο δάσκαλος (the teacher), which is 3rd person singular.

Both are correct and very common:

• μιλάει – slightly more “full” form
• μιλά – slightly shorter form

They are completely interchangeable in modern Greek in most contexts:

• Ο δάσκαλος μιλάει ελληνικά.
• Ο δάσκαλος μιλά ελληνικά.

Both mean: “The teacher speaks Greek.”

So the sentence could also be Ο δάσκαλος μιλά ελληνικά πολύ αργά στην τάξη with the same meaning.

For languages, Greek usually uses no article:

• Μιλάω ελληνικά. – I speak Greek.
• Μαθαίνω γαλλικά. – I’m learning French.

Using the article (τα ελληνικά) is also possible, but it slightly changes the feeling:

• Μιλάει ελληνικά. – neutral: he speaks Greek (as a language)
• Μιλάει τα ελληνικά. – can sound more specific or emphatic, e.g. “He speaks the Greek (language)” in contrast with some other language; often unnecessary in simple statements.

So in most cases, including your sentence, the natural form is μιλάει ελληνικά (no article).

ελληνικά here is:

• Neuter
• Plural
• Accusative case

It comes from the adjective ελληνικός, -ή, -ό (Greek).

In Greek, many languages are expressed as neuter plural forms used as nouns:

• τα ελληνικά – Greek
• τα αγγλικά – English
• τα γαλλικά – French
• τα ισπανικά – Spanish

When the article is dropped (as in μιλάει ελληνικά), the form ελληνικά still keeps that neuter plural morphology, but it functions like the noun “Greek (language)”.

πολύ (very) usually comes before the word it intensifies:

• πολύ αργά – very slowly
• πολύ γρήγορα – very quickly
• πολύ καλά – very well

Putting πολύ after the adverb (αργά πολύ) is not natural in standard Greek for this meaning.

So μιλάει πολύ αργά is the normal word order: he speaks very slowly.

In this sentence αργά is an adverb meaning slowly.

It comes from the adjective αργός (slow). In Greek, many adverbs are formed from the neuter singular form of the adjective, often ending in -α or -ος:

• αργός (slow) → αργά (slowly)
• γρήγορος (fast) → γρήγορα (quickly)
• καλός (good) → καλά (well)

So μιλάει αργά = he speaks slowly.

πολύ modifies αργά, not the verb itself.

• μιλάει αργά = he speaks slowly
• μιλάει πολύ αργά = he speaks very slowly

So:

• μιλάει – speaks
• αργά – slowly
• πολύ αργά – very slowly

The combination πολύ αργά works together as “very slowly.”

στην is a contraction of:

• σε
  • την → στην

Where:

• σε = in / at / to
• την = the (feminine, singular, accusative)

So στην τάξη literally means “in the class”.

Other common contractions:

• σε + τον → στον (e.g. στον δρόμο – in/on the road)
• σε + το → στο (e.g. στο σπίτι – at home)

Both στην and στη exist. The final -ν (called “νι eufonico”) is often:

• Kept before vowels and some consonants (κ, π, τ, ξ, ψ, μπ, ντ, γκ)
• More likely dropped before other consonants in everyday speech

So:

• στην τάξη – natural (τάξη starts with τ)
• στην Αθήνα – natural (Αθήνα starts with a vowel)
• στη δουλειά – many people say στη δουλειά (no -ν) in speech

In careful or written Greek, στην τάξη is the standard form.

τάξη (class) is in the accusative singular feminine.

Reason:

• The preposition σε (→ στην) takes the accusative case.
• The noun τάξη is feminine: η τάξη (nominative) → την τάξη (accusative).
• With the contraction σε την τάξη → στην τάξη, τάξη stays in the accusative.

So στην τάξη = in the class / in class (feminine accusative after σε).

ο δάσκαλος is:

• Nominative
• Masculine
• Singular

You can tell because:

• ο is the nominative masculine singular article (the).
• The nominative is normally used for the subject of the sentence.

Here, ο δάσκαλος is the one doing the action (speaking), so it is the subject, and thus in the nominative.

Yes:

• ο δάσκαλος – the (male) teacher
• η δασκάλα – the (female) teacher

So you could also say:

• Η δασκάλα μιλάει ελληνικά πολύ αργά στην τάξη.
  The (female) teacher speaks Greek very slowly in class.

Yes. Greek word order is fairly flexible because of its case system.

All of these are grammatical and natural, with slightly different emphasis:

1. Ο δάσκαλος μιλάει ελληνικά πολύ αργά στην τάξη.
   – Neutral: describes how he speaks in class.

2. Ο δάσκαλος στην τάξη μιλάει ελληνικά πολύ αργά.
   – Slight emphasis on “in class” (not necessarily elsewhere).

3. Στην τάξη ο δάσκαλος μιλάει ελληνικά πολύ αργά.
   – Stronger emphasis on “in class” at the beginning.

Basic rule for learners: Subject – Verb – Objects/Adverbs – Place (as in the original) is a very safe and natural pattern.

Modern Greek present tense covers both English:

• simple present (“speaks”)
• present continuous (“is speaking”)

So Ο δάσκαλος μιλάει ελληνικά πολύ αργά στην τάξη can mean:

• The teacher speaks Greek very slowly in class. (general habit)
  or
• The teacher is speaking Greek very slowly in class. (right now / these days)

Context decides which reading is intended.