Learn Hardcore Greek: Στο μάθημα ελληνικών κάνω επανάληψη τακτικά, και βλέπω μεγάλη πρόοδο. - In the Greek lesson I revise regularly, and I see great progress.

Prepositions like σε always take the accusative.
Neuter nouns in Greek have the same form in nominative and accusative singular:
- το μάθημα (nom.)
- το μάθημα (acc.)

So στο μάθημα = σε + το + μάθημα in the accusative, even though it looks like nominative because neuters don’t change form there.

Why is ελληνικών in the genitive plural, and what does this structure μάθημα ελληνικών mean?

Ελληνικών is the genitive plural of ελληνικά (Greek, as a language).

το μάθημα = the lesson
(των) ελληνικών = of Greek (language)

So μάθημα ελληνικών literally means “lesson of Greek”, i.e. Greek class / Greek lesson.

This “noun + genitive” pattern is very common in Greek for school subjects:

μάθημα ελληνικών – Greek (language) lesson
μάθημα αγγλικών – English lesson
μάθημα μαθηματικών – maths class
μάθημα ιστορίας – history class

Often the article in the genitive (των ελληνικών) is dropped in this kind of fixed school-subject phrase, so μάθημα ελληνικών sounds very natural and standard.

Could we also say στο ελληνικό μάθημα or στο μάθημα ελληνικά? What’s the difference?

Στο ελληνικό μάθημα

Grammatically correct, but it does not naturally mean “Greek (language) class” in the school-subject sense.
It sounds more like:

“the Greek lesson” as opposed to, say, “the French lesson”
or a lesson that happens to be Greek in some way (perhaps about Greek culture).

For “the Greek (language) class” as a subject, το μάθημα ελληνικών is the normal expression.

Στο μάθημα ελληνικά

This is not correct in standard Greek for “in Greek class.”
You cannot just put ελληνικά (accusative) after μάθημα like that. You need the genitive (ελληνικών) or a fuller phrase:

στο μάθημα ελληνικών (natural)
στο μάθημα της ελληνικής γλώσσας (more formal: “in the lesson of the Greek language”)

Why is there no article before επανάληψη in κάνω επανάληψη?

In κάνω επανάληψη, the noun επανάληψη is used in a general, indefinite sense: “I (do) review / I revise.”

Greek often omits the article when:

the noun refers to an activity in general, not a specific instance, and
it’s part of a fixed light-verb expression.

Compare:

κάνω επανάληψη – I review / I do revision (in general)
κάνω γυμναστική – I exercise / I work out
κάνω δουλειά – I do (some) work

If you add the article, you usually refer to a specific review:

κάνω την επανάληψη – I am doing the revision (the particular review we planned / that is required, etc.)

So here, with a habitual, general meaning, no article is the natural choice: κάνω επανάληψη τακτικά.

Why does Greek use κάνω επανάληψη instead of a single verb meaning “to review”?

Greek frequently uses a “light verb + noun” structure for activities, similar to English “do exercise”, “take a look”, etc.

κάνω επανάληψη literally: “I do repetition/review”
Meaning: I revise / I review (the material).

There is a single verb: επαναλαμβάνω = “I repeat / I say/do again / I review.”
However, in the context of studying for school, tests, etc., κάνω επανάληψη is:

very common,
slightly more colloquial/everyday than επαναλαμβάνω (την ύλη).

For a student talking about homework or exam prep, κάνω επανάληψη is the most idiomatic phrase.

Where can the adverb τακτικά go in the sentence, and does its position change the meaning?

Common and natural positions with almost the same meaning:

Στο μάθημα ελληνικών κάνω επανάληψη τακτικά – (original)
Στο μάθημα ελληνικών κάνω τακτικά επανάληψη
Στο μάθημα ελληνικών τακτικά κάνω επανάληψη

All mean “In Greek class I review regularly.” The differences are mostly in emphasis:

κάνω επανάληψη τακτικά: neutral, adverb at the end (very common).
κάνω τακτικά επανάληψη: slight emphasis that the action of “doing repetition” is regular.
τακτικά κάνω επανάληψη: emphasizes how often before we even hear what you do (“regularly, I do revision”).

So the meaning doesn’t really change; it’s mostly stylistic and about what you stress in the sentence.

Is the present tense κάνω and βλέπω here more like English “I do / I see” or “I am doing / I am seeing”?

Modern Greek present tense covers both:

English simple present: “I do, I see”
English present continuous: “I am doing, I am seeing”

The exact nuance comes from context.

In this sentence:

κάνω επανάληψη τακτικά → “I (regularly) review” / “I (am) review(ing) regularly”
Here it clearly expresses a habitual action.
βλέπω μεγάλη πρόοδο → “I see great progress” / “I am seeing great progress”
This describes an ongoing state/perception.

In natural English we’d say:

“In Greek class I review regularly, and I’m seeing great progress.”
or
“I review regularly in Greek class, and I see a lot of progress.”

Both are compatible with the Greek present.

Why is it βλέπω μεγάλη πρόοδο and not βλέπω μεγάλη πρόοδος?

Because πρόοδο is the direct object of the verb βλέπω, so it must be in the accusative case.

Nominative singular: η πρόοδος (subject form)
Accusative singular: την πρόοδο (object form)

In the sentence:

Subject: (εγώ) – implied “I”
Verb: βλέπω – I see
Object: μεγάλη πρόοδο – great progress (accusative)

So:

βλέπω μεγάλη πρόοδο = correct (I see great progress)
βλέπω μεγάλη πρόοδος = wrong (mixes nominative where an accusative is required)

Why is μεγάλη in the feminine form here, and what are the other main forms of this adjective?

Adjectives in Greek must agree with the noun they modify in gender, number, and case.

πρόοδος is a feminine noun (η πρόοδος, της προόδου, την πρόοδο).
It is singular accusative in this sentence: πρόοδο.
Therefore, μεγάλη must also be feminine singular accusative.

The basic singular forms of the adjective “big/great”:

Masculine: μεγάλος (ο μεγάλος φίλος)
Feminine: μεγάλη (η μεγάλη πρόοδος)
Neuter: μεγάλο (το μεγάλο σπίτι)

So μεγάλη πρόοδο is feminine–feminine agreement:

(βλέπω) μεγάλη (adj.) πρόοδο (noun)

Why is there no article before μεγάλη πρόοδο? Could we say βλέπω τη μεγάλη πρόοδο instead?

Both are possible, but they have different nuances.

βλέπω μεγάλη πρόοδο (no article)
- General, indefinite sense: “I see a lot of progress / great progress (in general).”
- Very natural when describing an overall improvement without referring to a specific, previously identified “chunk” of progress.
βλέπω τη μεγάλη πρόοδο (with article)
- More specific/definite: “I see the great progress.”
- Sounds like you and the listener already know about this particular big improvement or you are stressing a specific, notable progress.

In this context (a learner speaking generally about their development), without the article is more natural: βλέπω μεγάλη πρόοδο.

Is the comma before και in ..., και βλέπω μεγάλη πρόοδο. necessary in Greek?

The comma before και here is optional and mostly a matter of style and rhythm.

Without comma:
- Στο μάθημα ελληνικών κάνω επανάληψη τακτικά και βλέπω μεγάλη πρόοδο.
- This is a single, smooth sentence, like English “I review regularly and I see great progress.”
With comma:
- Στο μάθημα ελληνικών κάνω επανάληψη τακτικά, και βλέπω μεγάλη πρόοδο.
- The comma gives a slight pause, making the second part sound a bit more independent, closer to:
  - “I review regularly in Greek class, and I (also) see great progress.”

Both are grammatically correct. Many writers omit the comma when και just links two verb phrases with the same subject; others use it for extra emphasis or a pause.