Learn Hardcore Turkish: Öğrenci matematik dersinde not alıyor. - The student is taking notes in math class.

Turkish normally follows a Subject–Object–Verb (SOV) structure. Here Öğrenci is the subject, matematik dersinde not covers the adverbial phrase (“in math class”) and the object (“notes”), and alıyor is the verb. That’s why the action alıyor (“is taking”) comes last.

What does Öğrenci mean, and why isn’t there a word for “the” or “a”?

Öğrenci simply means student. Turkish has no articles like the or a/an. If you want to say a student, you can say bir öğrenci. To point out that/the student, you might say o öğrenci. Otherwise context decides whether it’s definite or indefinite.

What role does matematik play in this sentence? Why doesn’t it get a case ending?

Here matematik is a noun acting as an adjective modifying ders (“class”). In Turkish, when one noun modifies another, the first noun stays in the basic form (nominative) without its own suffixes. So matematik ders means math class, and only ders carries the case endings.

What does dersinde mean, and why isn’t it just derste?

Dersinde = in the class (here: in the math class). It’s built from ders + the definite/3rd-person marker -i (think “the class”) + the locative case -de (“in/at”). If you said derste (without -i), it would mean in a class (indefinite).

What does not alıyor translate to, and how should I understand not here?

Not is a noun meaning note (as in “lecture notes”), and alıyor is “is taking.” Together, not almak is an idiom meaning to take notes, so not alıyor = is taking notes.

How is the present continuous tense formed in alıyor?

You take the verb stem al- (from almak, “to take”) and add -ıyor (vowel-harmonized form of -iyor) for the progressive aspect, giving alıyor. For 3rd person singular you add no further suffix.

Why is there no subject pronoun like o (he/she) in this sentence?

Turkish usually drops subject pronouns because the verb ending already shows person and number. Here the lack of any extra personal suffix on alıyor implies 3rd person singular. You could add o (i.e. O öğrenci…) for emphasis or contrast.

What case is not in, and why doesn’t it have an accusative ending?

Not here is the direct object. In Turkish, definite or specific direct objects get the accusative suffix -ı/-i/-u/-ü, but indefinite objects remain unmarked. Since not is indefinite (“notes in general”), it stays without an ending.

Can not almak ever mean to get a grade instead of to take notes?

Yes. Not can also mean grade in academic contexts, so not almak can mean to receive/get a grade, as in Sınavdan iyi not aldım (“I got a good grade on the exam”). Context decides if it’s “notes” or “grades.”

How would you say The students are taking notes in math class (plural)?

Make the subject plural: Öğrenciler. You can optionally pluralize the verb with -lar for clarity:
Öğrenciler matematik dersinde not alıyorlar.
Or drop -lar on the verb (third-person plural is still clear from öğrenciler):
Öğrenciler matematik dersinde not alıyor.