"Я думаю о моей ученице."

Translation: I am thinking about my student.

[pheonican]

What is dative doing here?

[Shady_arc]

it is Prepositional.

[pheonican]

So the preposition "о" takes the prepositional case as a rule instead of the genitive?

[Shady_arc]

Yes. It is primarily used with Prepositional. There is only one use of о/об with Accusative, the one of coming into physical contact (by hitting, rubbing, leaning, stumbling, getting your clothes caught on something sticking out):

• Я споткнулся об камень. = I stumbled upon a stone.
• Я поранил руку, ударившись о стенку контейнера. = I wounded my arm, having bumped into a wall of the container. (partiticples, physical contact, verbs we do not have in the course —pretty advanced stuff here :))

[pheonican]

Спасибо болшое!
I already speak a slavic language(serbo-croatian) and the grammar is in many ways similiar. But the language is still so grippingly fascinating. Thank you for this course.