Why no article? Is Greek, like some other languages, not very eager to to put indefinite articles before people? Would a sentence like "I am a teacher" also be without an a? Or is there a different reason?
In Greek many times the use of articles is optional and most speakers don't use it for brevity
EDIT Yes, you can say είμαι ένας δάσκαλος and είμαι δάσκαλος. Both are used and are correct.
Is it bad that I can only recognize the word for child because it sounds like baby?
Imho whatever suits you is fine, I also use various kinds of mnemonics that help me memorise a new word I'm learning as well. Why don't you try to relate it with "pediatrician" which actually derives from the word "παιδί"? I think that these words sound even more close too. Hope it helps :)
But..."you are child" shouldn't be the English translation, as that's not grammatically correct in English. Doesn't seem consistent with how duolingo typically structures these exercises
Thank you for your comment. I just corrected this one. "You are child" in English would only make some kind of sense if it was said or written like "You are, child." with a comma, indicating a pause to tell the first part from the second one. But there is no comma, so yeah. It was incorrect ^.^
I translated: " eσυ εισαι ενα παισει" into English: You are a child. According to Duo, my answer was incorrect. For Duo, the correct answer is: You are a child. The same thing I wrote!