When attending my Japanese classes, my teacher would sometimes ask me
だいじょうぶですか。

How should I respond to such a question? Usually, I would reply
はい，だいじょうぶです。But the reply seems weird, and my teacher does not seem to
acknowledge it. Or does this question not warrant any reply?

How do I respond to だいじょうぶですか?
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politeness
How do I respond to だいじょうぶですか?
You are very much correct! I feel like a lot of people ignore my achievements
in replying are ignored too, so maybe Sensei doesn't think to reply with
"おめでとう!"

Maybe you were quiet or they didn't hear?

If you watch your favourite anime and a character gets hurt, others usually
say "だいじょうぶか?", and the character replies, "だいじょうぶ !". This is very informal,
because they didn't use 'です', or even 'だ', but you get the jist - it's correct
in Japan. I also have friends who are about JLPT N2-1 level, and even some
Japanese 'friends', if you'd call them that, and they use it. Two good reasons
why it's correct.

Just by the way, the kanji for 'だいじょうぶ' is '大丈夫'. Easy and 3-4-5 strokes, but
order of which of the three go where may be confusing.

頑張って！(がんばって！)

~よし
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I feel that there are at least two things to consider here.

1) Whether used in statements or questions, 「だいじょうぶ」 has **_so many_**
different meanings and usages.

**2) You might be missing the non-verbal ways of communication employed by
your teacher.**

Seriously, 「だいじょうぶ」 is like a king of expressions in informal daily speech. It
can mean:

> "O.K.", "all right", "will do", "satisfy", "convenient for one", "not
> injured", "enough", "safe", "fine", "right", etc.

I could keep going if I were willing to ruin my autumnal 3-day weekend. You
stated in your comment above:

> When I asked my teacher some questions, she will reply to them but follow up
> with 大丈夫ですか。Or when my teacher taught my class something new, she will also
> ask us 大丈夫ですか。

This 「大丈夫ですか。」 would mean something along the lines of " ** _Do you understand
my explanation?_** ", " ** _Are you following me?_** ", etc. as @Chocolate
stated above.

You could reply, 「（はい、）だいじょうぶです。」 or just 「はい。」 to that question from the
teacher if she were speaking specifically to you.

If, however, she were speaking to the entire class, not everyone would need to
verbally reply. You can choose to just nod or just let your eyes "say"
「だいじょうぶ」.

Would the teacher reply, in return, to that verbal reply by a student? She
might not verbally do so, but she might non-verbally by nodding and/or eye
contact. Japanese-learners miss this all the time. They tend to expect actual
words to be uttered, so they feel like their teacher is not acknowledging
their 「はい、だいじょうぶです。」.

It would take some time,but you will eventually learn to communicate non-
verbally with Japanese-speakers.
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