1. What did you learn in math class today?

Question

2. She is a music teacher. She is very strict.

3. He is a career teacher. He is kind-hearted.

4. He is a Chinese characters teacher. He is humorous.
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Are they all correct? Do we have to capitalize "career"? It was used a subject name. • English - Writeacher, Tuesday, March 14, 2017 at 8:35am
All sentences look good.

Usually, when someone teaches a class in the US in which students learn about careers, it's called Careers -- with capital C and in plural form.

I'd rephrase #4 like this:
He is a teacher of Chinese characters.
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Thank you. then, which expressions are correct?

5. He is a career teacher.
6. He is a Careers teacher.
7. He is a teacher of career.
8. He is a teacher of Careers.

Answer 1

If "Careers" is the name of the class, then, yes, it should be capitalized. Above, #5, if it was used as an adjective to describe what kind of teacher he was/is, it is not capitalized.