1. What did you learn in math class today?
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.
Are they all correct? Do we have to capitalize "career"? It was used a subject name.
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.
posted by Writeacher