You should understand that the two normal departments, Modern Chinese and Advanced Mathematics, are not only different in teaching materials, but also in professional teaching and training, so they are not so suitable. Besides, your teacher qualification certificate is also a problem. If you want to go to the Education Bureau to change the teacher file and teacher qualification certificate, it may not be approved, and the school may not agree. There are too many trivial things.
I don't recommend doing this. As for work, you can apply for a school to teach music and information.
Even for students, you can't make such a choice irresponsibly.