Is raising one's voice with some of the post-prayer remembrances (dhikr) for the purpose of teaching students considered an innovation (bid‘ah) or a transgression? And is it better to combine tasbih (Subhan Allah), tahmid (Alhamdulillah), and takbir (Allahu Akbar) in dhikr, or to say each one separately?

Reciting dhikr aloud after prayer is permissible, especially for teaching students, based on the hadith (definition) of Ibn Abbas in the Sahihayn. Imam Shafi'i said that the loud recitation was for teaching the manner of dhikr. It is permissible to combine tasbeeh (SubhanAllah), tahmeed (Alhamdulillah), and takbeer (Allahu Akbar) and repeat each of them 33 times, or to recite each of them individually 33 times. The latter is preferable due to the apparent meaning of the hadith.