A proclaiming tone is an intonation pattern that either rises and then falls, or just falls. A proclaiming tone shows that the speaker is giving new information. It can be compared to a referring tone, which shows that the speaker is referring to something everybody already knows.
In the sentence ‘That guy we met at the party is my new teacher', there is a proclaiming tone on ‘is my new teacher' because it is new information.
In the classroom
Proclaiming tones are often more difficult for learners to produce than referring tones. Encouraging learners to exaggerate the falling intonation and move their head and body downwards at the same time can help.