There are a number of references to hearing in the first four chapters of this book. It may be worth having a look back at them. This article, though is about the specific issue of hearing our own voices.
The problem is that we can't actually hear ourselves properly. Because sound travels efficiently through bone as well as through air, and because the head resonator is right adjacent to the inner ear, and because the eustachion tubes carry the sound from the pharynx to the inner ear, we hear a cacophonic mashup of sound in our ears when we are singing.
It is quite unlike the voice that other people actually hear. It is very weird to think that until very very recently thoughout history singers had no idea what they sounded like! The mind boggles. Because of course today we all have so much awesomely good sound recording gear available so cheaply that no singer needs to go without hearing themselves recorded, even if only occasionally.
At first, it is almost impossible to judge head/chest balance. Because of bone-conduction, we hear much more head-voice in the tone than there actually is. This is a great problem for many learners: A belief that they are sounding 'too heady' prevents them from allowing a free head-voice path, and leads them to try to direct more chest in the tone. Which of course creates throat tension, rising larynx, over-compression and so on... especially as it combines with the loss of the air stream on the hard palate as detailed in the previous article.
However there are not only negatives: on the positive side, you will begin to hear the buzzing sound of the singers' formant in your ears. This is your guide. 'Follow the buzz' is something I tell students, and many have said how this has really helped them. Hearing that buzz in your ears feels really great. There are neurological and psychoacoustic reasons for this: It energises the brain and feeds us feel-good endorphins. Just the same as when we hear other singers, but way more powerfully so because of the other associated mental and physical activity involved in creating the sound.
Once we have that buzz in the ears, at first it may just sound weird, like 'that's not my voice' but very soon we learn to 'follow the buzz', to do everything within the singing procees to maximise it and, as we develop, to leverage that sound for creative purposes.
As we first find the singers' formant in our tone, it usually comes in short moments, perhaps on one or two notes of an excercise. We may interpret it as a fault, as if it were a crackle or an unwanted break. Watch for this. Your teacher will probably be getting excited when it happens at first. As you exercise, try to make sure that every note of an exercise has the buzz in it. The more you work it, the more it will develop. In due course you will realise that the key to singing powerfully above second bridge is to leverage the buzz, to allow it to as it were take the place of chest voice. If we have the buzz in our ears, we can rely on it just like we rely on chest tone. Soon you will discover that chest tone is a red-herring, and that if you follow the buzz all the way bottom to top and back again, using it as a guide which tells you how to produce your voice, the buzzy tone actually takes over entirely, and becomes your voice.
Of course, we do need an external reference, so recording yourself is very important, just like a dancer needs a mirror to perfect her moves. Once you do you will be reassured as how the buzzy voice, which feels perhaps like you have an alien in your throat doing the singing, actually sounds just like you... but so very much better than before. Smooth and expressive and professional.