When I was a child taking piano lessons, I clearly remember having to learn new pieces of music in a very specific way. I would have to learn the right hand and left hand parts separately until each part was known really well before putting both right hand and left hand parts together. Many piano teachers did this and many piano teachers still teach this way.
I must admit I hated doing things this way. For me it was so annoying because I would learn each part so well and then when I would start to put the two parts of right hand and left hand together, it would sound like garbage. My piano teacher probably thought that it sounded adequate, but to me it sounded like garbage and it often felt like I had wasted a couple of months perfecting both the right hand part and the left hand part. I would have much preferred to start all my piano pieces with both my hands and maybe not be expected to get as far through the piece of music.
My thoughts about this didn’t change when I became a piano teacher. I made the conscious decision to not get my students to spend a whole heap of time learning the right hand and left hand parts separately. I have never changed my mind on this and even my current piano students learn their new music with two hands playing right from the get go.
I have noted over the years that of all the piano students I have taught from their very first lesson, have never asked to learn a piece of new music with their right hand and left hand being separate. Not once. The reason for this is that playing a new piece of music straight away with both hands together is normal for them. They probably think that everyone learns this way and so they don’t question it.
The students that I have that had previously learned from another teacher, do complain about learning new pieces of music with both hands together from the very beginning. This is because they are not used to this way of doing things and I think they are scared that they can’t actually play a new piece of music without learning it with separate hands first. After a few months of lessons with me, these students stop complaining, probably because they have gotten used to my way of doing things. Once they are used to doing things the way I expect, there is never another complaint. This is not because they have come to accept that there is no changing my mind, their facial expressions tell me that they are okay to start a piece of music with both hands together.
I find it interesting that among other piano teachers, I am unorthodox in this area but to other instrumental teachers, who teach instruments like violin, cello, flute, clarinet, trumpet, trombone, saxophone, agree with me. The reason why these other instrumental teachers agree with me is that their instruments need the coordination of both hands to produce any and all of their notes. It would be impossible for them to learn each hand part separately.
I’m fine with being unorthodox in this way because I do get results. Students do learn new music and the students that choose to do formal piano exams are successful. Obviously, other piano teachers have successful students too. It really doesn’t matter if you think my way is the way to learn any new music or whether you think I am completely wrong. The truth is that both ways work.
So if you are playing the piano in your retirement and don’t need formal lessons to help you remember everything that you have previously learned, you have a choice of the way you learn new music. Both ways work.
If you are needing piano lessons, then I strongly advise you to do what your piano teacher asks you to do because they have worked out their own way of doing things over the years. They know what they are doing and they will get you to your desired goal.
However, if this is something that you have formed a strong opinion one way or the other, then talk to your piano teacher. One of the great things about being an adult student is that you can ask more questions and not appear to be rude or impertinent.
As with just about everything else in life, there is more than one way to accomplish a goal or a set of skills. Learning or re-learning to play the piano is no different.