We don't have a 'working', 'middle' or any other 'class'. We were founded as a free people where anyone can succeed. There should be no 'class' divides.... these are labels, created by politicians, to keep people focused on each other rather than on the politicians.
I don't think that a sense of 'classness' is just a political division. My parents income was about 5 times the national average for the first 15 years, then jumped to about 8 times until they retired. However, they had bought their first home from my dad's older brother for about 1/2 it's worth in 1952. So, we lived in a very exclusive Chicago suburb, while definitely still middle class.
Oh, actually felt 'poor' at times, we didn't do vacations, my parents had bought a summer home and that was it. My mom was extremely frugal, if she was going to spend money on 'fun,' why not have it in property?

During the 1960's those with a college degree in my suburb was at 85%. Even post-grad was over 25%. Why? Many professors at both the suburban university and from Loyola Medical Center doctors lived there. There was also a hospital in the suburb, the doctors from there too live in town.
My parents were both raised on Chicago's West Side, though my dad's family moved to the suburb while he was in high school. This would have been in the 30's. Seems he'd get out of school, walk to the train, head back to the city to be with his friends. No one thought that weird.
So, one can have more than necessary, live in an area known for affluence, yet still feel very different and like you don't belong. I was lucky though, had very good friends and my parents were sticklers for manners. I realized by my college years, that I did fit in, probably always did.
I know there are many more sociological studies on poor kids, that have more than their surrounding peers. It may be both parents or a parent that emphasizes studies and individuality. These are the kids that somehow succeed beyond the expectations and can break out as adults.