I can't speak for everyone but I can say that I have learned many things aside from math, English, science, history and etc. My geometry teacher would often tell us stories of her life during class. I remember once she told us how she lets her daughters have sex as long as they use protection. "They could bring a boy home, go to the bedroom, lock the door and have sex as long as they used protection. I even have a drawer with condoms if they would ever need so they have no excuses". That's basically what she said and it made me realized that she's smart because she knew that sex can't be prevented but pregnancy could. Also I'm have another class where we would often talk about how you should do act of kindness more and why you should. I noticed that as time passed by, the teachings grew on many of my fellow class mates as they matured into kind loving students.
Wisdom is defined by Webster as
": knowledge that is gained by having many experiences in life
: the natural ability to understand things that most other people cannot understand
: knowledge of what is proper or reasonable : good sense or judgment"
While school may give one facts and maybe even methods, wisdom is reserved to those who spend the time to gain it. It is earned, but not given.
Knowledge is the facts and methods one has learned from books, schools, teachers, etc. Wisdom is the application of said knowledge, and it is experience in said application. Schools can't teach wisdom, as wisdom is experience in applying the knowledge that schools teach. However, that does not mean there is no wisdom to be gained, as you apply knowledge of how school works in general and how to complete tasks, etc.
The aspects of today's common schools don't ensure that we have wisdom. School is a place where you learn and get educated, but not a place to gain wisdom. Wisdom is more or less something the individual may or may not have, not something that can be "taught" by average teachers.