Which Theories and Historical Influences Should Most Impact the Schools We'd Like to Have?

I do not know much about the theories and historical influences that impact schools, but I should hope that the ones that do impact schools are the most successful and/or beneficial ones. Theories change constantly throughout history, and the most effective theories should be the ones that remain in place in schools.  We do not want theories that have negatively impacted schools to remain in effect, but we can use these theories to better understand what works and what does not work in the schools.  The same goes for the historical influences:  we do not want bad influences having an effect on the schools because the school would in turn perform badly.  Instead, I would like to see only the truly beneficial historical influences impacting schools.  I hope to soon learn what theories seem to be effective in schools and what historical influences positively impact schools.

What theories and historical influences do impact schools? This is an entirely new topic to me!